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Flotation technique: Its mechanisms and design parameters
Accepted Manuscript Title: Flotation Technique: Its Mechanisms and Design Parameters Authors: Ritesh Prakash, Subrata Kumar Majumder, Anugrah Singh PII: DOI: Reference:
S0255-2701(18)30250-2 https://doi.org/10.1016/j.cep.2018.03.029 CEP 7239
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
28-2-2018 26-3-2018 28-3-2018
Please cite this article as: Prakash R, Majumder SK, Singh A, Flotation Technique: Its Mechanisms and Design Parameters, Chemical Engineering and Processing (2010), https://doi.org/10.1016/j.cep.2018.03.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Flotation Technique: Its Mechanisms and Design Parameters Ritesh Prakash* [email protected] , Subrata Kumar Majumder* [email protected] ,
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Anugrah Singh
Department of Chemical Engineering, Indian Institute of Technology Guwahati, India-781039
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Corresponding author
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Prof. S. K. Majumder/ Mr. Ritesh Prakash
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Department of Chemical Engineering, Indian Institute of Technology Guwahati, India-781039
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Research Highlights
The overview of the flotation techniques and design parameters.
Details in design, analysis, optimization, operation, modelling is reported.
Breakthrough analysis of flotation mechanism is done.
Critical discussion on hydrodynamic parameters is reported.
The measuring techniques of design parameters are also described.
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Abstract
A knowledge of hydrodynamic characteristics is important because it helps in design, control, analysis, optimization, operation, and modelling of the system, which enhances the performance of process unit. This paper aims to provide the evaluation of the techniques of flotation and design parameters, which is required improving the separation efficiency of the flotation processes. Different components of flotation columns, flotation mechanism and design parameters like flow
regime, gas holdup, bubble size and its distribution, mixing characteristics and carrying capacity are critically discussed. The measuring techniques of design parameters for flotation process are also described. The present article on flotation technique and its research components may provide
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in hand information on the flotation process to the researcher and designer of flotation unit.
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Keywords: Flotation; hydrodynamics; design parameter; flotation kinetics
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Nomenclature Area of electrode (m2)
Ab
Surface area of a single bubble (m2)
a
Gas-liquid specific interfacial area (m-1)
B
Constant (-)
BIV
Bubble image velocimetry
Bl
Bubble load (ton/m3)
bm
Eddy turbulent acceleration (m/s2)
C
Tracer concentration (mol/l)
C
Dimensionless concentration (-)
C(ti)
Concentration of tracer that is function of time (mol/l)
Ca
Carrying capacity (kg/hr m-2)
CA
Carrying capacity per unit area (ton/h m-2)
CA
Carrying capacity per unit area (ton/h m-2)
Cb
Concentration of gas bubble (-)
CG
Carrying capacity per unit volume of gas (ton/h m-3)
CL
Carrying capacity per unit length (ton/h m-1)
Cm
Maximum carrying capacity (kg/h m-2)
Cp
Concentration of solid particle (kg/m3) Axial dispersion coefficient (m2/s) Sauter-mean bubble diameter (m) Mean particle size (50% “finer than” size) (m) Product of 80% passing size diameter (m)
db
Bubble diameter (m)
ds
Sparger diameter (-)
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d80
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d50
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A
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Solid concentration (kg/m3)
Cs
d32
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dp
Particle diameter (m)
db,max, db,min
Maximum and minimum bubble diameter (m)
dbe
Equivalent spherical bubble diameter (m)
dc
Column Diameter (m)
De
Equivalent column diameter (m) 3
Particle size (m)
DL
Liquid axial dispersion (m2/s)
DL
Diffusion coefficient in liquid phase (m2/s)
dp
Particle diameter (m)
dpi
Mean particle diameter of size i (m)
dpore
Sparger pore diameter (m)
ds
Sauter diameter (m)
ds
Sparger diameter (m)
dT
Tube diameter (m)
E
Activation energy (J /mol)
E(t)
Residence time distribution (time-1)
Efi
Entrainment factor represents gangue-water recovery ratio (-)
Ei
Degree of entrainment (-)
Ei
Degree of entrainment (-)
El
Volumetric flow of entrained material (m3/s)
ENTi
Degree of entrainment (-)
ES
Solid recovery by entrainment (kg)
fsp
Single phase friction factor (-)
fthree-phase
Three-phase friction factor (-)
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Di
Acceleration due to gravity (m/s2)
g
Gk H
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Hf
Electrical conductance (siemens) Production of kinetic energy term (-)
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G
Collection zone height (m) Froth height (m) Clear liquid-solid height after disengagement process (m)
hm
Total height of gas-liquid-solid mixture (m)
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hl
hr
Height of the reactor (m)
I
Intensity of scattered light (candela)
Jb
Bias water flow rate in the froth (m/s)
Jf
Superficial feed rate (m/s)
jgl
Volumetric flux (m/s) 4
K
Rate constant (s-1)
ks
Stoke’s number (-)
K
Boltzmann constant (J/K)
k
Constant correcting the number of particles that can attach to the available
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bubble surface area due to the hydrophobicity effect of the particles (-) Empirical parameters (-)
k1, k2
Conductivities of continuous and dispersed phase (s/m)
k∞
Rate constant at prolonged flotation time (s-1)
ke
Electrictrical conductivity (s/m)
kl
Electrical conductivity of the liquid (s/m)
Kl-d
Effective conductivity of the dispersion (s/m)
kl-g
Electrical conductivity of liquid-gas mixture (s/m)
kl-s
Electrical conductivity of liquid-solid mixture (s/m)
Kl-s-g
Electrical conductivity of dispersion for three phase (s/m)
krc
Local value of mixture conductivity distribution (-)
l
Distance between two electrodes (m)
L
Height of gas-liquid dispersion (m)
L
Vessel length (m)
lp
Optical path length (m)
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K1, K2
m
Parameter (-)
mp
n
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N
Weight of penetrating liquid (kg)
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ml
Mass of the particle (kg) Number of mechanical cells (-) Parameter depends on flow regime (-) Vessel dispersion number (-)
ni
Number of bubbles (-)
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ND
np
Number of particles that can attach to a bubble (-)
P
Probability of collection of the solid particle on gas bubbles (-)
P
Absolute liquid pressure (pa)
Pa
Probability of attachment (-)
Pc
Probability of bubble particle collision (-) 5
Pr
Operating pressure (Pa)
R
Overall recovery (-)
Rc
Collection zone recovery (-)
Rf
Froth zone recovery (-)
R*
Maximum recovery (-)
r, s
Orders of concentration term (-)
rb
Radius of a bubble (m)
rp
Particle radius (m)
Rfw
Water recovery from the feed (kg)
S
Source term in continuity equation (-)
S2
Scattering function (-)
Sb
Surface area of the rising bubble (m2)
T
Temperature (k)
t
Time (s)
t0
Coefficient (-)
tat
Attachment time (s)
tc
Contact time (s)
tfl
Time of flow (s)
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Probability of detachment (-)
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Pd
ti
Induction time (s)
ts U
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ub
Mean residence time (s) Sliding time (s)
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tm
Interstial liquid velocity (m/s) Bubble rise velocity (m/s) Superficial gas velocity (m/s)
ul
Liquid velocity (m/s)
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ug
usl
Slurry superficial velocity (m/s)
uT
Superficial total velocity (sum of gas and liquid superficial velocity) (m/s)
ut
Terminal velocity (m/s)
usp
Single phase velocity (m/s)
V
Froth volume (m3) 6
Bubble velocity (m/s)
vbs
Volume of a single bubble (m3)
vcl
Total volume of collected bubble (m3)
vg
Superficial gas velocity (m/s)
Vg
Volume of the gas (m3)
Vl
Volume of the liquid (m3)
vp
Particle velocity (m/s)
w
Location of a particle at the liquid-vapour interface (-)
wr
Water recovery (Kg/m2 s-1)
Wsolid-air
Force required to break the bubble particle interface (N/m)
X
Axial position in the column (m)
Z
Dimensionless position (-)
Ar
Archimedes number (-)
Eo
Eotvos number (-)
Fr
Froude number (-)
Gr
Grashof number (-)
Pe
Peclet number (-)
Pr
Prandtl number (-)
Reb
Reynolds number of bubble (-)
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Reynolds number of liquid (-) Schemedit number (-)
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Reynolds number of gas (-)
Rel
Sh
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Reg
Sc
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vb
Sherwood number (-) Surface tension (N/m) Phases (-) Gas holdup (-)
l
Volume fraction or phase holdup of liquid phase (-)
d
Volume fraction or phase holdup of dispersed non-conducting phase (-)
l
Liquid density (kg/m3)
m
Mixture density (kg/m3)
g
Gas density (kg/m3)
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g
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Particle density (kg/m3)
sl
Slurry density (Kg/m3)
sp
Single phase density (kg/m3)
pulp
Pulp density (kg/m3)
f
Density of fluid (kg/m3)
Δ
Specific density difference between solid and water (kg/m3)
ΔH
Height difference between pressure transducer (m)
ΔPTP
Total pressure drop (pa)
ΔPfTP
Frictional pressure drop (pa)
ΔPh
Hydrostatic head (pa)
ΔPa
Pressure drop due to acceleration (pa)
ΔPf,sp
Single phase frictional pressure drop (pa)
ΔPf,three-phase
Three-phase frictional pressure drop (pa)
ΔL
Difference between two-pressure tap (m)
Δ
Density difference between particle and fluid (kg/m3)
ƛ
Fraction of light transmitted (-)
Wavelength (m)
ent
Residence time of the entrained material (s)
Drainage parameter (-)
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mi l ν
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eff
Parameter related to mean particle size (-)
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η
Solid loading (-)
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s
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p
Viscosity of liquid (Kg/m.s) Effective viscosity (Kg/m.s) Frequency (Hz) Slurry kinetic viscosity (m2/s)
Dynamic shape factor (-)
Dimensionless concentration (-)
𝜎𝜃2
Normalized variance (-)
2
Variance (-)
c
Contact angle (-) 8
Maximum collision angle (-)
θ
Dimensionless time , = t / (-)
Ø
Azimuthal angle (-)
Dimensionless number (-)
Mean residence time (s)
rg
Ratio of specific heats of the gas (-)
Entrainment parameter (-)
c
Stream function which characterizes the grazing trajectory (-)
0c
Stream function at the bubble equator ( =900) (-)
Dimensionless concentration (-)
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m
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Contents
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1. Introduction 2. Type of flotation and its application 2.1. Cyclonic-Static Micro-Bubble Flotation Column (FCSMC) 2.2 Electroflotation (EF) 2.3. Induced or dispersed air flotation (IAF) 2.4. Dissolved air flotation (DAF) 2.5. Column flotation 2.6. Jet flotation 2.7. Centrifugal flotation or air-sparged hydrocyclone (ASH) 2.8. Gas aphrons based flotation 2.9. Ion flotation 3. Design parameters of flotation process 3.1. Flow regime 3.1.1. Methodology 3.1.1.1. Visual observation technique 3.1.1.2. Drift flux analysis 3.2. Gas holdup 3.2.1. Measurement techniques 3.2.1.1. Phase isolation technique 3.2.1.2. Conductivity method 3.2.1.3. Pressure drop method 3.2.1.4. Dynamic gas disengagement technique (DGD) 3.2.1.5. Electrical resistance tomography (ERT) 3.3. Pressure drop 3.4. Bubble size and its distribution 3.4.1. Measurement method of bubble size 3.4.1.1. Photographic technique 3.4.1.2. Acoustic method 3.4.1.3. Light scattering method 3.4.1.4. Inverted funnel method 3.4.1.5. Phase Doppler anemometry (PDA) 3.4.2. Bubble rise velocity 3.4.2.1. Particle image velocimetry (PIV) 3.4.3. Interfacial area 3.4.3.1. Methodology 3.4.3.2. Physical method 3.4.3.3. Light transmission technique 3.5. Carrying capacity 3.6. Mixing characteristics 3.6.1. Methodology and analysis of mixing characteristics 3.6.1.1. Residence time distribution 3.7. Entrainment Characteristics 3.7.1. Entrainment theory and empirical correlations 3.8. Flotation kinetics 3.8.1. Induction time 10
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3.8.2. Separation analysis of flotation column by kinetic model 4. Importance and perspective of future research 4.1. Flow regime characteristics 4.2. Holdup characteristics 4.3. Bubble size and its distribution 4.4. Entrainment Characteristics 4.5. Mixing characteristics Nomenclature References 1. Introduction
Flotation is a widely used, cost-effective separation technique for wastewater treatment [1], mineral beneficiation [2], micro-oxygenation of wine [3], fermentation [4], ink removal [5], plastic recycling [6] etc. Flotation techniques are used for the various chemical, mineral and biological
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industries. In this technique, components like fine particles, oil droplets, contaminants etc. are separated from the mixture based on their hydrophobic or hydrophilic surface properties. The
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essence of the flotation process depends on using the gas bubbles to capture the particles based on
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their surface hydrophobicity and hydrophilicity [7]. The gas bubbles produced in conventional
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flotation columns are in the size range of 1.0 - 1.5 mm in diameter [8]. The gas bubbles are used to adhere the hydrophobic particles selectively and carry them to the surface of the liquid, hence
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they form a froth zone where it can be separated while the hydrophilic particles are discharged from the bottom outlet as the tailing. The efficiency of the flotation process is a function of the
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probability of particle-bubble collision, particle-bubble attachment, and particle-bubble detachment. Froth flotation is an extensively accepted separation technique where the separation
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characteristics depend on narrow particle size range between approximately 10 to 100 μm. Beyond this particle size range, the separation efficiency of flotation process reduces notably because of
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difficulty to attachment of weak hydrophobic particles to gas bubbles [9]. Fine particles have large specific surface areas and low mass due to which the probability of bubble-particle collision is limited therefore results in slow separation rate [10]. Conventional flotation machines does not
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generate bubble size less than 600 m for which its application is limited to separate the coarser particles only [11]. Very fine particles may float with smaller size bubbles and fine or mid-sized particles with the bigger size bubbles [12]. Flotation of fine particle (< 37 m) and ultrafine particle (< 8-13 m) is a key challenge. Feed in flotation consists of wide range of particle size, therefore, flotation column needs to have wider bubble size to target fine as well as coarse size particles [13,
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14]. So, flotation of fine particles is one of the major challenging tasks. Research is conducted to explore the mineral-bacteria interaction in order to understand the mechanisms of selectivity of microorganism towards specific particle [15]. Perez-Garibay et al. [16] investigated the effect of bubble size distribution, superficial gas velocity, surfactant concentrating and three different particle sizes such as coarse (100 m), medium (39 m) and fine (15 m) on the flotation
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characteristics. Investigation reports that particular particle-size distribution needed an optimum bubble-size distribution profile, bubble size ranges between 150 to 1050 m diameter and gas holdup ranging from 0.2% and 1.3%. The wide range of bubbles can be produced using dissolved air flotation technique in combination with a surfactant. This technique is able to produce coarse bubbles (400-800 m) and nanobubble (200-720 nm) where nanobubbles are obtained by selective separation from the microbubble. The separation efficiency of the particles in presence of a
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combination of coarse and nanobubbles are compared with only coarse bubbles which reported
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that separation can be improved by 20-30 % for the very fine particles (8-74 μm) while a slightly
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low separation is reported for coarse particles (67-118 μm) [17]. Lim et al. [18] proposed that integration of microbubble with macrobubble reduces the macrobubbles-oil attachment time by
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82%, enhance the bubble-oil contact angle by 40.35 and interfacial surface area of attachment by 54.5%. Many studies are focused on the mineral-bacteria interaction in order to understand the
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mechanisms behind the floatability and mineral selectivity achieved in the beneficiation process.
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Recent studies demonstrate the microorganisms aided mineral beneficiation with the modern advancement in biotechnology. Microorganisms specifically involve to remove the gangue
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particles which are detrimental as responsive flotation reagents [19]. Flotation columns are simple in construction and mostly suited for carrying out the separation of the desired element from the
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liquid or solid mixture in a multiphase environment. Flotation columns are multiphase contacting device where the liquid is in continuous phase while the gas and particles are in dispersed phase. In counter current operation, the feed is introduced after conditioning with reagents, which enters
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into the flotation column approximately at 2/3 of the column height where it mixes with liquid and interacts with the swarm of gas bubbles that is introduced from the bottom of the column through a gas distributor [20]. The relative motion of particles and gas bubbles governs the probability of the bubble-particle attachment, bubble loading, and flotation rate. Counter current movement of feed and gas bubble
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results in reduction of rise velocity of the bubbles, which increases their retention time in the slurry, hence decreases the compressed air requirement and increases the specific throughput of the column. In the counter current operation, the probability of bubble-particle collision is high because of the large aerated mixture in the column, the long distance of the transport of the bubble and particle along the column length and low longitudinal slurry mixing [21]. In some cases, the
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co-current operation is useful during the treatment of coarse particle in which particle-laden bubble rise time is reduced and residence time of the particle increases [22]. The flotation column can be divided into three specific zones: recovery zone, cleaning zone and froth zone. Recovery zone or collection zone: the zone between feed slurry inlet and sparger. In the recovery zone, the downflow feed slurry interacts with upflow gas bubbles where the attachment of the particles to the bubble takes place. The zone controls the degree of the capacity of flotation columns because the capacity
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of the flotation column depends on the intensity of bubble-particle collision, the probability of
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attachment and surface area of the gas bubble. Cleaning zone: the zone above feed slurry to froth interface level. Froth zone: the zone above the interface. Dead zone: the zone below the sparger
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zone. The volume below the sparger (dead volume) does not help in flotation but is used to expel
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tailings. Hydrophobic solid particles attached to the air bubbles are collected by froth while the hydrophilic particles are left in the slurry. It is not always the case of making a solid particle
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hydrophobic, but in some cases, a solid particle is made to be hydrophilic using reagent
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(depressant) so that their attachment to the bubble does not take place and settle down in flotation column. Generally, four steps are required during froth flotation such as: conditioning of desired solid particles during which hydrophobicity imparted to the surface
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of the solid
the introduction of feed slurry to the flotation column where collision and attachment of
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solid particles to gas bubbles take place stable froth formation on the surface of flotation column and
the removal of mineral-laden froth or tailing from the flotation cell.
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In industrial flotation column, the entrainment of gangue particle is common, so several stages of flotation columns are involved to meet the economically acceptable quality of the desired mineral in the product. In this review article, the details of various design parameters of flotation process and the effect of operating and geometric variables influencing the separation efficiency are 13
described. The optimization of different hydrodynamic characteristics is also discussed, and some strategies are suggested for improving the working principle of flotation devices. 2. Type of flotation and its application Numerous techniques of flotation processes based on different working principles are briefed as
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follows:
2.1. Cyclonic-Static Micro-Bubble Flotation Column (FCSMC)
Cyclonic-static micro-bubble flotation column has been successfully incorporated and industrialized for whole flotation circuit for mineral separation in China. Cyclonic-static microbubble flotation column started commercial production in 1994 and patented in 1999 [23].
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Separation process like column flotation use a single step of froth flotation process but the FCSMC
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is the combination of series of a process like a column flotation, cyclone separation and microbubble generator [23]. The microbubble generator directly influences the bubble size and its
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distribution hence the gas holdup in the column flotation zone in the FCSMC. Consequently, this
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equipment significantly affects the separation efficiency of the flotation column [24]. The cyclone separation zone comprises of concentric conical structure which separated particle into three
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different densities. The pulp comprises of highest bubble concentration rises to the column
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separator while the pulp with the high-density particle is expelled directly as tailings. The rest pulp with the intermediate bubble concentration is pumped as the circulating pulp through the external bubble generation device for further beneficiation [25]. Wang et al. [26] reported the effect of
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cone angle (380, 480, 580 and 680) in cyclonic separation zone and recommended that too small (380) and too large (680) cone angle is not suitable for effective separation. Larger cone angle
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decreases the separation which is due to the high centrifugal intensity whereas the overflows from cyclonic flotation zone reduce gradually. The cone angle of 480 is recommended for effective
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separation environment which is the optimized cone angle for proper overflow from the cyclone zone. Li et al. [27] reported the separation efficiency of fine oil droplet (< 10 m) from treated wastewater effluent and compared the separation efficiency of FCSMC with dissolved air flotation technique. They observed higher oil removal efficiency in FCSMC than dissolved air flotation column. The obtained oil removal efficiencies are 92.19% and 76.65% respectively in FCSMC
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and dissolved air flotation with lower oil concentration in FCSMC. A schematic of FCSMC is shown in Fig. 1. 2.2. Electroflotation (EF) The EF technique is potentially applied for separation of ions or solid particles, suspended or
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dissolved in the liquid phase, by attaching on bubbles produced on the electrodes and moves upward in the flotation column [28]. In EF technique, when liquid waste is exposed between the electrodes (cathode and anode) and energy supplied to the electrode, an electric field established between electrodes due to the conductance of the liquid which causes the generation of tiny bubbles of hydrogen and oxygen on cathode and anode electrode. Conventional flotation techniques are able to produce bubble sizes in the range of 600-1000 m in diameter [29], which
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are not very much efficient to float particle sizes less than 20 m [30]. Electroflotation technique
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can produce bubble size in the range of 15 -80 m [31,32]. Variables, which affect the bubble
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diameter, bubble number, and current density in EF technique are pH, type of electrolyte (NaOH, HCl, NaCl) and retention time. EF technique has some advantages such as generation of very fine
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and uniform bubbles of average size of 20 µm, changing of concentration by varying the current density to increase the probability of collision [33]. The conventional technique fails to clean
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wastewater for very dilute solutions having contamination level below 50 mg/dm3 due to high
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operational cost and low removal capacity [34]. Mota et al. [28] used the EF technique on synthetic wastewater containing lead, barium, and zinc and successfully removed the 97% of these heavy
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metal. Membrane separation processes are also in use to clean wastewater but membranes are prone to fouling during their use where gas sparging required to overcome it. A hybrid flotation cell can overcome their limitation by integrating both dispersed air flotation and membrane
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separation [35]. Aoudj et al. [36] investigated the separation of chromium (VI) and fluoride by electrocoagulation-electroflotation by developing hybrid Fe-Al electrode. Fine cassiterite particles
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are separated by EF technique using bioreagent and reported 64.5% recovery [32]. 2.3. Induced or dispersed air flotation (IAF) Dispersed air flotation operates by dispersing or inducing gas bubble into the liquid [37]. In large agitated columns, the gas is injected from the base of the mechanical agitator shaft and small bubbles are generated by the shearing action of the impellers [38]. In a small column, sparger or 15
gas distributor is often used for the production of bubbles. The range of bubble size is about 7001500 µm [39]. High-speed rotating impeller or diffuser cause mechanical mixing of gas and liquid causes production of bubbles, which transported directly into the flotation column. Suspended particles adhere to the bubble surface and float to the surface of the liquid where it is removed by the skimming device. IAF technique is widely used to treat industrial wastewater from oil in the
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refinery, natural gas processing plant, petrochemical, and chemical plant [40]. 2.4. Dissolved air flotation (DAF)
In DAF technique, the air is pressurised to dissolve it into the water then saturated water is passed through a pressure-reducing valve to generate the microbubbles. The produced micro-bubbles size is between 20 to 100 µm diameter [41]. DAF is the one of the potential separation technique used
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to separate the water contaminant like particles, droplets or microorganisms in a size range of 10 to 100 µm. Radzuan et al. [42] investigated the oil droplet separation efficiency from oil-in-water
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mixtures where the oil droplets were in size range of 15 to 80 µm. They developed a correlation
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for separation efficiency based on various experimental data and observed that predicted results
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were below the 6% error. Rao et al. [43] reported the removal of algae and cyanobacteria in water treatment using positively charged microbubble. The bubbles made positively charged by cationic
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flotation reagent. Some other gasses like nitrogen, methane and carbon dioxide can also be used to form microbubbles in some specific cases [44]. DAF is widely used for the water treatment to
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restrict the dissolved and colloidal impurities formation in process water and to improve process ability. In DAF operation the suspended particles removal efficiency is about 90% but the
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dissolved organics removal is only 10% which reveals that still, it is a great challenge to obtain the absolute effluent free water [45]. Some important applications of DAF technique are: Separation of metal ions such as copper, nickel, zinc, ferric from the aqueous solution [46].
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Separation of zinc from hydroxide precipitate [47].
Separation of feldspar mineral from feldspathic slime and iron containing minerals [48].
Separations of mercury, arsenic and selenium ions from gold cyanide leach solutions [49].
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2.5. Column flotation Flotation column is intensively used in the mineral processing industry. The success of column flotation depends on the hydrophobic and hydrophilic nature of particles or it may be imparted 16
using reagent. Bubbles generated at the bottom of the column on which hydrophobic mineral particles are attached and rise up with bubble. Separation efficiency of conventional flotation cell reduces as the size of the particle becomes smaller [10]. To overcome this problem, flotation technique like column flotation, pneumatic free jet flotation [50] and Jameson cell can be used [51]. Conventional mechanically agitated flotation column are substituted by column flotation to
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improve the flotation efficiency. Liu and Schwarz [52] reported the particle size effect on probability of particle-bubble collision in conventional flotation column and concluded that it decreases with the particle size. The separation efficiency can be enhanced using smaller bubble size. Agitated columns are more prone to backmixing and entrainment, so column flotation operations are maintained at streamline conditions in the flotation zone to avoid back mixing and entrainment. The details of differences between conventional and column flotation are provided
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by Reddy et al. [53]. Other applications of flotation are treatment of oil riches wastes, food wastes,
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dairy wastes, textile fibre waste, rubber waste, asbestos waste, polymer waste, paper industry
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waste, dye, electroplating waste, vegetable waste, poultry processing waste etc.
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2.6. Jet flotation
In this technique, a jet is used to induce air to generate the bubble to make froth. Microcell, Davcra
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cell, and Bahr cell are examples of this type of flotation. These flotation machines are high-
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intensity flotation machines. The schematic of Jameson flotation cell is shown in Fig. 2. In the Jameson cell slurry and air are introduced at the top which proceeds downward in the downcomer and forms a liquid jet. Consequently, air is entrained into the plunging jet because of
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the vacuum effect and generates a large number of tiny bubbles as a result of high shear rate [55]. In the downcomer region, the collection of particles on bubble takes place due to rapid mixing.
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Compared to conventional flotation cell the Jameson cell is designed for rapid flotation based on a high bubble surface area flux due to large number of fine bubbles produced by high shearing
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action in the downcomer. The size of produced bubbles in the cell is in the range of 0.1- 0.6 mm diameter [56,57]. Another feature of Jameson cell is that its downcomer can work under vacuum which causes high-intensity contact time (1-10 seconds) [54,57]. Some of the research claim that Jameson flotation cell can produce a large number of bubbles of size < 600 μm in diameter, so this device can be potentially used for the fine particle separation [58]. A comparison study between Jameson cell and other flotation cells like (Canadian column, Flotaire column, Microcel) done by 17
different authors. The comparative study reports minimum residence time and high particle carrying capacity of Jameson cell over another flotation cell. Separation of emulsified oil studied in a modified Jameson cell that results in increased separation efficiency (85%) in MJC (modified Jameson cell) than CJC (conventional Jameson cell) (80%) [59]. Guney et al. [50] studied the beneficiation of fine coal particles, which results in 72.4% recovery. Guney et al. [60] investigated
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the removal efficiency of asphaltite through jet flotation technique. A quite good 55% removal efficiency observed as initial sample contains 43.69% ash while the processed asphaltite has 19.66% ash content. You et al. [61] studied the effect of bubble-particle interaction in downcomer section of the Jameson cell by determining flotation rate constants based on the velocity, bubble and particle size distribution, bubble-particle contact angle and turbulence intensity. The observed average gas holdup and mean bubble diameter in the downcomer section are 55.84% and 0.72 mm
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respectively.
2.7. Centrifugal flotation or air-sparged hydrocyclone (ASH)
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ASH is mainly famous for extremely high throughput per unit volume and suitable for fine
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particles. It consists of two concentric right vertical tubes. In ASH, a centrifugal force is generated by converting pressure head into the rotational motion of swirl flow. Centrifugal force breaks the
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film that leads to the attachment of particle to gas bubble. Gas is distributed through the inner
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porous tube where the outer tube (non-porous) acting as air blanket, which guides the even distribution of gas through the inner tube. The generation of gas bubble takes place through the perforation of air from the innermost cylindrical tube. Slurry is introduced tangentially to the ASH
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where slurry moves axially down to the central cylinder where mixing of slurry takes place with gas bubbles. Hydrophobic particles are attached to the air bubbles and reach to the overflow section
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and discharge with the help of the vortex finder [62]. Chu et al. [63] studied the copper recovery in modified ASH and reported increment in recovery.
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2.8. Gas aphrons based flotation Colloidal gas aphrons (CGA) are multi-layered stable bubbles surrounded by a thin surfactant layer. Small size aphron bubbles have high interfacial area as well as stability so that it can be transported by pump like water without collapsing. These bubbles follow the same charge as of the surfactants used to produce them [64]. CGA technique uses the diffusion of microbubbles into 18
an aqueous solution. CGA bubbles can be generated by both cationic and anionic surfactants. CGA technique is able to generate extremely stable microbubble (10-100 µm) using stirrer which rotates at around 8000 rpm [65]. CGA technique can be applied to fine particles (4-20 m in diameter) separation [66]. Treatment of nanoparticle effluent is a major challenge due to the low probability of bubble-particle collision causing from Brownian motion. The separation efficiency becomes
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lowest when the particle size is < 100 nm. The separation efficiency can be enhanced by controlling the Brownian motion of nanoparticles and interfacial forces between particles and bubbles [67]. Zhang and Guiraud [68] applied modified CGA technique to generate charged microbubbles (42.1 m diameter) in presence of a surfactant to float the silica nanoparticles. The removal efficiency of the nanoparticle is observed to be 90-99%. Some applications of CGA technique are as follows: Separation of ZnO, CuO, and Al2O3 [66]
Separation of protein [69]
Separation of cellulose fibers from paper mill wastewater [70]
Separation of pyrene using the biodegradable surfactant [71]
Extraction of glucoamylase [72]
Extraction of gallic acid [73]
Separation of natural phenolic extract [74]
Separation of pulp using the natural surfactant [75]
Separation of organic dye from water [76]
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2.9. Ion flotation
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Ion flotation involves the metal ions separation using suitable surfactant where the charged gas
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microbubble introduced through the aqueous solution to float the oppositely charged ions [77]. The bubble can be made charged using surfactants. Hoseinian et al. [78] studied the Ni(II) ion
A
removal efficiency using ion flotation and check the effect of different parameters; chemical interactions, separation mechanism, ion removal rate, pH, surfactant concentration, and gas type. They concluded that pH of the solution significantly affects the separation efficiency. With increasing pH upto optimal value, the ion removal rate increases, increasing surfactant concentration removal rate reduces due to the formation of ion-surfactant intermediate complexes, the presence of other ions in the solution reduces the removal rate. The use of nitrogen and oxygen 19
gas reports higher ion removal efficiency compared to the air as gas type. Taseidifar et al. [79] investigated the heavy metal removal efficiency of arsenic, mercury, lead, cadmium and chromium ions from an aqueous solution. Ion flotation technique used in groundwater reports that contamination level of 5 mg/l of heavy metal can be reduced to acceptable levels of about 0.01
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mg/l. 3. Design parameters of flotation process
In the subsequent section, the hydrodynamic characteristics like flow regimes, gas holdup, bubble size and its distribution, pressure drop, wetting phenomena, RTD, mixing characteristics, channelling, induction time, entrainment, settling velocity and interfacial area are described.
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3.1. Flow regime
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Knowledge of flow regime plays an important role in design, operation, control, analysis, and scale-up of flotation column. Multiphase flow can be termed as the interacting flow of two or more
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phases where the interface among the phases influenced by their motion. The factors which affect
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the flow regime are geometric variables (diameter, length, sparger pore diameter, particle size, and cross-sectional area) of the column, dynamic variables (flow rate of flowing fluids) and physical
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properties (density, viscosity, and surface tension) of the flowing fluid. The transition of flow
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regime depends on column dimension, sparger design and physical property of the system [80]. The adjacent boundary of two regimes is called flow regime transition. Knowledge of flow regime is required because it helps in to upgrade the performance of the column by directing the heat &
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mass transfer, mixing, pressure fluctuation, momentum loss and volume productivity [81]. At low superficial gas velocity, the flow regime is homogeneous while at high superficial gas flow rate
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the flow regime turns to heterogeneous. There are mainly two types of flow regimes occur in flotation columns: bubbly (homogeneous) and churn-turbulent (heterogeneous). Bubbly flow takes
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place at low to moderate superficial gas velocity in the continuous liquid phase and gas as a dispersed phase in the column. In bubbly flow, the size of bubbles formed is approximately uniform in size [82]. Homogeneous flow regime is observed at the superficial gas velocity less than 5 cm/s in semi-batch column [83]. Nature of gas distribution and physical property of the liquid decides the size of air bubble formation. Bubbly flow is known as homogeneous flow regime in which there is no coalescence and breakup of bubbles [80]. The travel paths of bubbles are 20
vertical with minor transverse and axial oscillation. The distribution of gas holdup in the bubbly flow regime is radially uniform. In bubbly flow regime, a uniform distribution of bubble and uniform mixing are observed across the cross-sectional area [84]. With the further increase in air flow rate, the shape of bubbles become longer until they break and cause a random, and chaotic mixture propagating through the tube. This kind of flow pattern is known as churn flow. It is highly
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unstable and oscillatory in nature, which can be differentiated from slug flow by the absence of the periodic character. Churn turbulent flow regime is likely to occur at a superficial gas velocity greater than 5 cm/s. Beyond the limit of the bubbly flow regime, a disordered form of the homogeneous gas-liquid system is developed due to the turbulent motion of the gas bubble and liquid recirculation. The flow regime trend at various column diameter and superficial gas velocity
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is reported in Fig. 3.
Under this turbulent condition, coalescence of bubbles occurs due to high gas throughput which
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leads to the development of large bubbles with short residence time and unsteady flow pattern in
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the column [82]. Bubble size distribution is wide in this flow regime due to coalescence and
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breakup of the gas bubbles. This flow regime possesses the mixture of small to large bubble, which varies from millimetre to centimetre in diameter [86]. Churn turbulent flow is generally observed
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in the large diameter column [84]. The generation of the number of bubbles increases with the further increase of gas flow rate, which leads to coalescence of bubble and formation of elongated
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bubbles having the shape of the spherical nose and cylindrical tail. The shape of the formed bubble is similar to the shape of an axisymmetric bullet, which is known as Taylor bubble or gas slug.
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The formed slug may be more than or equal to the diameter of the column. In slug flow, the Taylor bubbles are detached by liquid slugs, which may or may not be aerated. In the Taylor bubble
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regions, the liquid flows downward as a thin annular film from the preceding to the succeeding liquid slug. This forms a wake region when it meets the liquid slug. The vorticity induced in the wake shears bubbles from the tail of the Taylor bubble and aerates the liquid slugs. Slug flow is
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always unsteady in nature, in spite of fixing the flow rate of gas and liquid at column inlet. Slug flow regime is observed to occur in small diameter column at the high superficial gas flow rate [84]. Phase holdup, gas & liquid velocity and mixing in a flotation process are dependent on each other which makes the complex flow behaviour in the flotation column. Hence, the complex flow characteristics significantly influence the flotation efficiency [20].
21
3.1.1. Methodology There are various methods available to observe flow regime and its transition. Some of the methods
Visual observation [87,88,89]
Drift flux analysis [90]
Particle image velocimetry (PIV) [91]
Electrical capacitance tomography (ECT) [92]
Laser Doppler anemometry (LDA) [93]
γ-ray computed tomography (CT) [94]
Conductivity probe [88]
Temperature variation using a heat transfer probe [95]
Neural network [96]
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are:
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A
Some of the important measurement techniques are described as follows:
3.1.1.1. Visual observation technique
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It is one of the simplest technique for estimation of flow pattern in a flotation column. This
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technique can be used only when the column is transparent. In the homogeneous flow regime, the slow movement of the bubble can be observed but in the heterogeneous regime, the gross
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circulation and intensity of interaction of bubbles are very high, so it is not possible to identify the accurate transition velocity. A fast video technique is used for visual observations and, combined
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with image processing to interpret flow regime [87,88]. 3.1.1.2. Drift flux analysis
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Wallis [97] first suggested the drift flux theory for predicting the flow regime and its transition for two-phase system. Drift flux theory can be applied to obtain the transition point separating the homogeneous and heterogeneous flow regimes. In this method, the drift flux, jgl (the volumetric flux of either phase relative to a surface moving at the volumetric average velocity) is plotted against the gas holdup in which sudden change of slope of the curve denotes the transition point. The drift flux relation can be represented as [90] 22
jgl usg (1 g ) usl g
(1)
where usg is the superficial gas velocity and usl is the superficial liquid velocity. The sign indicates the counter-current and co-current flow of liquid relative to the gas phase. Drift flux plot represents the phase velocity at which the bubble flow changes into the churn turbulent region,
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due to steeply increase of drift flux at that point [98]. Plot representing transition point which is function of gas holdup and drift flux is shown in Fig. 4. 3.2. Gas holdup
The gas holdup can be expressed as the volume fraction occupied by the gas phase in the total volume of the two or three phase mixture in the column. Gas holdup in the flotation column
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depends on bubbles, the local flow velocity, the presence of backmixing flow, and the rising
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velocity of the bubbles [99]. In flotation columns, the desired recovery has a great dependence on the determination of gas holdup and flow regime. Particle and liquid residence time cannot be
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estimated without the knowledge of gas holdup and flow regime. Particle recovery is greatly
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dependent on gas flow rate and bubble diameter both of which influence the gas holdup. Finch et al. [100] observed a linear relationship between bubble surface area flux and the gas holdup for
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different types of flotation column and operating variables. According to Massinaei et al. [101]
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linear correlation reported between flotation rate constant and the gas holdup in the industrial flotation column. Tavera et al. [102] investigated the radial gas holdup in presence of vertical baffle which is known for providing even distribution of gas bubble and suppressing the mixing
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effect. Author claimed that the radial differences in gas holdup is due to the sparger system arrangement which is unable to provide the even distribution of the bubble. Vinnett et al. [103]
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reported an indirect technique for measurement of local gas holdup in the collection zone of flotation column. This technique is based on the model structure which is the function of percent
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area occupied by gas bubbles in binary images and the superficial gas velocity. Images are obtained using a bubble viewer and more than 250 images of bubbles are generally analysed to get the appropriate percent area approximations. The model structure is capable of measuring the gas holdup in the range of 2.5 to 15% in laboratory flotation column and 6.0 to 21.0% in industrial flotation column. Li et al. [104] studied the gas holdup in presence of Carboxymethyl cellulose (CMC) and sodium dodecyl sulfate and nitrogen were used as a gas phase. They observed that gas 23
holdup increases by increasing the superficial gas velocity and decreasing with increase of CMC concentration. Bhunia et al. [105] investigated the effect of particle on the gas holdup. Experimental result shows that gas holdup decreases in presence of particle. This reduction is more toward increasing concentration and smaller particle size that results in moderately higher gas holdup than the bigger size. Particle size addition increases the slurry viscosity hence coalescence
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behaviour of the gas bubble increases which causes reduction in gas holdup. According to Joshi et al. [106], the gas holdup in the column depends on the number of bubbles, average bubble size and its rise velocity. One can define gas holdup as the ratio of column volume occupied by the gas phase to the total column volume, which is expressed by [105] Vg
g
(2)
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Vg Vl
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Some of the recently developed correlations of gas holdup for the flotation column are given in
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Table 1.
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3.2.1. Measurement techniques
There are several methods available to measure the gas holdup in the column. Some of the
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available methods for measurement of the gas holdup in the column are phase isolation,
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conductivity [111], pressure drop [102,112], electrical resistance tomography [113], dynamic gas disengagement [114], an optical probe [115], γ ray densitometry [116] etc. Some of the methods
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are described in the following subsection. 3.2.1.1. Phase isolation technique
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Phase isolation technique is used to estimate the average gas holdup in any system. Gas holdup can be obtained by measuring the difference in height between the level of clear liquid before
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aeration and the gas-liquid-solid mixture level after aeration. This technique gives reliable value only when measurement is accomplished at the steady state during operation. The average gas holdup can be calculated as [117]
g
hm hl
(3)
hm
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where g is the overall gas holdup, hm is the height of gas-liquid-solid mixture and hl is the clear liquid-solid height. 3.2.1.2. Conductivity method Electrical conductivity is defined as the ability of a substance to conduct electric current. All
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substances have the ability to conduct electricity to some degree. The accuracy of phase isolation method reduces when to deal with reducing bubble size and liquid volume under test. So, to counter this problem electrical conductivity method is used to measure the gas holdup. According to Maxwell [118], the electrical conductivity of dispersion (a continuous phase plus one or two dispersed phase) is given by
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k l
(4)
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1 d k l d 1 0.5 d
where kl-d is the effective conductivity of the dispersion, kl is the electrical conductivity of the
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liquid and d is the volume fraction or phase holdup of dispersed non conducting phase. For two-
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phase (gas-liquid), by putting g for gas instead of d (indicate dispersed phase) the gas holdup is estimated by
kl 0.5kl g
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kl kl g
(5)
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g
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where kl is electrical conductivity of liquid and kl-g is the electrical conductivity of liquid-gas mixture. Two grid electrodes covering the cross-section of the column are used to can measure the electrical conductivity. Conductivity probes measurement is an invasive technique which may
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interrupts the flow field consequently may impact the performance of the system [113]. The grid electrodes should be inserted in such a way so that they do not disturb the flow field in the column.
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The conductivity of the liquid and liquid-gas is related to measured conductance (G) which can be calculated as [119] A G ke l
(6)
25
where ke is the electrical conductivity, A is the area of electrode and l is the distance between two electrodes. The ratio of (A/l) is known as cell constant. The electrical conductivity of dispersion for three-phase (solid-liquid-gas) (kl-s-g) is calculated by empirical correlations [120]
kl s g kl s l ( solid free basis)
(7)
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where l is the phase holdup or volume fraction of the liquid phase. Another correlation available to predict the gas holdup, proposed by Begovich and Watson [121] which is tested on 4-6 mm glass alumina and plexiglass beads is
k l s g kl l
(8)
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3.2.1.3. Pressure drop method
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This method is one of the standard methods for calculating the gas holdup in two and three-phase
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systems. If the gas density, frictional force, and accelerative force are neglected then the local gas holdup between the two points in the column can be calculated as [102,112]
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P sl Lg
(9)
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g 1
where ΔP is the pressure difference between two points, ΔL is the difference between two pressure
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tap, g is the acceleration due to gravity, sl is the slurry density. This method can be used to estimate the axial gas holdup by taking the pressure measurement at the different axial location. Wencheng
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et al. [99] reported the gas holdup measurement using the differential pressure technique in a cyclone-static micro-bubble flotation column. Gas holdup measurement obtained from the
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differential pressure technique are compared with the volume expansion technique and relative error between them are used to optimize the measurement positions. They suggested that
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measurement position should be in the middle of the column and in the region half way from the center to the wall. The gas holdup in the axial direction is lower at the bottom and higher at the top of the flotation column. 3.2.1.4. Dynamic gas disengagement technique (DGD)
26
Sriram and Mann [114] first introduced DGD technique. When the system is at steady state at a given velocity, the gas flow is quickly shut down by a quick closing valve and start measuring the decaying gas-liquid dispersion height or pressure at the different level with respect to time. Initially, the decay in liquid level is fast due to disengagement of the large bubble and after some time, the decay in liquid level decreases due to disengagement of small bubbles. The decaying
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level of gas-liquid dispersion level can be estimated by a video camera [122], visual observation, pressure profile (pressure transducer signal) [123] and X-ray [124]. The change of decaying height of gas-liquid dispersion with time (is known as dynamic gas disengagement profile) is used to estimate the holdup structure prior to the gas flow shut down. The basic assumptions are: (i) initially at the time (t = 0) the dispersion is axially homogeneous, (ii) constant rate of disengagement process in which every bubble disengages with each other independently, (iii) there
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is no coalescence and break up of bubble occurs, and (iv) the cross-sectional area occupied by the
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bubbles remains unaltered during disengagement process. The liquid surface is not determined clearly due to waviness. The waviness of the liquid surface creates uncertainty during direct
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estimation of liquid level. This problem is countered by measuring the average liquid level.
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Resistance probe sensor is used to measure the liquid level, which provides the time-average value,
average mean liquid level.
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if the resistance probe estimates the local value, multiple probes are needed to get the surface
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3.2.1.5. Electrical resistance tomography (ERT) Electrical resistance tomography technique is used to measure the radial and axial gas holdup
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profile in two or three phase process. ERT technique can be potentially applied in many industrial applications to monitor the flow and holdup characteristics in multiphase flow system [125] due
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to its high-speed competence, low price measurement, robust sensors and non-intrusive nature [126]. The ERT technique comprises of electrodes, data acquisition system, and image
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reconstruction system. A particular number of ERT sensor positioned along the column length and for each plane which is equally spaced, a fixed number of electrode is installed in the inner wall of the column. The size of the electrode varies according to column diameter, fluid velocity, image speed, and fluid conductivity. The data acquisition system follows the adjacent measurement approach by implementing a current between two adjacent electrodes and measuring the corresponding voltage between all other electrode pairs. The installed electrodes are attached to 27
the data acquisition system by coaxial wire. The data acquisition system is connected to the computer for data processing using suitable image repair algorithm. For each sensor plane (m×n) pixel array can be generated using an algorithm, and after excluding pixel (k) belongs to the outside reactor perimeter, the remaining pixels (m×n-k) can be incorporated into the repair of the circular image [89]. If there are r number of planes, the total of (m×n-k)r number of conductivity
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measurement is acquired for each frame. Using the conductivity data obtained from the ERT, the local gas holdup can be measured by applying Maxwell equation which relates conductivity to concentration of dispersed phase as [127]
g
(2k1 k 2 2k rc (k rc k 2 / k1 )) k rc k rc k 2 / k1 2(k1 k 2 )
(10)
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where k1 and k2 are the conductivities of continuous and dispersed phase respectively. The
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parameter krc is the mixture conductivity distribution of two phases. Considering disperse phase as
2k1 2k rc k rc 2k1
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g
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non-conducting material, the Eq. (10) can be rewritten as [113]
(11)
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Phase holdup characteristics of the three-phase system as a function of impeller Reynold number
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and particle loading can also be estimated by ERT technique [128]. 3D gas holdup characteristics in flotation column are estimated by three-dimensional ERT technique [129]. Vadlakonda and
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Mangadoddy [113] applied ERT technique to estimate the effect of operating variable, surfactant concentration and gas distributor porosity on phase holdup. They concluded that gas holdup is enhanced by the increase of superficial gas velocity, gas distributor porosity, feed flow rate and
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initial liquid height.
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3.3. Pressure drop The difference in pressure between two points of fluid carrying network is called pressure drop Pressure drop measurement determines the requirement of flow energy for the transportation of fluids in the multiphase system. The notion of pressure drop provides the energy dissipation pattern, which helps in modelling and assessment of the performance of the system [89]. The main cause of pressure drop is the frictional forces which are due to the resistance to flow, change in 28
elevation of fluid, extra pressure gain due to any fluid which is added using a pump, turbulence generated by sharp changes in fluid flow direction and friction inside the column. Resistance to flow of fluid caused by fluid velocity, viscosity, surface roughness (friction between fluid and wall of column), bend, convergence (sudden contraction) and divergence (sudden enlargement) of the tube, and friction between adjacent layers of fluid etc. The high flow rate or high viscosity leads
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to higher-pressure drop while low flow rate lowers or no pressure drop. Gas holdup increases as gas density increases [130]. The total pressure drop (ΔPTP) in the system can be described as
PTP PfTP Ph Pa
(12)
which is the summation of all the three frictional pressure drop (ΔPfTP), hydrostatic head (ΔPh) and pressure drop due to acceleration (ΔPa). Hydrostatic pressure drop depends on the density of the
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two-phase or three-phase system and height of the gas-liquid-solid mixture, which can be
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represented as
(13)
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Ph m ghm
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where m is the mixture density and hm is the vertical height of the two or three-phase mixture. Pressure drop due to the acceleration can be neglected compared to the total pressure drop in a
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tube of uniform cross section and also in adiabatic condition [89]. For single-phase flow, the
2 2 f sp spu sp L
dc
(14)
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Pf ,sp
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frictional pressure drop is related to the fanning’s friction factor as [89]
where fsp is the single-phase friction factor, sp is the single phase density, usp is the single-phase
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velocity and L the difference between the two pressure tapping over which the pressure drop has been measured. In similar way, three-phase frictional pressure drop based on the superficial gas
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velocity in the column can be defined as Pf ,three phase
2 2 fthree phasemusg hm
(15)
dc
3.4. Bubble size and its distribution
29
Interfacial area available for the particle adhesion characterizes the separation efficiency of the system which helps in the design and scale-up of the flotation column. The interfacial area is directly affect the flotation rate constant [131]. The interfacial area in flotation column depends on the bubble size, gas holdup, superficial gas velocity [132], gas distributor design, properties of phases, and column geometry. Smaller bubbles coalesce to form a larger bubble, the interfacial
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area for the collision of bubble-particle reduces which causes reduction in attachment probability of particle on the bubble hence flotation efficiency decreases. Gas holdup and bubble size in flotation column depend on the physco-chemical property of the system and type of gas distributor used [133]. The probability of collision in pulp phase of flotation decreases with an increase in bubble size, which results in a decrease in recovery [12]. Dissolved air flotation (DAF) and electroflotation (EF) are some other important process, which is able to generate even small-sized
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bubble in the range of 10-100 µm diameter. Some of the methods like Mie scattering technique
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[134], Bayesian magnetic resonance technique [135], Coulter count method or pore electrical resistance method [136], dynamic gas disengagement technique [113] are utilized to estimate the
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bubble size. Image analysis technique is most widely used to estimate the bubble size but there are
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some drawbacks like it requires a transparent wall for image capture, low bubble concentration, complicated experimental setup, and time-consuming process. Laser diffraction technique is used
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to measure the size distribution of microbubble for dissolved air flotation process. Bubbles below
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1 mm [137] or have diameter few hundred m or less are considered as microbubbles [138]. A new microfluidic device known as fluidic oscillator that can be used to convert steady gas flow
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into oscillatory flow which in turn results in the production of microbubble. Fluidic oscillator is easy in design which contains no moving part. Microbubbles produced from porous plate combining oscillatory flow technique may be 10 times smaller in bubble diameter and 2-3 orders
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of magnitude less energy consumption as compared with conventional microbubble generation method based on sparging, cavitation, agitation, electrolysis, and fluid jets [139]. Brittle et al.
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[137], attempted to further decrease the size and population of the microbubble by optimizing the frequency of the oscillating gas supply in a fluid oscillator. They applied frequency optimization on three different microbubble production systems; an acoustic oscillation system with a mesh membrane, a fluidic oscillator employed with a single orifice membrane and a fluidic oscillator with a porous gas distributor. Experimental results show that in some of the cases a bubble size reduction is about 73% as compared with non-optimal operating frequencies. In some cases, a 30
reduction in bubble size of upto 73% was achieved as compared with non-optimal operating frequencies. A current novel innovation demonstrates that microbubbles smaller than 100 μm can be economically produced by incorporating oscillatory airflow pattern [140]. Rehman et al. [141] investigated the volumetric mass transfer coefficient and bubble diameter in the oscillatory flow and compared the results with steady flow. The oscillatory flow environment results in 55%
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improvement in volumetric mass transfer coefficient and able to produced bubble size in the range of 80-120 m diameter than 1 mm in the steady flow condition. Various techniques of bubble
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generation and bubble size distribution measurement are shown in Table 2 and Table 3.
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3.4.1. Measurement method of bubble size
There are several methods available to measure the bubble size in flotation column. Some of the
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methods are photographic [172,173], acoustic [172,174], optical, light scattering [134], inverted
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funnel [175], phase Doppler anemometry (PDA) [176], Bayesian magnetic resonance [135]. Driftflux analysis can be also applied to estimate the bubble size using technique given by [105,177].
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Some of the bubble size measurement methods are described as follows.
3.4.1.1. Photographic technique
It is one of the simple technique for estimation of bubble diameter. Since a decade, numerous
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intrusive and non-intrusive techniques are invented to measure the bubble sizes. The bubble size is estimated by photographic technique followed by image analysis. The generated bubbles are
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captured by a high-speed camera. Columns wall should be transparent so that the high-speed camera can capture the bubbles. A light source can be placed opposite to the camera to get a clear
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picture of bubbles. The captured images are analysed by the image processing software to estimate the bubble size. In this technique, bubble size can be measured by manually identifying each of the bubbles. Photographic technique is limited to resolve large bubble clusters [173] and captures only those bubbles, which are nearby the wall of the column. The mean bubble diameter is also known as Sauter mean bubble diameter which can be expressed as [16,173]
31
n
d 32
n d
3 bi
n d
2 bi
11 n 11
i
i
(16)
where ni is the number of bubbles of diameter dbi. Schematic of photographic technique and fitting
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of bubbles through Stat-Fit software is shown Fig. 5.
The 2-D shape bubbles are assumed as elliptical and their minimum and maximum axes computed automatically by image analysis software [178]. Using the known values of the maximum and minimum axes of the 2-D bubble, the equivalent spherical bubble diameter dbe can be calculated as [179]
(17)
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d be (d b2,max d b,min )1/ 3
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where db,max and db,min are maximum and minimum bubble diameter.
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3.4.1.2. Acoustic method
The acoustic method is based on excessive attenuation of the acoustic wave or scattering and
D
changes in sound velocity. Minnaert [174] first introduced an acoustic method in which sound generated by bubbles are investigated and based on this an equation developed between bubble
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sizes and their natural frequency of oscillation. The resonance frequency of the acoustic wave can
1 d b
3 rg P
(18)
l
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be expressed as [180]
where is the Minnaert frequency , db is the bubble diameter, γrg is the ratio of specific heats of
A
the gas, l is the liquid density, P is the absolute liquid pressure. In this technique produced bubbles are passed through the acoustic perturbation and at same time recording and analysing the response. The bubble volumetric vibration at small amplitude, which is recorded by the harmonic oscillator can be used to calculate the bubble size. This setup consists of a hydrophone which is a kind of microphone designed in such a way that it can do underwater recording or listen to underwater sounds. The working principle of hydrophone is based on a piezoelectric transducer. 32
A piezoelectric transducer is a device, which generates electricity when experiences pressure change. In this method, the hydrophone is placed at sufficient distance from the bubble generator so that it does not affect the bubble size. It is connected to a wireless microphone so that it can amplify and transform the electric signal into acoustic one. Acoustic technique can also be applied to investigate the bubble size [68,175], bubble coalescence phenomena in presence of solid
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particles [181] and mass loading on the bubble [182]. Kracht and Moraga [172], estimated the bubble size using the acoustic technique in the flotation column. Authors claimed that acoustics technique is able to measure the bubbles in the range of 0.75-3 mm diameter in two and threephase system which is sufficient to cover the range of interest in the flotation. Bubble size obtained from the acoustic technique is correlated well with photographic technique.
U
3.4.1.3. Light scattering method
N
Light scattering technique is based on the principle of Mie scattering theory [183]. Intensity of
A
scattered light is related to the radius of the air bubble as given by [134]
M
2 I 2 2 2 2 4 rb S 2 cos
(19)
D
where I is intensity of scattered light, is wavelength, rb is the radius of the bubble, is an
TE
azimuthal angle and S2 is the scattering function. Here scattering light intensity is inversely proportional to the radius of the bubble. Takahashi et al. [184], reported the size and concentration
EP
of fine bubble suspension using the light scattering technique. Author proposed that dynamic light scattering technique based on the Mie theory is more suitable than laser diffraction for
CC
measurement of all kinds of particles if the shape of the particle is known. In case of the fine bubbles, the scattering profile is same as that of a water droplet in the air which supposed to be spherical. Couto et al. [149], estimated the bubble size distribution of microbubble produced from
A
the dissolved air flotation using the laser diffraction technique. 3.4.1.4. Inverted funnel method Inverted funnel technique is used to measure the bubble size. This technique was first introduced by the Leighton and Walton [185]. An inverted transparent glass funnel is used to capture the air bubble. The syringe piston is used to generate a bubble. Length of the air bubbles is measured by 33
drawing captured bubble into the capillary tube. In this technique, the mean volume of the air bubble is estimated by calculating the total volume of the air bubble accumulated in an inverted liquid filled cylinder, which is then divided by the total number of bubbles. The sound emitted by the bubble is caught by the hydrophone. The hydrophone works based on the principle of the piezoelectric transducer, which converts pressure changes into electricity. The generated electric
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signal is amplified and then stored on a transient recorder to display on a cathode ray oscilloscope or processing on a spectrum analyser. Vazquez et al. [175] demonstrate the bubble size measurement by three different techniques, inverted funnel, photographic, acoustic. They observed 0.5% repeatability error with a 50 bubble set in inverted funnel technique while an accuracy between 86% to 99% with a 5% repeatability error in photographic technique. The acoustic technique provided an accuracy of 97% and 99% with a repeatability of 0.3%. Author concluded
U
that the acoustic technique can provide precise bubble size measurement than other two
N
techniques. Inverted funnel technique also can be applied to measure the rise velocity of the
M
3.4.1.5. Phase Doppler anemometry (PDA)
A
bubbles in the viscous solution [186].
Phase Doppler anemometry (PDA) method is used for estimation of size, concentration, and
D
velocity of a spherical particle like bubbles and droplets in gaseous or liquid phase [176,187]. PDA
TE
technique can be used to measure the turbulence characteristics in the flotation column [176]. This method is based on the light scattering interferometry. In this technique, coherent laser beams used to focus the measurement location. When the fluid particle passes through the measurement
EP
location scatters the waves from two incident laser beams. Photo detectors receive the Doppler signal in different phases and the phase shift between the Doppler signals is proportional to the
CC
fluid particle diameter. The frequency of the Doppler signal is directly proportional to the velocity of the fluid particle [187]. An advantage of this method is that it can measure the size and velocity
A
of each fluid particle simultaneously. This technique provides online real time data [188]. 3.4.2. Bubble rise velocity There are several methods available to measure bubble velocity in the column. Some of the available methods for measurement of the bubble velocity in the column are conductivity method [189], laser Doppler anemometry (LDV) [190], Particle Image Velocimetry (PIV) [176], optical 34
fiber probe [191] ultrasonic Doppler etc. A detail explanation of PIV technique is provided in the subsection. 3.4.2.1. Particle image velocimetry (PIV) PIV is a non-intrusive technique used to measure the instantaneous whole field velocity vector of
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flowing field. This technique is suitable to measure the fluid velocity vector at many points at one instant of time. PIV technique can measure 2D or 3D velocity component for whole area simultaneously. The fluid of interest is seeded with neutrally buoyant tiny tracer particles/markers, which makes flow field visible under the light source (laser sheet, which ensures better illumination of tracer particle). The CCD (charge-coupled device) camera is used to capture the images of these tracer particles at different interval of times [192]. The instantaneous velocity field
U
is determined from the displacement of tracer particle between two successive images in a period
N
[193]. A suitable software (e.g., PIV-SLEUTH) can be used to do the image analysis in which each image is divided into the mesh of small segment called as interrogation area. Cross-correlation
A
method is used to calculate the mean displacement (Δx) in the interrogation area, which is divided
M
by inter-frame time interval (Δt) to get the mean flow velocity [194]. The velocity map over the whole target area is determined by repeating cross-correlation method for each interrogation area
D
over two image frames recorded by the camera. Another software can be used to do the analysis
TE
of images is PIVlab, which is an open source software. PIVlab is an open source MATLAB code, which can be used to determine the velocity distribution within the image pair and can also be used to derive display and export multiple parameters of the flow pattern [195]. Tracer particle can be
EP
either solid/liquid/gas during measurement of fluid velocity. In the case of liquid flows, the tracer particle like hollow glass sphere, aluminium, polystyrene, and polyamide within the size range of
CC
(5-100 µm) are generally used. In the case of gas flows the tracer particle are oil drops with the size range of 1-5 µm. PIV techniques are executed considering following assumptions: (I)
A
homogeneous distribution of tracer particles, (II) tracer particles obey the fluid flow/motion ideally, and (III) uniform displacement within interrogation region. The criteria to select the tracer particles are: (I) tracer particles should be easily detectable/visible (Light reflecting particle), (II) tracer particle does not disturb the fluid flow, and (III) for better precision, the density of tracer particle should be close enough to the density of fluid. In the case of single phase (liquid), the flow measured with the help of tracer particle, which is illuminated by laser light sheet. In the case of 35
two-phase (liquid/gas) flow, the liquid seeded with tracer particles and both tracer and bubble scatter light, which enables to distinguish tracer from bubbles. Measurement of the local displacement of tracer particle and gas bubble enables to calculate the velocity of both phases [196]. PIV technique is also used to measure the bubble diameter, shape, acceleration, and instantaneous velocity field [197]. Flow regime and its transition are mapped by PIV technique
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[91]. PIV technique can also be used to characterize the turbulence by capturing the fringe visibility within the error of less than 10 % [198]. Fig. 6, represents the subsequent steps of PIV measurement.
PIV technique can be successfully employed to study the fluid flow movement in a flotation column. The computational fluid dynamics (CFD) and particle image velocimetry (PIV) are used
U
to estimate the flow pattern in presence of strong vortex generated by rotor. An excellent agreement is obtained between the simulation results and experimental measured flow characteristics for the
N
flotation column [199]. Darabi et al. [200], studied the turbulence characteristics in the flotation
A
column using PIV technique. Authors reported, local turbulence characteristics vary in presence
M
of gas bubbles due to average velocity, turbulent kinetic energy dissipation and turbulent kinetic
3.4.3. Interfacial area
D
energy.
TE
The knowledge of the gas-liquid interfacial area is essential for scale-up and design of the multiphase system. The overall degree of separation in the flotation column can be controlled by
EP
interfacial area. The interfacial area depends on gas holdup and bubble size distribution and bubble velocity [201].
CC
3.4.3.1. Methodology
There are several methods available to measure the gas-liquid interfacial area. Some of the
A
important techniques are video imaging [202], dynamic gas disengagement [203], Laser Doppler anemometry [204], conductivity probes [205], chemical method [204,206] and light transmission method [207]. Physical and light transmission technique are described in the subsequent section. 3.4.3.2. Physical method
36
If gas holdup and Sauter mean bubble diameter is known, then the gas-liquid interfacial area can be calculated as [149]
a
6 g
(20)
d 32
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where a is the gas-liquid specific interfacial area (interfacial area per volume), g is the gas phase holdup and d32 is the Sauter-mean bubble diameter. 3.4.3.3. Light transmission technique
Light transmission technique is used for calculation of gas-liquid interfacial area. A detailed study of a light transmission technique is reported by Ghiassi et al. [201]. Calderbank et al. [207],
U
introduced light transmission method, in which transmitted beam of light allowed to pass through
N
the gas-liquid dispersion. The intensity of emerging beam is estimated by a photo-multiplier or
A
photosensitive device. The fraction of light transmitted (ƛ) is related to the gas-liquid interfacial
al p 4
(21)
D
e
M
area and optical path length which can be expressed as [208]
TE
where a is gas-liquid specific interfacial area and lp is optical path length. Light attenuation method is restricted to a value of alp < 20.
EP
3.5. Carrying capacity
Carrying capacity can be defined as the maximum capacity of the gas bubble to transport the solids
CC
particles or removal capability of solids by the gas bubble in flotation column [22]. The capacity of the flotation column depends on the number of free bubble surfaces area available for
A
attachment of particle [209]. As bubble loading starts, contact time decreases because of reduction of particle trajectory along the free bubble surface. The rate of collection of solids by the gas bubble decreases as solid loading increases by the gas bubble. Carrying capacity of the smaller bubble size is greater than the bigger when the column is operated at a constant gas flow rate [16,22,131,177]. According to Finch and Dobby [177], the theoretical carrying capacity can be expressed as 37
Ca ,max
d p p u sg ,max 2d b
(22)
where usg,max denotes maximum superficial gas velocity. The amount of particle, which is carried by the gas bubble, depends on the size of the gas bubble. The degree of carrying capacity is
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controlled by the availability of total surface area [210]. A correlation proposed by Princen and Peplinski [211] to predict the load carrying capacity of the gas bubble which can be expressed as Bl 4.84 p rb rp r 2
(23)
where Bl denotes bubble load, rb is the bubble radius, rp is the particle radius and p is the particle
coverage which can be mathematically expressed as
(24)
A
N
Bl K1d p p / d b
U
density. According to Li et al. [212] the bubble load can be determined from the bubble surface
where K1 is the fraction of bubble surface occupied. Bubble loading can be demonstrated as ratio
(25)
D
mcl (vcl / vb ) Ab
TE
Bl
M
of mass of collected solid particles to the total surface of bubbles which can be expressed as [154]
where mcl is the mass of loaded particles, vb is the volume of single bubble, and Ab is the surface
EP
area of the single bubble. The carrying capacity can be normalized as per unit length (CL), per unit area (CA) and per unit volume of the gas (CG) [213]. Flotation column generally operates at 60% of their maximum carrying capacity [214]. Some correlations for carrying capacity are given in
CC
Table 4.
A
3.6. Mixing characteristics Mixing and dispersion in the flotation column are due to the pulp recirculation and turbulence of bubble and feed slurry motion. Mixing in flotation column affect particle suspension, fine bubble generation and dispersion consequently bubble-particle collision takes place [217]. Mixing and dispersion characteristics play an important role in designing and scaling up of the flotation columns [147]. The degree of mixing can be estimated by residence time distribution (RTD) 38
technique. The variation of gas holdup radially or axially cause pressure variation, therefore responsible for liquid circulation, and back mixing of the phases [89]. Liquid circulation direct the rate of mixing and recovery efficiency of flotation column. Mills et al. [218] studied the mixing characteristics of the flotation column using the RTD technique. In collection zone of flotation column, it is assumed that axial dispersion model controls the flow structure. Author reported that
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the axial dispersion model is superior to other models dealing with column diameter 10 cm to 150 cm. For modelling of small diameter column, either dispersion model or tank in series model can be used. The solid dispersion coefficient is more than the liquid dispersion coefficient and solid dispersion coefficient increases with increase in particle loading in laboratory test column but remains unaltered in large column [218]. The performance of flotation cell when they are arranged
t N 1e tN /
N
N 1 !
A
N
(26)
N
E (t )
U
in series for continuous operation can be modelled using N perfect mixer in series by RTD as [219]
M
where E(t) is the RTD function, N is the number of mechanical cells, is the mean residence time and t is the time. Bubble size, bubble number, particle settling velocity, slurry rate, collection zone
D
height, and diameter of the column influences the dispersion number [22]. The intensity of axial mixing increases with the increase in column diameter [220]. Mixing of phases inside the flotation
TE
column significantly affects the bubble-particle attachment and bubble-particle detachment process. The study of mixing characteristics helps in optimization and design of the flotation
EP
column [221].
CC
3.6.1. Methodology and analysis of mixing characteristics Flotation column never obeys the ideal flow pattern. The non-ideal behaviour is due to (i) channel formation, (ii) recycling of fluid, (iii) vortices and turbulence at inlet and outlet of the vessel, (iv)
A
bypassing and short-circuiting of the fluid, and (v) formation of dead zone at the corner of the vessel. The amount of time spent by the molecule in the vessel called as the residence time of the molecule in the vessel. It is obvious that different particles use different routes to pass through the column takes a different amount of time and due to this, there will be the distribution of residence time of the molecules inside the vessel. The distribution length of time spent by different molecule inside the vessel, called residence time distribution (RTD) or exit age distribution (E). Tracer 39
technique is one of the simple methods to measure RTD [222]. The tracer should be non-reactive, should not be adsorbed on the vessel wall or other surfaces of the vessel, its physical property should be similar to the system, should be easily detectable, should be completely soluble in the system fluid [223]. Tracer is injected with feed at the time (t=0) and then measured the tracer concentration in the outlet of the vessel as a function of time. Pulse and step input method is
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commonly used for RTD measurement. RTD can be determined by a non-invasive sensor in case of radioactive tracer by locating it at an outlet of the vessel [217]. Particle RTD in the flotation column strongly depends on the superficial velocity of the feed and hindered settling velocity. Information entropy theory can be applied to analyse the quality of mixing in flotation column which is based on the information entropy theory [224]. Chegeni et al. [225] attempted to design the laboratory flotation column employing the axial dispersion and drift flux model considering
U
axial mixing coefficient, gas holdup, column length, vessel dispersion number and bubble size.
N
Applying the theory of the axial dispersion model and vessel dispersion model, the dimensions of the flotation column calculated for particular operating conditions. The study reports the axial
A
mixing coefficient of 0.003 (m2/s) and vessel dispersion number of 0.32. The required diameter
D
3.6.1.1. Residence time distribution
M
and height of the column are 0.0542 and 1.15 m.
TE
RTD is most widely accepted technique to examine the mixing characteristics. When liquid or solid tracer is introduced into the flotation column, assuming that mixing takes place axially, the axial dispersion model predicts the concentration of tracer at axial distance from the introduction
EP
point z and time t which is represented as [226] C 2C C D U 2 t X X
CC
(27)
A
where D is the axial dispersion coefficient of the liquid phase which accounts the mixing intensity during flow, U is the interstitial liquid velocity, C is the tracer concentration. The first term in the Eq. (27), characterizes the time dependence concentration and U( C/ x) term represents the convective flow in the axial direction and D(2C/X2) represents the diffusive action, which represents the convective flow. The dimensionless form of axial dispersion model can be expressed as 40
1 2 Pe Z 2 Z
(28)
where Pe is Peclet number Pe = UL/D, L is the column length (bubbling zone height), is the dimensionless concentration = C/C0, Z is the dimensionless position Z = X / L and is the
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dimensionless time = t / where = L /U is called mean residence time of the liquid in the system. Axial dispersion model employs vessel dispersion number to specify the RTD profiles in the flotation columns [227]. Vessel dispersion number is defined in terms of Peclet number as ND
1 D Pe UL
(29)
when ND tends to zero and ∞, vessel results in negligible dispersion (plug flow) and large
U
dispersion (perfect mixed flow). The analytical solution of the Eq. (28) for normalized response
N
curve using open-open boundary conditions is given as [226] (1 ) 2 Pe exp 4 2 / Pe
(30)
M
A
1
C
where C denotes (C/C0) and θ denotes (t/tm) are dimensionless concentration and time. If both
D
experimental and theoretical residence time are equal, it represents that the column is most likely
TE
well mixed. If the experimental mean residence time is smaller than theoretical, it specifies the presence of dead volumes, short-circuiting [228]. The mean residence time can be calculated by
tm
EP
first moment methods is represented as
t C (t )t C (t )t i
i
(31)
i
CC
i
i
The second moment about the mean is called square of standard deviation or variance (σ2) is
A
expressed as 2
(ti t m ) 2 C (ti )ti
C (t )t i
(32)
i
41
The magnitude of variance dictates the spread of the distribution. The greater will be variance, more is the spread of the distribution. The magnitude of moments related to axial dispersion number (1/Pe) is
2 t
2 m
2 8 2 Pe pe
(33)
SC RI PT
2
where 𝜎𝜃2 is the normalized variance. 3.7. Entrainment Characteristics
Entrainment is defined as the transportation of fine particle in froth phase from pulp phase (collection zone) by entrapment in eddies behind the rising gas bubble [22]. Entrainment of gangue
U
material decreases the selectivity of the flotation column hence limit the collection effectiveness
N
of the desired particle. Therefore, the knowledge of entrainment characteristics helps in reduction
A
of the collection of undesired particle which improves the column efficiency, increases optimization and control of the column. During processing of particles larger than 38 µm [229],
M
the entrainment problem is insignificant because gravitational force cause entrained solid particle to drop back from froth phase to collection zone. Entrainment of gangue material into the froth
D
dilutes the desired material and decrease the grade of the concentrate hence selectivity and
TE
performance of the column [230]. Wang et al. [231] suggested that the entrainment is not only the function of particle size but other variables like gas flow rate, the density of the undesired particle
EP
and impeller speed and froth height. The degree of entrainment effectively varies with flotation time during the course of each experiment. Yianatos et al. [232] reported the entrainment study using the radioactive tracer technique and checked the effect of three different particle sizes. They
CC
suggested that fine particle size (< 45 m) significantly affect the entrainment while the recovery of the coarse particle (> 150 m) by entrainment is 0.05% which signifies weak dependence on
A
entrainment.
3.7.1. Entrainment theory and empirical correlations There are two mechanisms of entrainment observed in flotation column. First, one is due to the introduction of feed water which contains suspended solid particle, swept into the froth and second is due to entrapment of fine particle (gangue) in rising bubble [6]. The issue of entrainment in froth 42
phase can be minimised by; film water drainage in which slow fall of entrained material takes place around the gas bubble surface, fall of an entrained particle due to shear forces results from the relative motion of the gas bubble, local froth collapse which results in fast vertical fall of an entrained solid particle [233]. Entrainment in column depends upon the size of feed particle, recovery of water, pulp phase density, the speed of impeller, dispersing agent, froth thickness and
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air flow rate [234]. Entrainment is low in case of particle size more than 50 µm [235]. The entrainment depends upon the depth and structure of the froth. Some other parameters which affect the entrainment are superficial feed rate, collection and cleaning zone height, superficial wash water rate [235-238]. The degree of entrainment decreases with decrease in particle size. Stable froth structure made up of small bubbles is responsible for the better recovery of both entrained particle and attached particle due to low drainage and coalescence tendency. Many authors
U
proposed different models and theories for predictions of entrainment [239]. The degree of
N
entrainment based on the pulp phase is proposed by Johnson [240], is defined as the ratio of the mass of free gangue particles of ith size interval in the concentrate to the mass of free gangue
1 K1ent ( p pulp )
D
1 K1ent ( p pulp ) exp( k 2 d p )
(34)
TE
Ei
M
entrained solid is given by [241,242]
A
particles of the ith size interval in the pulp. The degree of entrainment based on residence time of
where Ei denotes degree of entrainment, K1, K2 empirical parameter, dp is the particle size, pulp
EP
and p are the specific gravity of pulp phase and entrained solid particle and ent is froth residence time of the entrained material. The froth residence time of the entrained material can be calculated
CC
as V El
(35)
A
ent
where V is the froth volume and El is the volumetric flow of entrained material in the concentrate. Another way to calculate the froth residence time of the entrained material is given by [243]
ent
Hf
(36)
us g
43
where Hf is the froth height and usg is the superficial gas velocity. According to Subrahmanyam and Forssberg [244] and Kirjavainen [238], the degree of entrainment can be expressed as the ratio of recovery of the entrained species to the recovery of the water. Water recovery, solid concentration in the pulp, particle size, impeller speed, particle density, gas rate, froth height, froth retention time, froth structure are the prime factors which affect the entrainment characteristics
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[6]. Different methods of measurement of entrainment are discussed by Trahar [241], Warren [245], Savassi et al. [242]. There are several models developed by researchers to predict entrainment in the flotation column. Developed methods can be categorized as; estimating the entrainment flow directly, and by determining entrainment flow based on the estimation of the degree of entrainment, classification effect of pulp, and water recovery [6]. An empirical model that measures the entrainment flow is expressed as [236]
(37)
N
U
ES exp 0.0325 R fw exp 0.063d p
A
where Es is the solid recovery by entrainment, Rfw is the water recovery from the feed, Δ is the specific gravity difference between solid and water, dp is the particle diameter. Water recovery
(38)
D
R fw 2.58 j f 1e 13.1 jb
M
from the feed is expressed as
TE
where jf is the superficial feed rate and jb is the bias water flow rate in the froth (it is the difference between the superficial velocities for the wash water flow and the concentrate water flow). Model
EP
proposed by Savassi [242] shows relationship between degree of entrainment (ENTi) and particle size as
A
CC
d p d p ENTi 2 exp 2.292 exp 2.292
1
1 ln
dp exp
1
(39)
(40)
where is the entrainment parameter, is the drainage parameter, and dp is the particle diameter. Savassi [242] developed the model for degree of entrainment fits well with the number of industrial datasets and depends on particle size. According to Savassi [246], the degree of entrainment 44
defined as the ratio of mass transfer of entrained particle of the ith size interval to the concentrate by mass transfer of water to the concentrate. The froth height above the level of pulp significantly affects the performance of the flotation column. The wetness of the froth increases with increasing superficial gas flow rate. The grade of the concentrate can be upgraded by controlling the residence time of the froth and by skimming off the top layer of the froth. The upgrade of concentrate is due
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to drainage of water and gangue into the lower layer of the froth phase and drain back to the pulp phase. Yianatos and Contreras [239], proposed a dimensionless entrainment factor based on particle which is expressed as
d E fi exp 0.693 pi mi
(41)
U
where Efi denotes entrainment factor which represents gangue/water recovery ratio, dpi is the mean
N
particle diameter of size i, mi is the parameter related to the mean particle size and is the drainage
A
parameter which depends on mineral characteristics and cell operation conditions like cell design
M
and water recovery. Kirjavainen [237] studied the entrainment of a hydrophilic particle in the laboratory using quartz and phlogopite. Entrainment correlation does not include calculation of water recovery, so the proposed model is not suitable for wide range of flotation conditions. The
D
proposed entrainment factor that is based on particle mass, particle shape, water recovery rate, and
(42)
0.5 0.4
wr0.7 b 0.5 m p
EP
E fi
wr0.7
TE
slurry kinematic viscosity can be expressed as
CC
where Efi stands for entrainment factor, wr is the water recovery, mp is the mass of a particle, η is the slurry viscosity, is the dynamic shape factor and b is constant to be form from experiment.
A
3.8. Flotation kinetics Flotation rate constant can be defined as the ability of the species, how rapidly they float. Floatation is generally a first order process and a function of particle concentration [247]. Using chemical kinetic analogy, the kinetic of bubble-particle collision and attachment of particle to gas bubble in is given as [248]
45
dC p dt
KC pr Cbs
(43)
where Cp, Cb, K, and t are the concentration of solid particle, the concentration of gas bubble, rate constant, time of flotation and r, s represents respective orders of concentration terms. At constant
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air supply, the probability of change in concentration of air bubble is very small and using first order kinetic (r=1), the rate equation can be expressed as dC p dt
KC p
(44)
The model is useful for prediction of process analysis. A flotation kinetic determines the variation of the rate of change of recovery with time and recognizes the variables that affect the flotation
U
kinetics [249]. The removal rate of particles or probability of collection of solid particles on gas
N
bubbles in pulp phase in the flotation column is a function of the probability of collision, the
A
probability of adhesion and probability of detachment. According to Yoon and Luttrell [250], the
and surface area of the rising bubble.
D
3.8.1. Induction time
M
rate constant of flotation process is directly proportional to the probability of collection of particle
TE
Induction time governs the attachment of solid particle to gas bubble. The time needed for the particle and bubble to break the narrow film separating the particle and gas bubble is called
EP
induction time. Rupturing of the thin film takes place due to surface forces between particle and bubble. Attachment of gas bubble to particle occurs when the time in which the particle and gas bubble is in contact with each other is more than the required induction time. Induction time
CC
strongly depends on the fluid properties, particle and bubble sizes and the forces between the particle and bubble. According to Albijanicet al. [251], the particle and gas bubble attachment take
A
place only when
t at t c
(45)
where tat is the attachment time defined as the time required for attachment of solid particles to the gas bubble when both are very close and tc is the contact time. Multiple collision occurs on bubble surface due to rebound from the bubble surface where collision changes to sliding [252]. The 46
collision time is smaller than the sliding time. Some naturally hydrophobic particles like bitumen, coal, waxes, molybdenite, hydrocarbon, tar and talc do not require flotation reagents to make these particles hydrophobic [253]. The hydrophobicity of naturally occurring particle decreases due to oxidation, which changes the chemical and physical properties of the surface of particle resulting in an increment of attachment time which causes a decrease in recovery of the particle during
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flotation process and the probability of attachment. The attachment time decreases exponentially with increase in temperature due to thinning of liquid film as given by [254] E t at t 0 exp K T
(46)
where t0 is the coefficient, E is the activation energy, K is the Boltzmann constant and T is the
U
absolute temperature. The attachment time and recovery depend on the particle size [255,256]. Ye
N
et al. [255] reported an increase of attachment time and a decrease of recovery with the increase in particle size. The effect of conditioning time on attachment time of air bubble on bitumen is
A
studied by Su et al. [257]. They reported that the attachment time increases with the increase in
M
conditioning time. Contact angle and induction time strongly depends on the hydrophobicity of the particle [159]. The pH value of the mixture significantly affects the flotation kinetics. In
D
presence of cationic collector, at low pH flotation capacity reduces because of cation and hydrogen
TE
both are in competition to get a suitable site on the solid particle. In anionic collector environment, at high pH, flotation kinetic reduces because OH- ion and collector anion are in competition to search a suitable site on the solid particle during the adsorption process. pH value also alters the
EP
zeta potential of the bubble and particle. The effect of pH on the zeta potential of bubble and particle and flotation recovery are studied by Yoon and Yordan [256]. The experimental results
CC
show that at pH 4.5, the induction time is 10 millisecond and flotation recovery is 22% while at the pH 9.8 the induction time increased to 125 milliseconds and flotation recovery becomes zero.
A
pH of solution alters the electrical interaction between the bubble and particle. It controls the attractive or repulsive electrostatic force between particle and gas bubble. 3.8.2. Separation analysis of flotation column by kinetic model
47
The removal rate of particles or rate of flotation depends on the probability of bubble-particle collision Pc, the probability of bubble-particle attachment Pa and the probability of bubble-particle detachment Pd [159]
P Pc Pa (1 Pd )
(47)
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where 𝑃 is the probability of collection of the solid particle on the bubbles. The probability of collision in the flotation column is due to the relative motion of the solid particle and the gas bubble. Many researchers developed the probability of bubble-particle detachment model which is based on the force balance, energy balance and maximum floatable particle size [7]. The probability of detachment of fine solid particle is very small and can be omitted. The expression
U
for the probability of collision is given as
(48)
N
PC A( D p / Db ) n
A
where A and n are the parameters which are the function of Reynolds number. Reay and Ratcliff
M
[258] reported the values of parameter A (2/3) and n (2) are which are valid for stokes region. The values of parameter A and n are 3 and 1 under potential flow condition [259]. Probability of
d p d b
2
(49)
TE
3 / 16 Rel Pc 1.5 1 0.56 1 0.249 Re b
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collision under intermediate range is given by Weber and Paddock [260]
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Some of the important developed models for probability of collision are given in Table 5.
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The probability of attachment of solid particles to bubble is influenced by the hydrophobic nature of the solid particle. The mathematical expression for estimation of probability of attachment is
A
given by [159]
(45 8 Re 0.72 t u ) 2 b i b Pa Sin 2 arctan exp d b 15d b 1 d p
(50)
48
where ti, Reb, ub, db and dp stand for induction time, Reynolds number of bubble, bubble rise velocity, bubble diameter, and particle diameter. The rate constant (K) of the flotation process can be expressed as [159]
3P u sg K 2d b
SC RI PT
(51)
where usg is the superficial gas velocity, db is the bubble diameter. The probability of detachment (Pd) in the flotation can be described as [262]
2 c 6 sin ( ) 2 Pd exp 1 d p2 ( g pbm ) d p cos 2 ( c ) 2
U
(52)
N
where is the surface tension of the fluid, c is the contact angle between bubble and particle, dp
A
is the particle diameter, is the density difference between particle and fluid, p is the particle
M
density, and bm is the eddy turbulent acceleration. Some important flotation kinetic models [221,263,264] are provided in Table 6.
D
4. Importance and perspective of future research
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For a long time, flotation process has been used as a successful way of separating fine particles, wastewater treatment, deinking of paper etc. in chemical process industries. In spite of this, still,
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there are certain issues that are yet to be addressed to optimize the flotation process. After going through the literature it is observed that there is a huge uncovered area of research in
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hydrodynamics and microbubble assisted flotation process. Design parameters like flow pattern, gas holdup, mixing characteristics and bubble size & its distribution have a large number of applications in industries. Investigation of design parameters intensification facilitate the improved
A
transport processes. 4.1. Flow regime and its transition characteristics Today many industries are facing problems because of the complex flow behavior of gas-liquid or gas-liquid-solid in a multiphase system. Many researchers have explored flow pattern for several years to understand it in flotation technique. Researchers attempted to create a universally 49
applicable flow pattern map using non-dimensional quantities but these were validated against only a few experimental data sets. Most of the industrial operation works with different nonNewtonian liquids, so a thorough investigation of the flow regime and its transition at the quantitative range of gas and slurry flow rate is required to improve the efficiency of the flotation process. The design of flotation columns requires detailed information on the flow pattern and its
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characteristics because it directly influences the mixing characteristics of the phases and bubble stabilization, therefore governs the flotation effectiveness. Bubbles in the flotation system are presumed to be spherical in shape in most of the operation, but it is essentially governed by the flow regime. There is a lack of model development to interpret the flow pattern and its transition in the cyclonic-static micro-bubble flotation column and other flotation devices. Most of the noninvasive technique is most suitable for the two-phase system. Few authors studied the
U
measurement of flow regime in the three-phase system using a non-invasive technique. More
N
detailed studies on three-phase flow regime and its transition required incorporating non-invasive technique at different dynamic and geometric variables. Steady flow and oscillatory flow pattern
A
can be incorporated to produce the bubbles in the flotation column. The latter one results in
M
enhanced gas dispersion, improved foam stability, improved phase holdup, and axial mixing [265]. Although plenty of flow regime studies are reported in the literature, it is observed that important
D
information concerning the flow regime transition is often unnoticed. In particular, gas holdup and
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bubble size, that is considered in flow regime correlation model are rarely incorporated. The future experiment should consider the important variables which greatly influences the flow regime maps for numerical analysis, therefore can enhance the comparability study and the validation of
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experimental results. Computational fluid dynamics technique also required to be more advanced
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that can predict the complex behavior of the individual phases in the flotation system.
4.2. Holdup characteristics
A
The accurate interpretation of gas holdup is important for the appropriate design, operation, and scale-up of the flotation systems in a wide range of industrial application. Many authors have described the experimental measurements technique for measurement of average and radial gas holdup profile. A number of techniques such as phase isolation, electrical resistance tomography, dynamic gas disengagement, pressure drop etc. are in use to measure the local gas holdup. There is a number of empirical correlation proposed by different authors to predict the radial gas holdup 50
but these correlations are not universally applicable to any flotation system at the wide range of geometric variable, kinematic variable and physical property of the system. It is due to the complex behavior of the flotation system; no fundamental equation is available which can interpret the radial gas holdup profile. Smaller bubble size is recommended for the high gas holdup in the flotation process. Smaller bubble size has high interfacial area facilitate improvement in the
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bubble-particle interaction efficiency, induction time as well as carrying capacity, which in turn enhances the flotation efficiency. Knowledge of radial and axial variation of gas holdup plays an important role in the design and analysis of the flotation systems. Radial variation in gas holdup causes a rise in pressure fluctuation because of which liquid recirculation takes place in the flotation system. This liquid recirculation directs the mixing rate and transport efficiency. Successful implementation of CFD is still an open challenge to understand the radial and axial gas
N
U
holdup characteristics of the flotation system.
A
4.3. Bubble size and its distribution
M
High interfacial area facilitated by small bubbles allows them to improve the bubble-particle collection efficiency [137]. Reduced bubble size results in better process efficiency due to
D
enhanced mass transfer across the gas-liquid interface [266]. The non-invasive technique like PIV
TE
can be used to predict the flow pattern of the phases, bubble and particle size and its distribution, rise velocity and instantaneous velocity vector of a bubble. So, current bubble size measurement technique needs to be more advanced in order to work in presence of a large number of bubbles as
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well as measure the bubble size in any part of the column. The probability of bubble-particle collision, attachment, and detachment depend on the appropriate bubble and particle size. There is
CC
lack of studies on bubble size, bubble coalescence, bubble-particle collision, attachment and detachment phenomena in the vertical and horizontal direction in presence of the solid particle.
A
During particle separation, the feed contains a range of particle size from ultrafine to coarse size. Therefore, a flotation system must be designed in such way to target ultrafine particles as well as coarse size particle.
4.4. Entrainment Characteristics
51
Entrainment significantly reduces the recovery efficiency of the flotation process. There is a lack of studies on entrainment characteristics based on the effect of operating variables, geometric variables and physical properties of the system. Different entrainment models developed by different investigators are valid for mechanical and column flotation system. Implementation of these models needs further validation. For instance, the model of Yiantos and Contreras [239]
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demonstrates only the effect of particle size on entrainment behavior, however numerous other factors such as solid concentration in the feed, range of particle size, slurry viscosity, feed flow rate, particle density, slurry density are also significant to entrainment. Hence it is essential to examine the effect of the other factors influencing the entrainment characteristics. A general comprehensive mechanistic entrainment model needs to be formulated which covers all other important variables. Developing a model based on the process variable and operating parameter to
U
estimate the flotation efficiency is a major challenge in industrial application.
N
4.5. Mixing characteristics
A
Mixing characteristics is important for the modeling, design, and optimization of the flotation
M
processes. The intensity of mixing can be helpful to understand the degree of homogeneity of phases and is used to increase the transport efficiency of any system. Many authors have reported
D
considerable work on analysis of mixing characteristics using axial dispersion model but there is
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the scarcity of research work based on radial dispersion of the phases. Physical properties of the system greatly influence the mixing intensity. However, detail studies are required to analyze the effect of the flow pattern and physical properties on the mixing mechanism. Computation fluid
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[258] D. Reay, G.A. Ratcliff, Removal of fine particles from water by dispersed air flotation: effects of bubble size and particle size on collection efficiency, Can J Chem Eng 53 (1973) 178-
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185.
[259] L.R. Flint, W.J. Howarth, Collision efficiency of small particles with spherical air bubbles,
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Chem Eng Sci 26 (1971) 1155-1168. [260] M.E. Weber, D. Paddock, Interceptional and gravitational collision efficiencies for single
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collectors at intermediate Reynolds numbers J Colloid Interface Sci 94 (1983) 328-335. [261] Z. Dai, D. Fornasiero, J. Ralston, Particle-bubble collision models-a review, Adv colloid interface sci 85 (2000) 231-56.
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[262] G. Wang, A.V. Nguyen, S. Mitra, J.B. Joshi, G. J. Jameson, G.M. Evans, A review of the mechanisms and models of bubble-particle detachment in froth flotation, Sep Purif Technol 170 (2016) 155-172. [263] M. Polat, S. Chander, First-order flotation kinetics models and methods for estimation of the
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true distribution of flotation rate constants, Int J Miner Process 58 (2000) 145-166. [264] R.K. Tuteja, D.J. Spottiswood, V.N. Misras, Mathematical models of the column flotation process a review, Miner Eng 7 (1994) 1459-1472.
[265] J. Wang, L. Wang, J. Hanotu, W. B. Zimmerman, Improving the performance of coal flotation using oscillatory air supply, Fuel Process Technol 165 (2017) 131-137.
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[266] M.K. Al-Mashhadani, H.C.H. Bandulasena, W.B. Zimmerman, CO2 mass transfer induced
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through an airlift loop by a microbubble cloud generated by fluidic oscillation, Ind Eng Chem Res
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51 (2011) 1864-1877.
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Figures:
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Fig. 1. Schematic diagram of FCSMC [27].
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Downcomer Feed
Air inlet Nozzle Free Jet
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Plunging Jet
Mixing Zone
Recirculating Eddy
Pipe Flow Zone
Concentrate
Disengagement Zone
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Tailings
N
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Pulp Mixture
Cell
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Fig. 2. Schematic diagram of Jameson cell [54].
77
N
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Fig. 3. Schematic of flow regime map [85].
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Fig. 4. Plot of drift flux vs gas holdup applying Wallis [97].
Fig. 5. Schematic of photographic technique and BSD fitting in the air-water system.
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Acquisition
Seeding
Flow
Illumination
Imaging
Storing
Enhancement
Quantization Interrogation
Correlation
Sampling
Estimation
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Selection
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Pixelization
Analysis
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Result
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Fig. 6. Steps of PIV technique.
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Validation
Tables:
Table 1: Some correlations for gas holdup measurement. Author
dp db
ug usl
0.08
0.02
Shukla et al. [108]
H dc
Cs sl
0.433
Rel 1 Cs 0.594
0.3
d pore db
0.008
Bhunia et al. [105]
2.25
Abdulrahman [109]
1.196
1.16
d pore ds
2.86 0.264
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d g 2.2 Fr 1.07 Ar 0.84Eo 0.19 s dc
s 0.108
11
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d g 0.085 c hr
p sl
Kumar and Khanna [107]
0.235
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0.2
Pr 2 l ul
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g 244.6 Re
p sl
0.02 g
2.46
0.820
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g 290.69 Re
db d p
1.07 g
ug ul
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1.09
ud g 3.60 10 l l c l 7
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Gas holdup correlation
80
Anastasiou et al. [110]
Table 2: Bubble generation techniques. Flotation technique/device
Bubble generation system
Bubble size range (m)
Sebba [77], Jauregi and Varley [142] Bennet [143]
Gas aphrons
Mechanical agitation or gas aspiration nozzle
10-100
Induced air flotation (IAF) Nozzle Flotation
Mechanical agitation
700-1500*
Gas aspiration nozzle to draw air into recycled water Sparger of porous stainless steel or ceramic Gas aspiration nozzle to draw air into recycled water in a down comer Electrolysis of diluted aqueous solutions (H2 and O2 bubbles) Injection of water/air mixture through static mixtures Reducing water pressure which is supersaturated at high pressure via needle valve. Reducing water pressure which is supersaturated at high pressure Electrolysis of diluted aqueous conducting solution at electrodes (Bubble generation takes place on electrode). Gas-water circulation method followed by coupling of palladium electrode with ultrasonication Stirring Surfactant solution at high speed Air injection system or Mechanical agitator Ultrasonication of mixed surfactant solution upon mixing of octafluoropropan gas at regular interval. Supersaturated water passes through the nozzle (pressure reduction)
400-800*
Yianatos et al. [144] Jameson and Manlapig [56], Clayton et al. [57] Zouboulis et al. [145,146] Yoon et al. [147]
Column Flotation
Lazaridis et al. [46]
Dissolved air flotation (DAF)
Edzwald [148], Couto et al. [149] Hosny [33]
Dissolved air flotation (DAF) Electroflotation (EF)
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Jauregi et al. [65]
Colloidal Gas Aphrons Induced air flotation (IAF) Ultrasonication
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Ultrasonication
A
Oeffinger and Wheatley [151]
Takahashi et al. [152]
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Microcel Flotation
Dissolved air flotation (DAF)
N
Electroflotation
Kim et al. [150]
Rubio et al. [39]
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Jet flotation
A
Bennet [143]
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Author
81
0.0067-0.0012 100-600
20-40* 400* 30-100
10-100 40* 20
0.3-0.5
37-115.6 700-1500 0.4-0.7
5-40
Sarkar et al. [31] Kim et al. [153]
Chegeni et al. [154]
Electroflotation (EF) Dissolved air flotation (DAF) Column flotation
Hydrogen bubbles generated on platinum wire electrode. Reducing water pressure which is supersaturated at high pressure via nozzle. Sparger
15-23 19.2-54.2
800-2000
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*represents mean bubble size
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Table 3: Different techniques to measure bubble size distribution. Bubble size range (m)
Image analysis
Bubble sampling Bubble features generation methods Viewing box Orifice plate
Image analysis
Flat cell
Porous plate
75-655
Drift flux analysis
Calculated by measuring gas velocity and gas holdup Photographs captured after placing rectangular view box around the column filled with water
Ventury static mixer
420-900*
Yianatos et al. [144]
Image analysis (Zeiss digitizer)
Porous stainless steel or ceramic sparger
0.0067-0.0012*
O’Connor et al. [158]
Porous plate
O’Connor and Mills [158]
Refractive index of bubble and slurry (due to change in light intensity)
300-2000
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Unno and Inoue [155] Ahmed and Jameson [156] Dobby et al. [157]
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Methods
Drift flux analysis
Rijk et al. [160]
Image analysis
Tucker et al. [161]
Porous plate
Biswal et al. [162]
Optical
Rykaart and Haarhof [163]
Image analysis
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Drawing bubbles into a capillary tube Bubbles drawn into capillary under vacuum and transform its shape close spherical to cylindrical Calculated by measuring gas velocity and gas holdup Cuvette cell
Porous plate
1620-3340*
Sintered disc
0.261-0.290* (2-phase system) 0.261-0.291* (3-phase system)
Porous tube
320-770*
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Yoon [159]
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Author
Dissolved air flotation Drawing bubbles Induced air into a capillary flotation tube Drawing bubbles Synthetic filter into a capillary cloth tube Measuring Dissolved air module (with air flotation filter) 83
10-300 390-2230*
300-2000 29-77*
Filippov et al. [166]
Drift flux analysis
Chen et al. [167]
Image analysis
Chen et al. [167] Zhou et al. [168], Grau and Heiskanen [169] Han et al. [170]
Image analysis Image analysis
Han et al. [170]
Optical (opticalsensor Image processing
Perforated plate
3700-4100*
Drawing bubbles into a capillary tube Calculated by measuring gas velocity and gas holdup Bubble viewer
Induced air flotation
530-1450*
Ventury static mixer
350-1100*
Bubble viewer Viewing chamber
Electroresistivity Particle counters
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*Mean bubble diameter (µm)
Induced air flotation Porous plate Induced air flotation
350-1750
Dissolved air flotation DAF Electroflotation Induced air flotation Dissolved air flotation
13-96
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Particle counters (laser) Bubbles drawn into column (Special viewing chamber)
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Rodrigues and Rubio [171]
Optical fibre
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Optical (optical sensor) Porous plate
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Saberi et al. [164] Gorain et al. [165]
400-1200 1500-3600*
15-85 15-65 250-1500* 33-37.5*
Table 4: List of correlation for estimation of carrying capacity. Correlations
Espinosa-Gomez et al. [215]
Cm 0.068d80 p
Finch and dobby [177]
C A 0.05d80 p
Patwardhan and Honker [216]
C A n p d 3p p u g d b3
Patwardhan and Honker [216]
0.542 0.2 3 C A 522.54d 50 (n p d 50 p d b3 )usg
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Author
85
Table 5: Models of probability of collision [261]. Model name
model
Langmuir-Blodgett model Sutherland model
PcLB (ks /(0.2 k )) 2 , where ks is the stoke’s number
Gaudin model
Pc 1.5(d p / db ) 2
Flint-Howarth
Pc (v p /(v p vb ))
Anfruns-Kitchener
Pc ((1 d p db ) 2 /(1 (v p / vb ))) (v p / vb ) 2 c0 /(1 (d p db )) 2
Weber-Paddock model
Pcg sin 2 m (1 d p / db ) 2 (v p / vb ) ; collision efficiency due to
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Pc 3(d p / db )
interceptional effect
Pc 1.5(d p / db ) 2 ; Reb < 1
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Yoon-Luttrell model
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gravitational effect Pc (1 (2 /(1 37 / Reb0.85 )))(d p / db ) ; collision efficiency due to
Pc 3(d p / db ) ; at potential flow condition
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Pc (d p / db ) 2 (1.5 (4 Reb0.72/ 15)) ; at intermediate flow condition Pc 2 c /((1 v p / vb )vb Reb2 ) ; collision efficiency due to
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Schulze model
interceptional effect
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Pc (1 /(1 v p / vb ))(1 d p / db ) 2 )(k s /( ks a))b ; collision efficiency
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due to inertial effect
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Table 6: Flotation kinetic models.
4a exp( Pe / 2) R 1 2 2 (1 a ) exp( aPe / 2 (1 a )) exp( aPe / 2) Pe 4 K a Pe * R R (1 exp( Kt ))
Model Finch and dobby model, based on axial dispersion, R is overall recovery, Rc is collection zone recovery, Rf is froth zone recovery VPI model
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Model equation 100 Rc R f R 1 Rc R f Rc
0.5
First order model, R denotes recovery at time t, R* represents maximum flotation recovery at infinite time, K is rate constsnt First order model, Rectangular distribution of flotatiblities
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(1 exp( Kt )) R R * 1 kt
1 R R* 1 1 t / K
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kt R R * m (1 Kt ) ln(1 Kt ) R R* 1 Kt
Fully mixed model
R (1 z )(1 e Kt ) z (1 e K t )
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1 e Kt 2e Kt / 2 R R * 1 ( Kt / 2) 2 2
Second order model, Rectangular distribution of flotatiblities Three parameter model, fast (K) and slow K* flotatiblities Three parameter model, gamma distribution
*
a R R* 1 P at
Gas or solid adsorption model
Two parameter form, Triangular distribution 2nd order kinetic model
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R* K t R 1 R * Kt
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S0255-2701(18)30250-2 https://doi.org/10.1016/j.cep.2018.03.029 CEP 7239
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
28-2-2018 26-3-2018 28-3-2018
Please cite this article as: Prakash R, Majumder SK, Singh A, Flotation Technique: Its Mechanisms and Design Parameters, Chemical Engineering and Processing (2010), https://doi.org/10.1016/j.cep.2018.03.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Flotation Technique: Its Mechanisms and Design Parameters Ritesh Prakash* [email protected] , Subrata Kumar Majumder* [email protected] ,
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Anugrah Singh
Department of Chemical Engineering, Indian Institute of Technology Guwahati, India-781039
*
Corresponding author
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Prof. S. K. Majumder/ Mr. Ritesh Prakash
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Department of Chemical Engineering, Indian Institute of Technology Guwahati, India-781039
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Research Highlights
The overview of the flotation techniques and design parameters.
Details in design, analysis, optimization, operation, modelling is reported.
Breakthrough analysis of flotation mechanism is done.
Critical discussion on hydrodynamic parameters is reported.
The measuring techniques of design parameters are also described.
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Abstract
A knowledge of hydrodynamic characteristics is important because it helps in design, control, analysis, optimization, operation, and modelling of the system, which enhances the performance of process unit. This paper aims to provide the evaluation of the techniques of flotation and design parameters, which is required improving the separation efficiency of the flotation processes. Different components of flotation columns, flotation mechanism and design parameters like flow
regime, gas holdup, bubble size and its distribution, mixing characteristics and carrying capacity are critically discussed. The measuring techniques of design parameters for flotation process are also described. The present article on flotation technique and its research components may provide
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in hand information on the flotation process to the researcher and designer of flotation unit.
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Keywords: Flotation; hydrodynamics; design parameter; flotation kinetics
2
Nomenclature Area of electrode (m2)
Ab
Surface area of a single bubble (m2)
a
Gas-liquid specific interfacial area (m-1)
B
Constant (-)
BIV
Bubble image velocimetry
Bl
Bubble load (ton/m3)
bm
Eddy turbulent acceleration (m/s2)
C
Tracer concentration (mol/l)
C
Dimensionless concentration (-)
C(ti)
Concentration of tracer that is function of time (mol/l)
Ca
Carrying capacity (kg/hr m-2)
CA
Carrying capacity per unit area (ton/h m-2)
CA
Carrying capacity per unit area (ton/h m-2)
Cb
Concentration of gas bubble (-)
CG
Carrying capacity per unit volume of gas (ton/h m-3)
CL
Carrying capacity per unit length (ton/h m-1)
Cm
Maximum carrying capacity (kg/h m-2)
Cp
Concentration of solid particle (kg/m3) Axial dispersion coefficient (m2/s) Sauter-mean bubble diameter (m) Mean particle size (50% “finer than” size) (m) Product of 80% passing size diameter (m)
db
Bubble diameter (m)
ds
Sparger diameter (-)
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d80
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d50
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N
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Solid concentration (kg/m3)
Cs
d32
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dp
Particle diameter (m)
db,max, db,min
Maximum and minimum bubble diameter (m)
dbe
Equivalent spherical bubble diameter (m)
dc
Column Diameter (m)
De
Equivalent column diameter (m) 3
Particle size (m)
DL
Liquid axial dispersion (m2/s)
DL
Diffusion coefficient in liquid phase (m2/s)
dp
Particle diameter (m)
dpi
Mean particle diameter of size i (m)
dpore
Sparger pore diameter (m)
ds
Sauter diameter (m)
ds
Sparger diameter (m)
dT
Tube diameter (m)
E
Activation energy (J /mol)
E(t)
Residence time distribution (time-1)
Efi
Entrainment factor represents gangue-water recovery ratio (-)
Ei
Degree of entrainment (-)
Ei
Degree of entrainment (-)
El
Volumetric flow of entrained material (m3/s)
ENTi
Degree of entrainment (-)
ES
Solid recovery by entrainment (kg)
fsp
Single phase friction factor (-)
fthree-phase
Three-phase friction factor (-)
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Di
Acceleration due to gravity (m/s2)
g
Gk H
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Hf
Electrical conductance (siemens) Production of kinetic energy term (-)
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G
Collection zone height (m) Froth height (m) Clear liquid-solid height after disengagement process (m)
hm
Total height of gas-liquid-solid mixture (m)
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hl
hr
Height of the reactor (m)
I
Intensity of scattered light (candela)
Jb
Bias water flow rate in the froth (m/s)
Jf
Superficial feed rate (m/s)
jgl
Volumetric flux (m/s) 4
K
Rate constant (s-1)
ks
Stoke’s number (-)
K
Boltzmann constant (J/K)
k
Constant correcting the number of particles that can attach to the available
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bubble surface area due to the hydrophobicity effect of the particles (-) Empirical parameters (-)
k1, k2
Conductivities of continuous and dispersed phase (s/m)
k∞
Rate constant at prolonged flotation time (s-1)
ke
Electrictrical conductivity (s/m)
kl
Electrical conductivity of the liquid (s/m)
Kl-d
Effective conductivity of the dispersion (s/m)
kl-g
Electrical conductivity of liquid-gas mixture (s/m)
kl-s
Electrical conductivity of liquid-solid mixture (s/m)
Kl-s-g
Electrical conductivity of dispersion for three phase (s/m)
krc
Local value of mixture conductivity distribution (-)
l
Distance between two electrodes (m)
L
Height of gas-liquid dispersion (m)
L
Vessel length (m)
lp
Optical path length (m)
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K1, K2
m
Parameter (-)
mp
n
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N
Weight of penetrating liquid (kg)
EP
ml
Mass of the particle (kg) Number of mechanical cells (-) Parameter depends on flow regime (-) Vessel dispersion number (-)
ni
Number of bubbles (-)
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ND
np
Number of particles that can attach to a bubble (-)
P
Probability of collection of the solid particle on gas bubbles (-)
P
Absolute liquid pressure (pa)
Pa
Probability of attachment (-)
Pc
Probability of bubble particle collision (-) 5
Pr
Operating pressure (Pa)
R
Overall recovery (-)
Rc
Collection zone recovery (-)
Rf
Froth zone recovery (-)
R*
Maximum recovery (-)
r, s
Orders of concentration term (-)
rb
Radius of a bubble (m)
rp
Particle radius (m)
Rfw
Water recovery from the feed (kg)
S
Source term in continuity equation (-)
S2
Scattering function (-)
Sb
Surface area of the rising bubble (m2)
T
Temperature (k)
t
Time (s)
t0
Coefficient (-)
tat
Attachment time (s)
tc
Contact time (s)
tfl
Time of flow (s)
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Probability of detachment (-)
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Pd
ti
Induction time (s)
ts U
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ub
Mean residence time (s) Sliding time (s)
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tm
Interstial liquid velocity (m/s) Bubble rise velocity (m/s) Superficial gas velocity (m/s)
ul
Liquid velocity (m/s)
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ug
usl
Slurry superficial velocity (m/s)
uT
Superficial total velocity (sum of gas and liquid superficial velocity) (m/s)
ut
Terminal velocity (m/s)
usp
Single phase velocity (m/s)
V
Froth volume (m3) 6
Bubble velocity (m/s)
vbs
Volume of a single bubble (m3)
vcl
Total volume of collected bubble (m3)
vg
Superficial gas velocity (m/s)
Vg
Volume of the gas (m3)
Vl
Volume of the liquid (m3)
vp
Particle velocity (m/s)
w
Location of a particle at the liquid-vapour interface (-)
wr
Water recovery (Kg/m2 s-1)
Wsolid-air
Force required to break the bubble particle interface (N/m)
X
Axial position in the column (m)
Z
Dimensionless position (-)
Ar
Archimedes number (-)
Eo
Eotvos number (-)
Fr
Froude number (-)
Gr
Grashof number (-)
Pe
Peclet number (-)
Pr
Prandtl number (-)
Reb
Reynolds number of bubble (-)
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Reynolds number of liquid (-) Schemedit number (-)
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Reynolds number of gas (-)
Rel
Sh
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Reg
Sc
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vb
Sherwood number (-) Surface tension (N/m) Phases (-) Gas holdup (-)
l
Volume fraction or phase holdup of liquid phase (-)
d
Volume fraction or phase holdup of dispersed non-conducting phase (-)
l
Liquid density (kg/m3)
m
Mixture density (kg/m3)
g
Gas density (kg/m3)
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g
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Particle density (kg/m3)
sl
Slurry density (Kg/m3)
sp
Single phase density (kg/m3)
pulp
Pulp density (kg/m3)
f
Density of fluid (kg/m3)
Δ
Specific density difference between solid and water (kg/m3)
ΔH
Height difference between pressure transducer (m)
ΔPTP
Total pressure drop (pa)
ΔPfTP
Frictional pressure drop (pa)
ΔPh
Hydrostatic head (pa)
ΔPa
Pressure drop due to acceleration (pa)
ΔPf,sp
Single phase frictional pressure drop (pa)
ΔPf,three-phase
Three-phase frictional pressure drop (pa)
ΔL
Difference between two-pressure tap (m)
Δ
Density difference between particle and fluid (kg/m3)
ƛ
Fraction of light transmitted (-)
Wavelength (m)
ent
Residence time of the entrained material (s)
Drainage parameter (-)
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N
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mi l ν
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eff
Parameter related to mean particle size (-)
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η
Solid loading (-)
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s
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p
Viscosity of liquid (Kg/m.s) Effective viscosity (Kg/m.s) Frequency (Hz) Slurry kinetic viscosity (m2/s)
Dynamic shape factor (-)
Dimensionless concentration (-)
𝜎𝜃2
Normalized variance (-)
2
Variance (-)
c
Contact angle (-) 8
Maximum collision angle (-)
θ
Dimensionless time , = t / (-)
Ø
Azimuthal angle (-)
Dimensionless number (-)
Mean residence time (s)
rg
Ratio of specific heats of the gas (-)
Entrainment parameter (-)
c
Stream function which characterizes the grazing trajectory (-)
0c
Stream function at the bubble equator ( =900) (-)
Dimensionless concentration (-)
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m
9
Contents
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1. Introduction 2. Type of flotation and its application 2.1. Cyclonic-Static Micro-Bubble Flotation Column (FCSMC) 2.2 Electroflotation (EF) 2.3. Induced or dispersed air flotation (IAF) 2.4. Dissolved air flotation (DAF) 2.5. Column flotation 2.6. Jet flotation 2.7. Centrifugal flotation or air-sparged hydrocyclone (ASH) 2.8. Gas aphrons based flotation 2.9. Ion flotation 3. Design parameters of flotation process 3.1. Flow regime 3.1.1. Methodology 3.1.1.1. Visual observation technique 3.1.1.2. Drift flux analysis 3.2. Gas holdup 3.2.1. Measurement techniques 3.2.1.1. Phase isolation technique 3.2.1.2. Conductivity method 3.2.1.3. Pressure drop method 3.2.1.4. Dynamic gas disengagement technique (DGD) 3.2.1.5. Electrical resistance tomography (ERT) 3.3. Pressure drop 3.4. Bubble size and its distribution 3.4.1. Measurement method of bubble size 3.4.1.1. Photographic technique 3.4.1.2. Acoustic method 3.4.1.3. Light scattering method 3.4.1.4. Inverted funnel method 3.4.1.5. Phase Doppler anemometry (PDA) 3.4.2. Bubble rise velocity 3.4.2.1. Particle image velocimetry (PIV) 3.4.3. Interfacial area 3.4.3.1. Methodology 3.4.3.2. Physical method 3.4.3.3. Light transmission technique 3.5. Carrying capacity 3.6. Mixing characteristics 3.6.1. Methodology and analysis of mixing characteristics 3.6.1.1. Residence time distribution 3.7. Entrainment Characteristics 3.7.1. Entrainment theory and empirical correlations 3.8. Flotation kinetics 3.8.1. Induction time 10
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3.8.2. Separation analysis of flotation column by kinetic model 4. Importance and perspective of future research 4.1. Flow regime characteristics 4.2. Holdup characteristics 4.3. Bubble size and its distribution 4.4. Entrainment Characteristics 4.5. Mixing characteristics Nomenclature References 1. Introduction
Flotation is a widely used, cost-effective separation technique for wastewater treatment [1], mineral beneficiation [2], micro-oxygenation of wine [3], fermentation [4], ink removal [5], plastic recycling [6] etc. Flotation techniques are used for the various chemical, mineral and biological
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industries. In this technique, components like fine particles, oil droplets, contaminants etc. are separated from the mixture based on their hydrophobic or hydrophilic surface properties. The
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essence of the flotation process depends on using the gas bubbles to capture the particles based on
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their surface hydrophobicity and hydrophilicity [7]. The gas bubbles produced in conventional
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flotation columns are in the size range of 1.0 - 1.5 mm in diameter [8]. The gas bubbles are used to adhere the hydrophobic particles selectively and carry them to the surface of the liquid, hence
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they form a froth zone where it can be separated while the hydrophilic particles are discharged from the bottom outlet as the tailing. The efficiency of the flotation process is a function of the
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probability of particle-bubble collision, particle-bubble attachment, and particle-bubble detachment. Froth flotation is an extensively accepted separation technique where the separation
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characteristics depend on narrow particle size range between approximately 10 to 100 μm. Beyond this particle size range, the separation efficiency of flotation process reduces notably because of
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difficulty to attachment of weak hydrophobic particles to gas bubbles [9]. Fine particles have large specific surface areas and low mass due to which the probability of bubble-particle collision is limited therefore results in slow separation rate [10]. Conventional flotation machines does not
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generate bubble size less than 600 m for which its application is limited to separate the coarser particles only [11]. Very fine particles may float with smaller size bubbles and fine or mid-sized particles with the bigger size bubbles [12]. Flotation of fine particle (< 37 m) and ultrafine particle (< 8-13 m) is a key challenge. Feed in flotation consists of wide range of particle size, therefore, flotation column needs to have wider bubble size to target fine as well as coarse size particles [13,
11
14]. So, flotation of fine particles is one of the major challenging tasks. Research is conducted to explore the mineral-bacteria interaction in order to understand the mechanisms of selectivity of microorganism towards specific particle [15]. Perez-Garibay et al. [16] investigated the effect of bubble size distribution, superficial gas velocity, surfactant concentrating and three different particle sizes such as coarse (100 m), medium (39 m) and fine (15 m) on the flotation
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characteristics. Investigation reports that particular particle-size distribution needed an optimum bubble-size distribution profile, bubble size ranges between 150 to 1050 m diameter and gas holdup ranging from 0.2% and 1.3%. The wide range of bubbles can be produced using dissolved air flotation technique in combination with a surfactant. This technique is able to produce coarse bubbles (400-800 m) and nanobubble (200-720 nm) where nanobubbles are obtained by selective separation from the microbubble. The separation efficiency of the particles in presence of a
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combination of coarse and nanobubbles are compared with only coarse bubbles which reported
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that separation can be improved by 20-30 % for the very fine particles (8-74 μm) while a slightly
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low separation is reported for coarse particles (67-118 μm) [17]. Lim et al. [18] proposed that integration of microbubble with macrobubble reduces the macrobubbles-oil attachment time by
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82%, enhance the bubble-oil contact angle by 40.35 and interfacial surface area of attachment by 54.5%. Many studies are focused on the mineral-bacteria interaction in order to understand the
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mechanisms behind the floatability and mineral selectivity achieved in the beneficiation process.
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Recent studies demonstrate the microorganisms aided mineral beneficiation with the modern advancement in biotechnology. Microorganisms specifically involve to remove the gangue
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particles which are detrimental as responsive flotation reagents [19]. Flotation columns are simple in construction and mostly suited for carrying out the separation of the desired element from the
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liquid or solid mixture in a multiphase environment. Flotation columns are multiphase contacting device where the liquid is in continuous phase while the gas and particles are in dispersed phase. In counter current operation, the feed is introduced after conditioning with reagents, which enters
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into the flotation column approximately at 2/3 of the column height where it mixes with liquid and interacts with the swarm of gas bubbles that is introduced from the bottom of the column through a gas distributor [20]. The relative motion of particles and gas bubbles governs the probability of the bubble-particle attachment, bubble loading, and flotation rate. Counter current movement of feed and gas bubble
12
results in reduction of rise velocity of the bubbles, which increases their retention time in the slurry, hence decreases the compressed air requirement and increases the specific throughput of the column. In the counter current operation, the probability of bubble-particle collision is high because of the large aerated mixture in the column, the long distance of the transport of the bubble and particle along the column length and low longitudinal slurry mixing [21]. In some cases, the
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co-current operation is useful during the treatment of coarse particle in which particle-laden bubble rise time is reduced and residence time of the particle increases [22]. The flotation column can be divided into three specific zones: recovery zone, cleaning zone and froth zone. Recovery zone or collection zone: the zone between feed slurry inlet and sparger. In the recovery zone, the downflow feed slurry interacts with upflow gas bubbles where the attachment of the particles to the bubble takes place. The zone controls the degree of the capacity of flotation columns because the capacity
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of the flotation column depends on the intensity of bubble-particle collision, the probability of
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attachment and surface area of the gas bubble. Cleaning zone: the zone above feed slurry to froth interface level. Froth zone: the zone above the interface. Dead zone: the zone below the sparger
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zone. The volume below the sparger (dead volume) does not help in flotation but is used to expel
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tailings. Hydrophobic solid particles attached to the air bubbles are collected by froth while the hydrophilic particles are left in the slurry. It is not always the case of making a solid particle
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hydrophobic, but in some cases, a solid particle is made to be hydrophilic using reagent
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(depressant) so that their attachment to the bubble does not take place and settle down in flotation column. Generally, four steps are required during froth flotation such as: conditioning of desired solid particles during which hydrophobicity imparted to the surface
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of the solid
the introduction of feed slurry to the flotation column where collision and attachment of
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solid particles to gas bubbles take place stable froth formation on the surface of flotation column and
the removal of mineral-laden froth or tailing from the flotation cell.
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In industrial flotation column, the entrainment of gangue particle is common, so several stages of flotation columns are involved to meet the economically acceptable quality of the desired mineral in the product. In this review article, the details of various design parameters of flotation process and the effect of operating and geometric variables influencing the separation efficiency are 13
described. The optimization of different hydrodynamic characteristics is also discussed, and some strategies are suggested for improving the working principle of flotation devices. 2. Type of flotation and its application Numerous techniques of flotation processes based on different working principles are briefed as
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follows:
2.1. Cyclonic-Static Micro-Bubble Flotation Column (FCSMC)
Cyclonic-static micro-bubble flotation column has been successfully incorporated and industrialized for whole flotation circuit for mineral separation in China. Cyclonic-static microbubble flotation column started commercial production in 1994 and patented in 1999 [23].
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Separation process like column flotation use a single step of froth flotation process but the FCSMC
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is the combination of series of a process like a column flotation, cyclone separation and microbubble generator [23]. The microbubble generator directly influences the bubble size and its
A
distribution hence the gas holdup in the column flotation zone in the FCSMC. Consequently, this
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equipment significantly affects the separation efficiency of the flotation column [24]. The cyclone separation zone comprises of concentric conical structure which separated particle into three
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different densities. The pulp comprises of highest bubble concentration rises to the column
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separator while the pulp with the high-density particle is expelled directly as tailings. The rest pulp with the intermediate bubble concentration is pumped as the circulating pulp through the external bubble generation device for further beneficiation [25]. Wang et al. [26] reported the effect of
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cone angle (380, 480, 580 and 680) in cyclonic separation zone and recommended that too small (380) and too large (680) cone angle is not suitable for effective separation. Larger cone angle
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decreases the separation which is due to the high centrifugal intensity whereas the overflows from cyclonic flotation zone reduce gradually. The cone angle of 480 is recommended for effective
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separation environment which is the optimized cone angle for proper overflow from the cyclone zone. Li et al. [27] reported the separation efficiency of fine oil droplet (< 10 m) from treated wastewater effluent and compared the separation efficiency of FCSMC with dissolved air flotation technique. They observed higher oil removal efficiency in FCSMC than dissolved air flotation column. The obtained oil removal efficiencies are 92.19% and 76.65% respectively in FCSMC
14
and dissolved air flotation with lower oil concentration in FCSMC. A schematic of FCSMC is shown in Fig. 1. 2.2. Electroflotation (EF) The EF technique is potentially applied for separation of ions or solid particles, suspended or
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dissolved in the liquid phase, by attaching on bubbles produced on the electrodes and moves upward in the flotation column [28]. In EF technique, when liquid waste is exposed between the electrodes (cathode and anode) and energy supplied to the electrode, an electric field established between electrodes due to the conductance of the liquid which causes the generation of tiny bubbles of hydrogen and oxygen on cathode and anode electrode. Conventional flotation techniques are able to produce bubble sizes in the range of 600-1000 m in diameter [29], which
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are not very much efficient to float particle sizes less than 20 m [30]. Electroflotation technique
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can produce bubble size in the range of 15 -80 m [31,32]. Variables, which affect the bubble
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diameter, bubble number, and current density in EF technique are pH, type of electrolyte (NaOH, HCl, NaCl) and retention time. EF technique has some advantages such as generation of very fine
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and uniform bubbles of average size of 20 µm, changing of concentration by varying the current density to increase the probability of collision [33]. The conventional technique fails to clean
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wastewater for very dilute solutions having contamination level below 50 mg/dm3 due to high
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operational cost and low removal capacity [34]. Mota et al. [28] used the EF technique on synthetic wastewater containing lead, barium, and zinc and successfully removed the 97% of these heavy
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metal. Membrane separation processes are also in use to clean wastewater but membranes are prone to fouling during their use where gas sparging required to overcome it. A hybrid flotation cell can overcome their limitation by integrating both dispersed air flotation and membrane
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separation [35]. Aoudj et al. [36] investigated the separation of chromium (VI) and fluoride by electrocoagulation-electroflotation by developing hybrid Fe-Al electrode. Fine cassiterite particles
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are separated by EF technique using bioreagent and reported 64.5% recovery [32]. 2.3. Induced or dispersed air flotation (IAF) Dispersed air flotation operates by dispersing or inducing gas bubble into the liquid [37]. In large agitated columns, the gas is injected from the base of the mechanical agitator shaft and small bubbles are generated by the shearing action of the impellers [38]. In a small column, sparger or 15
gas distributor is often used for the production of bubbles. The range of bubble size is about 7001500 µm [39]. High-speed rotating impeller or diffuser cause mechanical mixing of gas and liquid causes production of bubbles, which transported directly into the flotation column. Suspended particles adhere to the bubble surface and float to the surface of the liquid where it is removed by the skimming device. IAF technique is widely used to treat industrial wastewater from oil in the
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refinery, natural gas processing plant, petrochemical, and chemical plant [40]. 2.4. Dissolved air flotation (DAF)
In DAF technique, the air is pressurised to dissolve it into the water then saturated water is passed through a pressure-reducing valve to generate the microbubbles. The produced micro-bubbles size is between 20 to 100 µm diameter [41]. DAF is the one of the potential separation technique used
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to separate the water contaminant like particles, droplets or microorganisms in a size range of 10 to 100 µm. Radzuan et al. [42] investigated the oil droplet separation efficiency from oil-in-water
N
mixtures where the oil droplets were in size range of 15 to 80 µm. They developed a correlation
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for separation efficiency based on various experimental data and observed that predicted results
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were below the 6% error. Rao et al. [43] reported the removal of algae and cyanobacteria in water treatment using positively charged microbubble. The bubbles made positively charged by cationic
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flotation reagent. Some other gasses like nitrogen, methane and carbon dioxide can also be used to form microbubbles in some specific cases [44]. DAF is widely used for the water treatment to
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restrict the dissolved and colloidal impurities formation in process water and to improve process ability. In DAF operation the suspended particles removal efficiency is about 90% but the
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dissolved organics removal is only 10% which reveals that still, it is a great challenge to obtain the absolute effluent free water [45]. Some important applications of DAF technique are: Separation of metal ions such as copper, nickel, zinc, ferric from the aqueous solution [46].
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Separation of zinc from hydroxide precipitate [47].
Separation of feldspar mineral from feldspathic slime and iron containing minerals [48].
Separations of mercury, arsenic and selenium ions from gold cyanide leach solutions [49].
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2.5. Column flotation Flotation column is intensively used in the mineral processing industry. The success of column flotation depends on the hydrophobic and hydrophilic nature of particles or it may be imparted 16
using reagent. Bubbles generated at the bottom of the column on which hydrophobic mineral particles are attached and rise up with bubble. Separation efficiency of conventional flotation cell reduces as the size of the particle becomes smaller [10]. To overcome this problem, flotation technique like column flotation, pneumatic free jet flotation [50] and Jameson cell can be used [51]. Conventional mechanically agitated flotation column are substituted by column flotation to
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improve the flotation efficiency. Liu and Schwarz [52] reported the particle size effect on probability of particle-bubble collision in conventional flotation column and concluded that it decreases with the particle size. The separation efficiency can be enhanced using smaller bubble size. Agitated columns are more prone to backmixing and entrainment, so column flotation operations are maintained at streamline conditions in the flotation zone to avoid back mixing and entrainment. The details of differences between conventional and column flotation are provided
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by Reddy et al. [53]. Other applications of flotation are treatment of oil riches wastes, food wastes,
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dairy wastes, textile fibre waste, rubber waste, asbestos waste, polymer waste, paper industry
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waste, dye, electroplating waste, vegetable waste, poultry processing waste etc.
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2.6. Jet flotation
In this technique, a jet is used to induce air to generate the bubble to make froth. Microcell, Davcra
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cell, and Bahr cell are examples of this type of flotation. These flotation machines are high-
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intensity flotation machines. The schematic of Jameson flotation cell is shown in Fig. 2. In the Jameson cell slurry and air are introduced at the top which proceeds downward in the downcomer and forms a liquid jet. Consequently, air is entrained into the plunging jet because of
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the vacuum effect and generates a large number of tiny bubbles as a result of high shear rate [55]. In the downcomer region, the collection of particles on bubble takes place due to rapid mixing.
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Compared to conventional flotation cell the Jameson cell is designed for rapid flotation based on a high bubble surface area flux due to large number of fine bubbles produced by high shearing
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action in the downcomer. The size of produced bubbles in the cell is in the range of 0.1- 0.6 mm diameter [56,57]. Another feature of Jameson cell is that its downcomer can work under vacuum which causes high-intensity contact time (1-10 seconds) [54,57]. Some of the research claim that Jameson flotation cell can produce a large number of bubbles of size < 600 μm in diameter, so this device can be potentially used for the fine particle separation [58]. A comparison study between Jameson cell and other flotation cells like (Canadian column, Flotaire column, Microcel) done by 17
different authors. The comparative study reports minimum residence time and high particle carrying capacity of Jameson cell over another flotation cell. Separation of emulsified oil studied in a modified Jameson cell that results in increased separation efficiency (85%) in MJC (modified Jameson cell) than CJC (conventional Jameson cell) (80%) [59]. Guney et al. [50] studied the beneficiation of fine coal particles, which results in 72.4% recovery. Guney et al. [60] investigated
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the removal efficiency of asphaltite through jet flotation technique. A quite good 55% removal efficiency observed as initial sample contains 43.69% ash while the processed asphaltite has 19.66% ash content. You et al. [61] studied the effect of bubble-particle interaction in downcomer section of the Jameson cell by determining flotation rate constants based on the velocity, bubble and particle size distribution, bubble-particle contact angle and turbulence intensity. The observed average gas holdup and mean bubble diameter in the downcomer section are 55.84% and 0.72 mm
N
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respectively.
2.7. Centrifugal flotation or air-sparged hydrocyclone (ASH)
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ASH is mainly famous for extremely high throughput per unit volume and suitable for fine
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particles. It consists of two concentric right vertical tubes. In ASH, a centrifugal force is generated by converting pressure head into the rotational motion of swirl flow. Centrifugal force breaks the
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film that leads to the attachment of particle to gas bubble. Gas is distributed through the inner
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porous tube where the outer tube (non-porous) acting as air blanket, which guides the even distribution of gas through the inner tube. The generation of gas bubble takes place through the perforation of air from the innermost cylindrical tube. Slurry is introduced tangentially to the ASH
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where slurry moves axially down to the central cylinder where mixing of slurry takes place with gas bubbles. Hydrophobic particles are attached to the air bubbles and reach to the overflow section
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and discharge with the help of the vortex finder [62]. Chu et al. [63] studied the copper recovery in modified ASH and reported increment in recovery.
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2.8. Gas aphrons based flotation Colloidal gas aphrons (CGA) are multi-layered stable bubbles surrounded by a thin surfactant layer. Small size aphron bubbles have high interfacial area as well as stability so that it can be transported by pump like water without collapsing. These bubbles follow the same charge as of the surfactants used to produce them [64]. CGA technique uses the diffusion of microbubbles into 18
an aqueous solution. CGA bubbles can be generated by both cationic and anionic surfactants. CGA technique is able to generate extremely stable microbubble (10-100 µm) using stirrer which rotates at around 8000 rpm [65]. CGA technique can be applied to fine particles (4-20 m in diameter) separation [66]. Treatment of nanoparticle effluent is a major challenge due to the low probability of bubble-particle collision causing from Brownian motion. The separation efficiency becomes
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lowest when the particle size is < 100 nm. The separation efficiency can be enhanced by controlling the Brownian motion of nanoparticles and interfacial forces between particles and bubbles [67]. Zhang and Guiraud [68] applied modified CGA technique to generate charged microbubbles (42.1 m diameter) in presence of a surfactant to float the silica nanoparticles. The removal efficiency of the nanoparticle is observed to be 90-99%. Some applications of CGA technique are as follows: Separation of ZnO, CuO, and Al2O3 [66]
Separation of protein [69]
Separation of cellulose fibers from paper mill wastewater [70]
Separation of pyrene using the biodegradable surfactant [71]
Extraction of glucoamylase [72]
Extraction of gallic acid [73]
Separation of natural phenolic extract [74]
Separation of pulp using the natural surfactant [75]
Separation of organic dye from water [76]
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2.9. Ion flotation
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A
N
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Ion flotation involves the metal ions separation using suitable surfactant where the charged gas
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microbubble introduced through the aqueous solution to float the oppositely charged ions [77]. The bubble can be made charged using surfactants. Hoseinian et al. [78] studied the Ni(II) ion
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removal efficiency using ion flotation and check the effect of different parameters; chemical interactions, separation mechanism, ion removal rate, pH, surfactant concentration, and gas type. They concluded that pH of the solution significantly affects the separation efficiency. With increasing pH upto optimal value, the ion removal rate increases, increasing surfactant concentration removal rate reduces due to the formation of ion-surfactant intermediate complexes, the presence of other ions in the solution reduces the removal rate. The use of nitrogen and oxygen 19
gas reports higher ion removal efficiency compared to the air as gas type. Taseidifar et al. [79] investigated the heavy metal removal efficiency of arsenic, mercury, lead, cadmium and chromium ions from an aqueous solution. Ion flotation technique used in groundwater reports that contamination level of 5 mg/l of heavy metal can be reduced to acceptable levels of about 0.01
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mg/l. 3. Design parameters of flotation process
In the subsequent section, the hydrodynamic characteristics like flow regimes, gas holdup, bubble size and its distribution, pressure drop, wetting phenomena, RTD, mixing characteristics, channelling, induction time, entrainment, settling velocity and interfacial area are described.
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3.1. Flow regime
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Knowledge of flow regime plays an important role in design, operation, control, analysis, and scale-up of flotation column. Multiphase flow can be termed as the interacting flow of two or more
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phases where the interface among the phases influenced by their motion. The factors which affect
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the flow regime are geometric variables (diameter, length, sparger pore diameter, particle size, and cross-sectional area) of the column, dynamic variables (flow rate of flowing fluids) and physical
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properties (density, viscosity, and surface tension) of the flowing fluid. The transition of flow
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regime depends on column dimension, sparger design and physical property of the system [80]. The adjacent boundary of two regimes is called flow regime transition. Knowledge of flow regime is required because it helps in to upgrade the performance of the column by directing the heat &
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mass transfer, mixing, pressure fluctuation, momentum loss and volume productivity [81]. At low superficial gas velocity, the flow regime is homogeneous while at high superficial gas flow rate
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the flow regime turns to heterogeneous. There are mainly two types of flow regimes occur in flotation columns: bubbly (homogeneous) and churn-turbulent (heterogeneous). Bubbly flow takes
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place at low to moderate superficial gas velocity in the continuous liquid phase and gas as a dispersed phase in the column. In bubbly flow, the size of bubbles formed is approximately uniform in size [82]. Homogeneous flow regime is observed at the superficial gas velocity less than 5 cm/s in semi-batch column [83]. Nature of gas distribution and physical property of the liquid decides the size of air bubble formation. Bubbly flow is known as homogeneous flow regime in which there is no coalescence and breakup of bubbles [80]. The travel paths of bubbles are 20
vertical with minor transverse and axial oscillation. The distribution of gas holdup in the bubbly flow regime is radially uniform. In bubbly flow regime, a uniform distribution of bubble and uniform mixing are observed across the cross-sectional area [84]. With the further increase in air flow rate, the shape of bubbles become longer until they break and cause a random, and chaotic mixture propagating through the tube. This kind of flow pattern is known as churn flow. It is highly
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unstable and oscillatory in nature, which can be differentiated from slug flow by the absence of the periodic character. Churn turbulent flow regime is likely to occur at a superficial gas velocity greater than 5 cm/s. Beyond the limit of the bubbly flow regime, a disordered form of the homogeneous gas-liquid system is developed due to the turbulent motion of the gas bubble and liquid recirculation. The flow regime trend at various column diameter and superficial gas velocity
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is reported in Fig. 3.
Under this turbulent condition, coalescence of bubbles occurs due to high gas throughput which
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leads to the development of large bubbles with short residence time and unsteady flow pattern in
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the column [82]. Bubble size distribution is wide in this flow regime due to coalescence and
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breakup of the gas bubbles. This flow regime possesses the mixture of small to large bubble, which varies from millimetre to centimetre in diameter [86]. Churn turbulent flow is generally observed
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in the large diameter column [84]. The generation of the number of bubbles increases with the further increase of gas flow rate, which leads to coalescence of bubble and formation of elongated
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bubbles having the shape of the spherical nose and cylindrical tail. The shape of the formed bubble is similar to the shape of an axisymmetric bullet, which is known as Taylor bubble or gas slug.
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The formed slug may be more than or equal to the diameter of the column. In slug flow, the Taylor bubbles are detached by liquid slugs, which may or may not be aerated. In the Taylor bubble
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regions, the liquid flows downward as a thin annular film from the preceding to the succeeding liquid slug. This forms a wake region when it meets the liquid slug. The vorticity induced in the wake shears bubbles from the tail of the Taylor bubble and aerates the liquid slugs. Slug flow is
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always unsteady in nature, in spite of fixing the flow rate of gas and liquid at column inlet. Slug flow regime is observed to occur in small diameter column at the high superficial gas flow rate [84]. Phase holdup, gas & liquid velocity and mixing in a flotation process are dependent on each other which makes the complex flow behaviour in the flotation column. Hence, the complex flow characteristics significantly influence the flotation efficiency [20].
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3.1.1. Methodology There are various methods available to observe flow regime and its transition. Some of the methods
Visual observation [87,88,89]
Drift flux analysis [90]
Particle image velocimetry (PIV) [91]
Electrical capacitance tomography (ECT) [92]
Laser Doppler anemometry (LDA) [93]
γ-ray computed tomography (CT) [94]
Conductivity probe [88]
Temperature variation using a heat transfer probe [95]
Neural network [96]
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are:
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A
Some of the important measurement techniques are described as follows:
3.1.1.1. Visual observation technique
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It is one of the simplest technique for estimation of flow pattern in a flotation column. This
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technique can be used only when the column is transparent. In the homogeneous flow regime, the slow movement of the bubble can be observed but in the heterogeneous regime, the gross
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circulation and intensity of interaction of bubbles are very high, so it is not possible to identify the accurate transition velocity. A fast video technique is used for visual observations and, combined
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with image processing to interpret flow regime [87,88]. 3.1.1.2. Drift flux analysis
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Wallis [97] first suggested the drift flux theory for predicting the flow regime and its transition for two-phase system. Drift flux theory can be applied to obtain the transition point separating the homogeneous and heterogeneous flow regimes. In this method, the drift flux, jgl (the volumetric flux of either phase relative to a surface moving at the volumetric average velocity) is plotted against the gas holdup in which sudden change of slope of the curve denotes the transition point. The drift flux relation can be represented as [90] 22
jgl usg (1 g ) usl g
(1)
where usg is the superficial gas velocity and usl is the superficial liquid velocity. The sign indicates the counter-current and co-current flow of liquid relative to the gas phase. Drift flux plot represents the phase velocity at which the bubble flow changes into the churn turbulent region,
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due to steeply increase of drift flux at that point [98]. Plot representing transition point which is function of gas holdup and drift flux is shown in Fig. 4. 3.2. Gas holdup
The gas holdup can be expressed as the volume fraction occupied by the gas phase in the total volume of the two or three phase mixture in the column. Gas holdup in the flotation column
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depends on bubbles, the local flow velocity, the presence of backmixing flow, and the rising
N
velocity of the bubbles [99]. In flotation columns, the desired recovery has a great dependence on the determination of gas holdup and flow regime. Particle and liquid residence time cannot be
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estimated without the knowledge of gas holdup and flow regime. Particle recovery is greatly
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dependent on gas flow rate and bubble diameter both of which influence the gas holdup. Finch et al. [100] observed a linear relationship between bubble surface area flux and the gas holdup for
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different types of flotation column and operating variables. According to Massinaei et al. [101]
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linear correlation reported between flotation rate constant and the gas holdup in the industrial flotation column. Tavera et al. [102] investigated the radial gas holdup in presence of vertical baffle which is known for providing even distribution of gas bubble and suppressing the mixing
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effect. Author claimed that the radial differences in gas holdup is due to the sparger system arrangement which is unable to provide the even distribution of the bubble. Vinnett et al. [103]
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reported an indirect technique for measurement of local gas holdup in the collection zone of flotation column. This technique is based on the model structure which is the function of percent
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area occupied by gas bubbles in binary images and the superficial gas velocity. Images are obtained using a bubble viewer and more than 250 images of bubbles are generally analysed to get the appropriate percent area approximations. The model structure is capable of measuring the gas holdup in the range of 2.5 to 15% in laboratory flotation column and 6.0 to 21.0% in industrial flotation column. Li et al. [104] studied the gas holdup in presence of Carboxymethyl cellulose (CMC) and sodium dodecyl sulfate and nitrogen were used as a gas phase. They observed that gas 23
holdup increases by increasing the superficial gas velocity and decreasing with increase of CMC concentration. Bhunia et al. [105] investigated the effect of particle on the gas holdup. Experimental result shows that gas holdup decreases in presence of particle. This reduction is more toward increasing concentration and smaller particle size that results in moderately higher gas holdup than the bigger size. Particle size addition increases the slurry viscosity hence coalescence
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behaviour of the gas bubble increases which causes reduction in gas holdup. According to Joshi et al. [106], the gas holdup in the column depends on the number of bubbles, average bubble size and its rise velocity. One can define gas holdup as the ratio of column volume occupied by the gas phase to the total column volume, which is expressed by [105] Vg
g
(2)
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Vg Vl
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Some of the recently developed correlations of gas holdup for the flotation column are given in
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Table 1.
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3.2.1. Measurement techniques
There are several methods available to measure the gas holdup in the column. Some of the
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available methods for measurement of the gas holdup in the column are phase isolation,
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conductivity [111], pressure drop [102,112], electrical resistance tomography [113], dynamic gas disengagement [114], an optical probe [115], γ ray densitometry [116] etc. Some of the methods
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are described in the following subsection. 3.2.1.1. Phase isolation technique
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Phase isolation technique is used to estimate the average gas holdup in any system. Gas holdup can be obtained by measuring the difference in height between the level of clear liquid before
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aeration and the gas-liquid-solid mixture level after aeration. This technique gives reliable value only when measurement is accomplished at the steady state during operation. The average gas holdup can be calculated as [117]
g
hm hl
(3)
hm
24
where g is the overall gas holdup, hm is the height of gas-liquid-solid mixture and hl is the clear liquid-solid height. 3.2.1.2. Conductivity method Electrical conductivity is defined as the ability of a substance to conduct electric current. All
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substances have the ability to conduct electricity to some degree. The accuracy of phase isolation method reduces when to deal with reducing bubble size and liquid volume under test. So, to counter this problem electrical conductivity method is used to measure the gas holdup. According to Maxwell [118], the electrical conductivity of dispersion (a continuous phase plus one or two dispersed phase) is given by
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k l
(4)
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1 d k l d 1 0.5 d
where kl-d is the effective conductivity of the dispersion, kl is the electrical conductivity of the
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liquid and d is the volume fraction or phase holdup of dispersed non conducting phase. For two-
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phase (gas-liquid), by putting g for gas instead of d (indicate dispersed phase) the gas holdup is estimated by
kl 0.5kl g
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kl kl g
(5)
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g
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where kl is electrical conductivity of liquid and kl-g is the electrical conductivity of liquid-gas mixture. Two grid electrodes covering the cross-section of the column are used to can measure the electrical conductivity. Conductivity probes measurement is an invasive technique which may
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interrupts the flow field consequently may impact the performance of the system [113]. The grid electrodes should be inserted in such a way so that they do not disturb the flow field in the column.
A
The conductivity of the liquid and liquid-gas is related to measured conductance (G) which can be calculated as [119] A G ke l
(6)
25
where ke is the electrical conductivity, A is the area of electrode and l is the distance between two electrodes. The ratio of (A/l) is known as cell constant. The electrical conductivity of dispersion for three-phase (solid-liquid-gas) (kl-s-g) is calculated by empirical correlations [120]
kl s g kl s l ( solid free basis)
(7)
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where l is the phase holdup or volume fraction of the liquid phase. Another correlation available to predict the gas holdup, proposed by Begovich and Watson [121] which is tested on 4-6 mm glass alumina and plexiglass beads is
k l s g kl l
(8)
U
3.2.1.3. Pressure drop method
N
This method is one of the standard methods for calculating the gas holdup in two and three-phase
A
systems. If the gas density, frictional force, and accelerative force are neglected then the local gas holdup between the two points in the column can be calculated as [102,112]
M
P sl Lg
(9)
D
g 1
where ΔP is the pressure difference between two points, ΔL is the difference between two pressure
TE
tap, g is the acceleration due to gravity, sl is the slurry density. This method can be used to estimate the axial gas holdup by taking the pressure measurement at the different axial location. Wencheng
EP
et al. [99] reported the gas holdup measurement using the differential pressure technique in a cyclone-static micro-bubble flotation column. Gas holdup measurement obtained from the
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differential pressure technique are compared with the volume expansion technique and relative error between them are used to optimize the measurement positions. They suggested that
A
measurement position should be in the middle of the column and in the region half way from the center to the wall. The gas holdup in the axial direction is lower at the bottom and higher at the top of the flotation column. 3.2.1.4. Dynamic gas disengagement technique (DGD)
26
Sriram and Mann [114] first introduced DGD technique. When the system is at steady state at a given velocity, the gas flow is quickly shut down by a quick closing valve and start measuring the decaying gas-liquid dispersion height or pressure at the different level with respect to time. Initially, the decay in liquid level is fast due to disengagement of the large bubble and after some time, the decay in liquid level decreases due to disengagement of small bubbles. The decaying
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level of gas-liquid dispersion level can be estimated by a video camera [122], visual observation, pressure profile (pressure transducer signal) [123] and X-ray [124]. The change of decaying height of gas-liquid dispersion with time (is known as dynamic gas disengagement profile) is used to estimate the holdup structure prior to the gas flow shut down. The basic assumptions are: (i) initially at the time (t = 0) the dispersion is axially homogeneous, (ii) constant rate of disengagement process in which every bubble disengages with each other independently, (iii) there
U
is no coalescence and break up of bubble occurs, and (iv) the cross-sectional area occupied by the
N
bubbles remains unaltered during disengagement process. The liquid surface is not determined clearly due to waviness. The waviness of the liquid surface creates uncertainty during direct
A
estimation of liquid level. This problem is countered by measuring the average liquid level.
M
Resistance probe sensor is used to measure the liquid level, which provides the time-average value,
average mean liquid level.
D
if the resistance probe estimates the local value, multiple probes are needed to get the surface
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3.2.1.5. Electrical resistance tomography (ERT) Electrical resistance tomography technique is used to measure the radial and axial gas holdup
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profile in two or three phase process. ERT technique can be potentially applied in many industrial applications to monitor the flow and holdup characteristics in multiphase flow system [125] due
CC
to its high-speed competence, low price measurement, robust sensors and non-intrusive nature [126]. The ERT technique comprises of electrodes, data acquisition system, and image
A
reconstruction system. A particular number of ERT sensor positioned along the column length and for each plane which is equally spaced, a fixed number of electrode is installed in the inner wall of the column. The size of the electrode varies according to column diameter, fluid velocity, image speed, and fluid conductivity. The data acquisition system follows the adjacent measurement approach by implementing a current between two adjacent electrodes and measuring the corresponding voltage between all other electrode pairs. The installed electrodes are attached to 27
the data acquisition system by coaxial wire. The data acquisition system is connected to the computer for data processing using suitable image repair algorithm. For each sensor plane (m×n) pixel array can be generated using an algorithm, and after excluding pixel (k) belongs to the outside reactor perimeter, the remaining pixels (m×n-k) can be incorporated into the repair of the circular image [89]. If there are r number of planes, the total of (m×n-k)r number of conductivity
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measurement is acquired for each frame. Using the conductivity data obtained from the ERT, the local gas holdup can be measured by applying Maxwell equation which relates conductivity to concentration of dispersed phase as [127]
g
(2k1 k 2 2k rc (k rc k 2 / k1 )) k rc k rc k 2 / k1 2(k1 k 2 )
(10)
U
where k1 and k2 are the conductivities of continuous and dispersed phase respectively. The
N
parameter krc is the mixture conductivity distribution of two phases. Considering disperse phase as
2k1 2k rc k rc 2k1
M
g
A
non-conducting material, the Eq. (10) can be rewritten as [113]
(11)
D
Phase holdup characteristics of the three-phase system as a function of impeller Reynold number
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and particle loading can also be estimated by ERT technique [128]. 3D gas holdup characteristics in flotation column are estimated by three-dimensional ERT technique [129]. Vadlakonda and
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Mangadoddy [113] applied ERT technique to estimate the effect of operating variable, surfactant concentration and gas distributor porosity on phase holdup. They concluded that gas holdup is enhanced by the increase of superficial gas velocity, gas distributor porosity, feed flow rate and
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initial liquid height.
A
3.3. Pressure drop The difference in pressure between two points of fluid carrying network is called pressure drop Pressure drop measurement determines the requirement of flow energy for the transportation of fluids in the multiphase system. The notion of pressure drop provides the energy dissipation pattern, which helps in modelling and assessment of the performance of the system [89]. The main cause of pressure drop is the frictional forces which are due to the resistance to flow, change in 28
elevation of fluid, extra pressure gain due to any fluid which is added using a pump, turbulence generated by sharp changes in fluid flow direction and friction inside the column. Resistance to flow of fluid caused by fluid velocity, viscosity, surface roughness (friction between fluid and wall of column), bend, convergence (sudden contraction) and divergence (sudden enlargement) of the tube, and friction between adjacent layers of fluid etc. The high flow rate or high viscosity leads
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to higher-pressure drop while low flow rate lowers or no pressure drop. Gas holdup increases as gas density increases [130]. The total pressure drop (ΔPTP) in the system can be described as
PTP PfTP Ph Pa
(12)
which is the summation of all the three frictional pressure drop (ΔPfTP), hydrostatic head (ΔPh) and pressure drop due to acceleration (ΔPa). Hydrostatic pressure drop depends on the density of the
U
two-phase or three-phase system and height of the gas-liquid-solid mixture, which can be
N
represented as
(13)
A
Ph m ghm
M
where m is the mixture density and hm is the vertical height of the two or three-phase mixture. Pressure drop due to the acceleration can be neglected compared to the total pressure drop in a
D
tube of uniform cross section and also in adiabatic condition [89]. For single-phase flow, the
2 2 f sp spu sp L
dc
(14)
EP
Pf ,sp
TE
frictional pressure drop is related to the fanning’s friction factor as [89]
where fsp is the single-phase friction factor, sp is the single phase density, usp is the single-phase
CC
velocity and L the difference between the two pressure tapping over which the pressure drop has been measured. In similar way, three-phase frictional pressure drop based on the superficial gas
A
velocity in the column can be defined as Pf ,three phase
2 2 fthree phasemusg hm
(15)
dc
3.4. Bubble size and its distribution
29
Interfacial area available for the particle adhesion characterizes the separation efficiency of the system which helps in the design and scale-up of the flotation column. The interfacial area is directly affect the flotation rate constant [131]. The interfacial area in flotation column depends on the bubble size, gas holdup, superficial gas velocity [132], gas distributor design, properties of phases, and column geometry. Smaller bubbles coalesce to form a larger bubble, the interfacial
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area for the collision of bubble-particle reduces which causes reduction in attachment probability of particle on the bubble hence flotation efficiency decreases. Gas holdup and bubble size in flotation column depend on the physco-chemical property of the system and type of gas distributor used [133]. The probability of collision in pulp phase of flotation decreases with an increase in bubble size, which results in a decrease in recovery [12]. Dissolved air flotation (DAF) and electroflotation (EF) are some other important process, which is able to generate even small-sized
U
bubble in the range of 10-100 µm diameter. Some of the methods like Mie scattering technique
N
[134], Bayesian magnetic resonance technique [135], Coulter count method or pore electrical resistance method [136], dynamic gas disengagement technique [113] are utilized to estimate the
A
bubble size. Image analysis technique is most widely used to estimate the bubble size but there are
M
some drawbacks like it requires a transparent wall for image capture, low bubble concentration, complicated experimental setup, and time-consuming process. Laser diffraction technique is used
D
to measure the size distribution of microbubble for dissolved air flotation process. Bubbles below
TE
1 mm [137] or have diameter few hundred m or less are considered as microbubbles [138]. A new microfluidic device known as fluidic oscillator that can be used to convert steady gas flow
EP
into oscillatory flow which in turn results in the production of microbubble. Fluidic oscillator is easy in design which contains no moving part. Microbubbles produced from porous plate combining oscillatory flow technique may be 10 times smaller in bubble diameter and 2-3 orders
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of magnitude less energy consumption as compared with conventional microbubble generation method based on sparging, cavitation, agitation, electrolysis, and fluid jets [139]. Brittle et al.
A
[137], attempted to further decrease the size and population of the microbubble by optimizing the frequency of the oscillating gas supply in a fluid oscillator. They applied frequency optimization on three different microbubble production systems; an acoustic oscillation system with a mesh membrane, a fluidic oscillator employed with a single orifice membrane and a fluidic oscillator with a porous gas distributor. Experimental results show that in some of the cases a bubble size reduction is about 73% as compared with non-optimal operating frequencies. In some cases, a 30
reduction in bubble size of upto 73% was achieved as compared with non-optimal operating frequencies. A current novel innovation demonstrates that microbubbles smaller than 100 μm can be economically produced by incorporating oscillatory airflow pattern [140]. Rehman et al. [141] investigated the volumetric mass transfer coefficient and bubble diameter in the oscillatory flow and compared the results with steady flow. The oscillatory flow environment results in 55%
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improvement in volumetric mass transfer coefficient and able to produced bubble size in the range of 80-120 m diameter than 1 mm in the steady flow condition. Various techniques of bubble
U
generation and bubble size distribution measurement are shown in Table 2 and Table 3.
N
3.4.1. Measurement method of bubble size
There are several methods available to measure the bubble size in flotation column. Some of the
A
methods are photographic [172,173], acoustic [172,174], optical, light scattering [134], inverted
M
funnel [175], phase Doppler anemometry (PDA) [176], Bayesian magnetic resonance [135]. Driftflux analysis can be also applied to estimate the bubble size using technique given by [105,177].
TE
D
Some of the bubble size measurement methods are described as follows.
3.4.1.1. Photographic technique
It is one of the simple technique for estimation of bubble diameter. Since a decade, numerous
EP
intrusive and non-intrusive techniques are invented to measure the bubble sizes. The bubble size is estimated by photographic technique followed by image analysis. The generated bubbles are
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captured by a high-speed camera. Columns wall should be transparent so that the high-speed camera can capture the bubbles. A light source can be placed opposite to the camera to get a clear
A
picture of bubbles. The captured images are analysed by the image processing software to estimate the bubble size. In this technique, bubble size can be measured by manually identifying each of the bubbles. Photographic technique is limited to resolve large bubble clusters [173] and captures only those bubbles, which are nearby the wall of the column. The mean bubble diameter is also known as Sauter mean bubble diameter which can be expressed as [16,173]
31
n
d 32
n d
3 bi
n d
2 bi
11 n 11
i
i
(16)
where ni is the number of bubbles of diameter dbi. Schematic of photographic technique and fitting
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of bubbles through Stat-Fit software is shown Fig. 5.
The 2-D shape bubbles are assumed as elliptical and their minimum and maximum axes computed automatically by image analysis software [178]. Using the known values of the maximum and minimum axes of the 2-D bubble, the equivalent spherical bubble diameter dbe can be calculated as [179]
(17)
N
U
d be (d b2,max d b,min )1/ 3
A
where db,max and db,min are maximum and minimum bubble diameter.
M
3.4.1.2. Acoustic method
The acoustic method is based on excessive attenuation of the acoustic wave or scattering and
D
changes in sound velocity. Minnaert [174] first introduced an acoustic method in which sound generated by bubbles are investigated and based on this an equation developed between bubble
TE
sizes and their natural frequency of oscillation. The resonance frequency of the acoustic wave can
1 d b
3 rg P
(18)
l
CC
EP
be expressed as [180]
where is the Minnaert frequency , db is the bubble diameter, γrg is the ratio of specific heats of
A
the gas, l is the liquid density, P is the absolute liquid pressure. In this technique produced bubbles are passed through the acoustic perturbation and at same time recording and analysing the response. The bubble volumetric vibration at small amplitude, which is recorded by the harmonic oscillator can be used to calculate the bubble size. This setup consists of a hydrophone which is a kind of microphone designed in such a way that it can do underwater recording or listen to underwater sounds. The working principle of hydrophone is based on a piezoelectric transducer. 32
A piezoelectric transducer is a device, which generates electricity when experiences pressure change. In this method, the hydrophone is placed at sufficient distance from the bubble generator so that it does not affect the bubble size. It is connected to a wireless microphone so that it can amplify and transform the electric signal into acoustic one. Acoustic technique can also be applied to investigate the bubble size [68,175], bubble coalescence phenomena in presence of solid
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particles [181] and mass loading on the bubble [182]. Kracht and Moraga [172], estimated the bubble size using the acoustic technique in the flotation column. Authors claimed that acoustics technique is able to measure the bubbles in the range of 0.75-3 mm diameter in two and threephase system which is sufficient to cover the range of interest in the flotation. Bubble size obtained from the acoustic technique is correlated well with photographic technique.
U
3.4.1.3. Light scattering method
N
Light scattering technique is based on the principle of Mie scattering theory [183]. Intensity of
A
scattered light is related to the radius of the air bubble as given by [134]
M
2 I 2 2 2 2 4 rb S 2 cos
(19)
D
where I is intensity of scattered light, is wavelength, rb is the radius of the bubble, is an
TE
azimuthal angle and S2 is the scattering function. Here scattering light intensity is inversely proportional to the radius of the bubble. Takahashi et al. [184], reported the size and concentration
EP
of fine bubble suspension using the light scattering technique. Author proposed that dynamic light scattering technique based on the Mie theory is more suitable than laser diffraction for
CC
measurement of all kinds of particles if the shape of the particle is known. In case of the fine bubbles, the scattering profile is same as that of a water droplet in the air which supposed to be spherical. Couto et al. [149], estimated the bubble size distribution of microbubble produced from
A
the dissolved air flotation using the laser diffraction technique. 3.4.1.4. Inverted funnel method Inverted funnel technique is used to measure the bubble size. This technique was first introduced by the Leighton and Walton [185]. An inverted transparent glass funnel is used to capture the air bubble. The syringe piston is used to generate a bubble. Length of the air bubbles is measured by 33
drawing captured bubble into the capillary tube. In this technique, the mean volume of the air bubble is estimated by calculating the total volume of the air bubble accumulated in an inverted liquid filled cylinder, which is then divided by the total number of bubbles. The sound emitted by the bubble is caught by the hydrophone. The hydrophone works based on the principle of the piezoelectric transducer, which converts pressure changes into electricity. The generated electric
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signal is amplified and then stored on a transient recorder to display on a cathode ray oscilloscope or processing on a spectrum analyser. Vazquez et al. [175] demonstrate the bubble size measurement by three different techniques, inverted funnel, photographic, acoustic. They observed 0.5% repeatability error with a 50 bubble set in inverted funnel technique while an accuracy between 86% to 99% with a 5% repeatability error in photographic technique. The acoustic technique provided an accuracy of 97% and 99% with a repeatability of 0.3%. Author concluded
U
that the acoustic technique can provide precise bubble size measurement than other two
N
techniques. Inverted funnel technique also can be applied to measure the rise velocity of the
M
3.4.1.5. Phase Doppler anemometry (PDA)
A
bubbles in the viscous solution [186].
Phase Doppler anemometry (PDA) method is used for estimation of size, concentration, and
D
velocity of a spherical particle like bubbles and droplets in gaseous or liquid phase [176,187]. PDA
TE
technique can be used to measure the turbulence characteristics in the flotation column [176]. This method is based on the light scattering interferometry. In this technique, coherent laser beams used to focus the measurement location. When the fluid particle passes through the measurement
EP
location scatters the waves from two incident laser beams. Photo detectors receive the Doppler signal in different phases and the phase shift between the Doppler signals is proportional to the
CC
fluid particle diameter. The frequency of the Doppler signal is directly proportional to the velocity of the fluid particle [187]. An advantage of this method is that it can measure the size and velocity
A
of each fluid particle simultaneously. This technique provides online real time data [188]. 3.4.2. Bubble rise velocity There are several methods available to measure bubble velocity in the column. Some of the available methods for measurement of the bubble velocity in the column are conductivity method [189], laser Doppler anemometry (LDV) [190], Particle Image Velocimetry (PIV) [176], optical 34
fiber probe [191] ultrasonic Doppler etc. A detail explanation of PIV technique is provided in the subsection. 3.4.2.1. Particle image velocimetry (PIV) PIV is a non-intrusive technique used to measure the instantaneous whole field velocity vector of
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flowing field. This technique is suitable to measure the fluid velocity vector at many points at one instant of time. PIV technique can measure 2D or 3D velocity component for whole area simultaneously. The fluid of interest is seeded with neutrally buoyant tiny tracer particles/markers, which makes flow field visible under the light source (laser sheet, which ensures better illumination of tracer particle). The CCD (charge-coupled device) camera is used to capture the images of these tracer particles at different interval of times [192]. The instantaneous velocity field
U
is determined from the displacement of tracer particle between two successive images in a period
N
[193]. A suitable software (e.g., PIV-SLEUTH) can be used to do the image analysis in which each image is divided into the mesh of small segment called as interrogation area. Cross-correlation
A
method is used to calculate the mean displacement (Δx) in the interrogation area, which is divided
M
by inter-frame time interval (Δt) to get the mean flow velocity [194]. The velocity map over the whole target area is determined by repeating cross-correlation method for each interrogation area
D
over two image frames recorded by the camera. Another software can be used to do the analysis
TE
of images is PIVlab, which is an open source software. PIVlab is an open source MATLAB code, which can be used to determine the velocity distribution within the image pair and can also be used to derive display and export multiple parameters of the flow pattern [195]. Tracer particle can be
EP
either solid/liquid/gas during measurement of fluid velocity. In the case of liquid flows, the tracer particle like hollow glass sphere, aluminium, polystyrene, and polyamide within the size range of
CC
(5-100 µm) are generally used. In the case of gas flows the tracer particle are oil drops with the size range of 1-5 µm. PIV techniques are executed considering following assumptions: (I)
A
homogeneous distribution of tracer particles, (II) tracer particles obey the fluid flow/motion ideally, and (III) uniform displacement within interrogation region. The criteria to select the tracer particles are: (I) tracer particles should be easily detectable/visible (Light reflecting particle), (II) tracer particle does not disturb the fluid flow, and (III) for better precision, the density of tracer particle should be close enough to the density of fluid. In the case of single phase (liquid), the flow measured with the help of tracer particle, which is illuminated by laser light sheet. In the case of 35
two-phase (liquid/gas) flow, the liquid seeded with tracer particles and both tracer and bubble scatter light, which enables to distinguish tracer from bubbles. Measurement of the local displacement of tracer particle and gas bubble enables to calculate the velocity of both phases [196]. PIV technique is also used to measure the bubble diameter, shape, acceleration, and instantaneous velocity field [197]. Flow regime and its transition are mapped by PIV technique
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[91]. PIV technique can also be used to characterize the turbulence by capturing the fringe visibility within the error of less than 10 % [198]. Fig. 6, represents the subsequent steps of PIV measurement.
PIV technique can be successfully employed to study the fluid flow movement in a flotation column. The computational fluid dynamics (CFD) and particle image velocimetry (PIV) are used
U
to estimate the flow pattern in presence of strong vortex generated by rotor. An excellent agreement is obtained between the simulation results and experimental measured flow characteristics for the
N
flotation column [199]. Darabi et al. [200], studied the turbulence characteristics in the flotation
A
column using PIV technique. Authors reported, local turbulence characteristics vary in presence
M
of gas bubbles due to average velocity, turbulent kinetic energy dissipation and turbulent kinetic
3.4.3. Interfacial area
D
energy.
TE
The knowledge of the gas-liquid interfacial area is essential for scale-up and design of the multiphase system. The overall degree of separation in the flotation column can be controlled by
EP
interfacial area. The interfacial area depends on gas holdup and bubble size distribution and bubble velocity [201].
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3.4.3.1. Methodology
There are several methods available to measure the gas-liquid interfacial area. Some of the
A
important techniques are video imaging [202], dynamic gas disengagement [203], Laser Doppler anemometry [204], conductivity probes [205], chemical method [204,206] and light transmission method [207]. Physical and light transmission technique are described in the subsequent section. 3.4.3.2. Physical method
36
If gas holdup and Sauter mean bubble diameter is known, then the gas-liquid interfacial area can be calculated as [149]
a
6 g
(20)
d 32
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where a is the gas-liquid specific interfacial area (interfacial area per volume), g is the gas phase holdup and d32 is the Sauter-mean bubble diameter. 3.4.3.3. Light transmission technique
Light transmission technique is used for calculation of gas-liquid interfacial area. A detailed study of a light transmission technique is reported by Ghiassi et al. [201]. Calderbank et al. [207],
U
introduced light transmission method, in which transmitted beam of light allowed to pass through
N
the gas-liquid dispersion. The intensity of emerging beam is estimated by a photo-multiplier or
A
photosensitive device. The fraction of light transmitted (ƛ) is related to the gas-liquid interfacial
al p 4
(21)
D
e
M
area and optical path length which can be expressed as [208]
TE
where a is gas-liquid specific interfacial area and lp is optical path length. Light attenuation method is restricted to a value of alp < 20.
EP
3.5. Carrying capacity
Carrying capacity can be defined as the maximum capacity of the gas bubble to transport the solids
CC
particles or removal capability of solids by the gas bubble in flotation column [22]. The capacity of the flotation column depends on the number of free bubble surfaces area available for
A
attachment of particle [209]. As bubble loading starts, contact time decreases because of reduction of particle trajectory along the free bubble surface. The rate of collection of solids by the gas bubble decreases as solid loading increases by the gas bubble. Carrying capacity of the smaller bubble size is greater than the bigger when the column is operated at a constant gas flow rate [16,22,131,177]. According to Finch and Dobby [177], the theoretical carrying capacity can be expressed as 37
Ca ,max
d p p u sg ,max 2d b
(22)
where usg,max denotes maximum superficial gas velocity. The amount of particle, which is carried by the gas bubble, depends on the size of the gas bubble. The degree of carrying capacity is
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controlled by the availability of total surface area [210]. A correlation proposed by Princen and Peplinski [211] to predict the load carrying capacity of the gas bubble which can be expressed as Bl 4.84 p rb rp r 2
(23)
where Bl denotes bubble load, rb is the bubble radius, rp is the particle radius and p is the particle
coverage which can be mathematically expressed as
(24)
A
N
Bl K1d p p / d b
U
density. According to Li et al. [212] the bubble load can be determined from the bubble surface
where K1 is the fraction of bubble surface occupied. Bubble loading can be demonstrated as ratio
(25)
D
mcl (vcl / vb ) Ab
TE
Bl
M
of mass of collected solid particles to the total surface of bubbles which can be expressed as [154]
where mcl is the mass of loaded particles, vb is the volume of single bubble, and Ab is the surface
EP
area of the single bubble. The carrying capacity can be normalized as per unit length (CL), per unit area (CA) and per unit volume of the gas (CG) [213]. Flotation column generally operates at 60% of their maximum carrying capacity [214]. Some correlations for carrying capacity are given in
CC
Table 4.
A
3.6. Mixing characteristics Mixing and dispersion in the flotation column are due to the pulp recirculation and turbulence of bubble and feed slurry motion. Mixing in flotation column affect particle suspension, fine bubble generation and dispersion consequently bubble-particle collision takes place [217]. Mixing and dispersion characteristics play an important role in designing and scaling up of the flotation columns [147]. The degree of mixing can be estimated by residence time distribution (RTD) 38
technique. The variation of gas holdup radially or axially cause pressure variation, therefore responsible for liquid circulation, and back mixing of the phases [89]. Liquid circulation direct the rate of mixing and recovery efficiency of flotation column. Mills et al. [218] studied the mixing characteristics of the flotation column using the RTD technique. In collection zone of flotation column, it is assumed that axial dispersion model controls the flow structure. Author reported that
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the axial dispersion model is superior to other models dealing with column diameter 10 cm to 150 cm. For modelling of small diameter column, either dispersion model or tank in series model can be used. The solid dispersion coefficient is more than the liquid dispersion coefficient and solid dispersion coefficient increases with increase in particle loading in laboratory test column but remains unaltered in large column [218]. The performance of flotation cell when they are arranged
t N 1e tN /
N
N 1 !
A
N
(26)
N
E (t )
U
in series for continuous operation can be modelled using N perfect mixer in series by RTD as [219]
M
where E(t) is the RTD function, N is the number of mechanical cells, is the mean residence time and t is the time. Bubble size, bubble number, particle settling velocity, slurry rate, collection zone
D
height, and diameter of the column influences the dispersion number [22]. The intensity of axial mixing increases with the increase in column diameter [220]. Mixing of phases inside the flotation
TE
column significantly affects the bubble-particle attachment and bubble-particle detachment process. The study of mixing characteristics helps in optimization and design of the flotation
EP
column [221].
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3.6.1. Methodology and analysis of mixing characteristics Flotation column never obeys the ideal flow pattern. The non-ideal behaviour is due to (i) channel formation, (ii) recycling of fluid, (iii) vortices and turbulence at inlet and outlet of the vessel, (iv)
A
bypassing and short-circuiting of the fluid, and (v) formation of dead zone at the corner of the vessel. The amount of time spent by the molecule in the vessel called as the residence time of the molecule in the vessel. It is obvious that different particles use different routes to pass through the column takes a different amount of time and due to this, there will be the distribution of residence time of the molecules inside the vessel. The distribution length of time spent by different molecule inside the vessel, called residence time distribution (RTD) or exit age distribution (E). Tracer 39
technique is one of the simple methods to measure RTD [222]. The tracer should be non-reactive, should not be adsorbed on the vessel wall or other surfaces of the vessel, its physical property should be similar to the system, should be easily detectable, should be completely soluble in the system fluid [223]. Tracer is injected with feed at the time (t=0) and then measured the tracer concentration in the outlet of the vessel as a function of time. Pulse and step input method is
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commonly used for RTD measurement. RTD can be determined by a non-invasive sensor in case of radioactive tracer by locating it at an outlet of the vessel [217]. Particle RTD in the flotation column strongly depends on the superficial velocity of the feed and hindered settling velocity. Information entropy theory can be applied to analyse the quality of mixing in flotation column which is based on the information entropy theory [224]. Chegeni et al. [225] attempted to design the laboratory flotation column employing the axial dispersion and drift flux model considering
U
axial mixing coefficient, gas holdup, column length, vessel dispersion number and bubble size.
N
Applying the theory of the axial dispersion model and vessel dispersion model, the dimensions of the flotation column calculated for particular operating conditions. The study reports the axial
A
mixing coefficient of 0.003 (m2/s) and vessel dispersion number of 0.32. The required diameter
D
3.6.1.1. Residence time distribution
M
and height of the column are 0.0542 and 1.15 m.
TE
RTD is most widely accepted technique to examine the mixing characteristics. When liquid or solid tracer is introduced into the flotation column, assuming that mixing takes place axially, the axial dispersion model predicts the concentration of tracer at axial distance from the introduction
EP
point z and time t which is represented as [226] C 2C C D U 2 t X X
CC
(27)
A
where D is the axial dispersion coefficient of the liquid phase which accounts the mixing intensity during flow, U is the interstitial liquid velocity, C is the tracer concentration. The first term in the Eq. (27), characterizes the time dependence concentration and U( C/ x) term represents the convective flow in the axial direction and D(2C/X2) represents the diffusive action, which represents the convective flow. The dimensionless form of axial dispersion model can be expressed as 40
1 2 Pe Z 2 Z
(28)
where Pe is Peclet number Pe = UL/D, L is the column length (bubbling zone height), is the dimensionless concentration = C/C0, Z is the dimensionless position Z = X / L and is the
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dimensionless time = t / where = L /U is called mean residence time of the liquid in the system. Axial dispersion model employs vessel dispersion number to specify the RTD profiles in the flotation columns [227]. Vessel dispersion number is defined in terms of Peclet number as ND
1 D Pe UL
(29)
when ND tends to zero and ∞, vessel results in negligible dispersion (plug flow) and large
U
dispersion (perfect mixed flow). The analytical solution of the Eq. (28) for normalized response
N
curve using open-open boundary conditions is given as [226] (1 ) 2 Pe exp 4 2 / Pe
(30)
M
A
1
C
where C denotes (C/C0) and θ denotes (t/tm) are dimensionless concentration and time. If both
D
experimental and theoretical residence time are equal, it represents that the column is most likely
TE
well mixed. If the experimental mean residence time is smaller than theoretical, it specifies the presence of dead volumes, short-circuiting [228]. The mean residence time can be calculated by
tm
EP
first moment methods is represented as
t C (t )t C (t )t i
i
(31)
i
CC
i
i
The second moment about the mean is called square of standard deviation or variance (σ2) is
A
expressed as 2
(ti t m ) 2 C (ti )ti
C (t )t i
(32)
i
41
The magnitude of variance dictates the spread of the distribution. The greater will be variance, more is the spread of the distribution. The magnitude of moments related to axial dispersion number (1/Pe) is
2 t
2 m
2 8 2 Pe pe
(33)
SC RI PT
2
where 𝜎𝜃2 is the normalized variance. 3.7. Entrainment Characteristics
Entrainment is defined as the transportation of fine particle in froth phase from pulp phase (collection zone) by entrapment in eddies behind the rising gas bubble [22]. Entrainment of gangue
U
material decreases the selectivity of the flotation column hence limit the collection effectiveness
N
of the desired particle. Therefore, the knowledge of entrainment characteristics helps in reduction
A
of the collection of undesired particle which improves the column efficiency, increases optimization and control of the column. During processing of particles larger than 38 µm [229],
M
the entrainment problem is insignificant because gravitational force cause entrained solid particle to drop back from froth phase to collection zone. Entrainment of gangue material into the froth
D
dilutes the desired material and decrease the grade of the concentrate hence selectivity and
TE
performance of the column [230]. Wang et al. [231] suggested that the entrainment is not only the function of particle size but other variables like gas flow rate, the density of the undesired particle
EP
and impeller speed and froth height. The degree of entrainment effectively varies with flotation time during the course of each experiment. Yianatos et al. [232] reported the entrainment study using the radioactive tracer technique and checked the effect of three different particle sizes. They
CC
suggested that fine particle size (< 45 m) significantly affect the entrainment while the recovery of the coarse particle (> 150 m) by entrainment is 0.05% which signifies weak dependence on
A
entrainment.
3.7.1. Entrainment theory and empirical correlations There are two mechanisms of entrainment observed in flotation column. First, one is due to the introduction of feed water which contains suspended solid particle, swept into the froth and second is due to entrapment of fine particle (gangue) in rising bubble [6]. The issue of entrainment in froth 42
phase can be minimised by; film water drainage in which slow fall of entrained material takes place around the gas bubble surface, fall of an entrained particle due to shear forces results from the relative motion of the gas bubble, local froth collapse which results in fast vertical fall of an entrained solid particle [233]. Entrainment in column depends upon the size of feed particle, recovery of water, pulp phase density, the speed of impeller, dispersing agent, froth thickness and
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air flow rate [234]. Entrainment is low in case of particle size more than 50 µm [235]. The entrainment depends upon the depth and structure of the froth. Some other parameters which affect the entrainment are superficial feed rate, collection and cleaning zone height, superficial wash water rate [235-238]. The degree of entrainment decreases with decrease in particle size. Stable froth structure made up of small bubbles is responsible for the better recovery of both entrained particle and attached particle due to low drainage and coalescence tendency. Many authors
U
proposed different models and theories for predictions of entrainment [239]. The degree of
N
entrainment based on the pulp phase is proposed by Johnson [240], is defined as the ratio of the mass of free gangue particles of ith size interval in the concentrate to the mass of free gangue
1 K1ent ( p pulp )
D
1 K1ent ( p pulp ) exp( k 2 d p )
(34)
TE
Ei
M
entrained solid is given by [241,242]
A
particles of the ith size interval in the pulp. The degree of entrainment based on residence time of
where Ei denotes degree of entrainment, K1, K2 empirical parameter, dp is the particle size, pulp
EP
and p are the specific gravity of pulp phase and entrained solid particle and ent is froth residence time of the entrained material. The froth residence time of the entrained material can be calculated
CC
as V El
(35)
A
ent
where V is the froth volume and El is the volumetric flow of entrained material in the concentrate. Another way to calculate the froth residence time of the entrained material is given by [243]
ent
Hf
(36)
us g
43
where Hf is the froth height and usg is the superficial gas velocity. According to Subrahmanyam and Forssberg [244] and Kirjavainen [238], the degree of entrainment can be expressed as the ratio of recovery of the entrained species to the recovery of the water. Water recovery, solid concentration in the pulp, particle size, impeller speed, particle density, gas rate, froth height, froth retention time, froth structure are the prime factors which affect the entrainment characteristics
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[6]. Different methods of measurement of entrainment are discussed by Trahar [241], Warren [245], Savassi et al. [242]. There are several models developed by researchers to predict entrainment in the flotation column. Developed methods can be categorized as; estimating the entrainment flow directly, and by determining entrainment flow based on the estimation of the degree of entrainment, classification effect of pulp, and water recovery [6]. An empirical model that measures the entrainment flow is expressed as [236]
(37)
N
U
ES exp 0.0325 R fw exp 0.063d p
A
where Es is the solid recovery by entrainment, Rfw is the water recovery from the feed, Δ is the specific gravity difference between solid and water, dp is the particle diameter. Water recovery
(38)
D
R fw 2.58 j f 1e 13.1 jb
M
from the feed is expressed as
TE
where jf is the superficial feed rate and jb is the bias water flow rate in the froth (it is the difference between the superficial velocities for the wash water flow and the concentrate water flow). Model
EP
proposed by Savassi [242] shows relationship between degree of entrainment (ENTi) and particle size as
A
CC
d p d p ENTi 2 exp 2.292 exp 2.292
1
1 ln
dp exp
1
(39)
(40)
where is the entrainment parameter, is the drainage parameter, and dp is the particle diameter. Savassi [242] developed the model for degree of entrainment fits well with the number of industrial datasets and depends on particle size. According to Savassi [246], the degree of entrainment 44
defined as the ratio of mass transfer of entrained particle of the ith size interval to the concentrate by mass transfer of water to the concentrate. The froth height above the level of pulp significantly affects the performance of the flotation column. The wetness of the froth increases with increasing superficial gas flow rate. The grade of the concentrate can be upgraded by controlling the residence time of the froth and by skimming off the top layer of the froth. The upgrade of concentrate is due
SC RI PT
to drainage of water and gangue into the lower layer of the froth phase and drain back to the pulp phase. Yianatos and Contreras [239], proposed a dimensionless entrainment factor based on particle which is expressed as
d E fi exp 0.693 pi mi
(41)
U
where Efi denotes entrainment factor which represents gangue/water recovery ratio, dpi is the mean
N
particle diameter of size i, mi is the parameter related to the mean particle size and is the drainage
A
parameter which depends on mineral characteristics and cell operation conditions like cell design
M
and water recovery. Kirjavainen [237] studied the entrainment of a hydrophilic particle in the laboratory using quartz and phlogopite. Entrainment correlation does not include calculation of water recovery, so the proposed model is not suitable for wide range of flotation conditions. The
D
proposed entrainment factor that is based on particle mass, particle shape, water recovery rate, and
(42)
0.5 0.4
wr0.7 b 0.5 m p
EP
E fi
wr0.7
TE
slurry kinematic viscosity can be expressed as
CC
where Efi stands for entrainment factor, wr is the water recovery, mp is the mass of a particle, η is the slurry viscosity, is the dynamic shape factor and b is constant to be form from experiment.
A
3.8. Flotation kinetics Flotation rate constant can be defined as the ability of the species, how rapidly they float. Floatation is generally a first order process and a function of particle concentration [247]. Using chemical kinetic analogy, the kinetic of bubble-particle collision and attachment of particle to gas bubble in is given as [248]
45
dC p dt
KC pr Cbs
(43)
where Cp, Cb, K, and t are the concentration of solid particle, the concentration of gas bubble, rate constant, time of flotation and r, s represents respective orders of concentration terms. At constant
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air supply, the probability of change in concentration of air bubble is very small and using first order kinetic (r=1), the rate equation can be expressed as dC p dt
KC p
(44)
The model is useful for prediction of process analysis. A flotation kinetic determines the variation of the rate of change of recovery with time and recognizes the variables that affect the flotation
U
kinetics [249]. The removal rate of particles or probability of collection of solid particles on gas
N
bubbles in pulp phase in the flotation column is a function of the probability of collision, the
A
probability of adhesion and probability of detachment. According to Yoon and Luttrell [250], the
and surface area of the rising bubble.
D
3.8.1. Induction time
M
rate constant of flotation process is directly proportional to the probability of collection of particle
TE
Induction time governs the attachment of solid particle to gas bubble. The time needed for the particle and bubble to break the narrow film separating the particle and gas bubble is called
EP
induction time. Rupturing of the thin film takes place due to surface forces between particle and bubble. Attachment of gas bubble to particle occurs when the time in which the particle and gas bubble is in contact with each other is more than the required induction time. Induction time
CC
strongly depends on the fluid properties, particle and bubble sizes and the forces between the particle and bubble. According to Albijanicet al. [251], the particle and gas bubble attachment take
A
place only when
t at t c
(45)
where tat is the attachment time defined as the time required for attachment of solid particles to the gas bubble when both are very close and tc is the contact time. Multiple collision occurs on bubble surface due to rebound from the bubble surface where collision changes to sliding [252]. The 46
collision time is smaller than the sliding time. Some naturally hydrophobic particles like bitumen, coal, waxes, molybdenite, hydrocarbon, tar and talc do not require flotation reagents to make these particles hydrophobic [253]. The hydrophobicity of naturally occurring particle decreases due to oxidation, which changes the chemical and physical properties of the surface of particle resulting in an increment of attachment time which causes a decrease in recovery of the particle during
SC RI PT
flotation process and the probability of attachment. The attachment time decreases exponentially with increase in temperature due to thinning of liquid film as given by [254] E t at t 0 exp K T
(46)
where t0 is the coefficient, E is the activation energy, K is the Boltzmann constant and T is the
U
absolute temperature. The attachment time and recovery depend on the particle size [255,256]. Ye
N
et al. [255] reported an increase of attachment time and a decrease of recovery with the increase in particle size. The effect of conditioning time on attachment time of air bubble on bitumen is
A
studied by Su et al. [257]. They reported that the attachment time increases with the increase in
M
conditioning time. Contact angle and induction time strongly depends on the hydrophobicity of the particle [159]. The pH value of the mixture significantly affects the flotation kinetics. In
D
presence of cationic collector, at low pH flotation capacity reduces because of cation and hydrogen
TE
both are in competition to get a suitable site on the solid particle. In anionic collector environment, at high pH, flotation kinetic reduces because OH- ion and collector anion are in competition to search a suitable site on the solid particle during the adsorption process. pH value also alters the
EP
zeta potential of the bubble and particle. The effect of pH on the zeta potential of bubble and particle and flotation recovery are studied by Yoon and Yordan [256]. The experimental results
CC
show that at pH 4.5, the induction time is 10 millisecond and flotation recovery is 22% while at the pH 9.8 the induction time increased to 125 milliseconds and flotation recovery becomes zero.
A
pH of solution alters the electrical interaction between the bubble and particle. It controls the attractive or repulsive electrostatic force between particle and gas bubble. 3.8.2. Separation analysis of flotation column by kinetic model
47
The removal rate of particles or rate of flotation depends on the probability of bubble-particle collision Pc, the probability of bubble-particle attachment Pa and the probability of bubble-particle detachment Pd [159]
P Pc Pa (1 Pd )
(47)
SC RI PT
where 𝑃 is the probability of collection of the solid particle on the bubbles. The probability of collision in the flotation column is due to the relative motion of the solid particle and the gas bubble. Many researchers developed the probability of bubble-particle detachment model which is based on the force balance, energy balance and maximum floatable particle size [7]. The probability of detachment of fine solid particle is very small and can be omitted. The expression
U
for the probability of collision is given as
(48)
N
PC A( D p / Db ) n
A
where A and n are the parameters which are the function of Reynolds number. Reay and Ratcliff
M
[258] reported the values of parameter A (2/3) and n (2) are which are valid for stokes region. The values of parameter A and n are 3 and 1 under potential flow condition [259]. Probability of
d p d b
2
(49)
TE
3 / 16 Rel Pc 1.5 1 0.56 1 0.249 Re b
D
collision under intermediate range is given by Weber and Paddock [260]
EP
Some of the important developed models for probability of collision are given in Table 5.
CC
The probability of attachment of solid particles to bubble is influenced by the hydrophobic nature of the solid particle. The mathematical expression for estimation of probability of attachment is
A
given by [159]
(45 8 Re 0.72 t u ) 2 b i b Pa Sin 2 arctan exp d b 15d b 1 d p
(50)
48
where ti, Reb, ub, db and dp stand for induction time, Reynolds number of bubble, bubble rise velocity, bubble diameter, and particle diameter. The rate constant (K) of the flotation process can be expressed as [159]
3P u sg K 2d b
SC RI PT
(51)
where usg is the superficial gas velocity, db is the bubble diameter. The probability of detachment (Pd) in the flotation can be described as [262]
2 c 6 sin ( ) 2 Pd exp 1 d p2 ( g pbm ) d p cos 2 ( c ) 2
U
(52)
N
where is the surface tension of the fluid, c is the contact angle between bubble and particle, dp
A
is the particle diameter, is the density difference between particle and fluid, p is the particle
M
density, and bm is the eddy turbulent acceleration. Some important flotation kinetic models [221,263,264] are provided in Table 6.
D
4. Importance and perspective of future research
TE
For a long time, flotation process has been used as a successful way of separating fine particles, wastewater treatment, deinking of paper etc. in chemical process industries. In spite of this, still,
EP
there are certain issues that are yet to be addressed to optimize the flotation process. After going through the literature it is observed that there is a huge uncovered area of research in
CC
hydrodynamics and microbubble assisted flotation process. Design parameters like flow pattern, gas holdup, mixing characteristics and bubble size & its distribution have a large number of applications in industries. Investigation of design parameters intensification facilitate the improved
A
transport processes. 4.1. Flow regime and its transition characteristics Today many industries are facing problems because of the complex flow behavior of gas-liquid or gas-liquid-solid in a multiphase system. Many researchers have explored flow pattern for several years to understand it in flotation technique. Researchers attempted to create a universally 49
applicable flow pattern map using non-dimensional quantities but these were validated against only a few experimental data sets. Most of the industrial operation works with different nonNewtonian liquids, so a thorough investigation of the flow regime and its transition at the quantitative range of gas and slurry flow rate is required to improve the efficiency of the flotation process. The design of flotation columns requires detailed information on the flow pattern and its
SC RI PT
characteristics because it directly influences the mixing characteristics of the phases and bubble stabilization, therefore governs the flotation effectiveness. Bubbles in the flotation system are presumed to be spherical in shape in most of the operation, but it is essentially governed by the flow regime. There is a lack of model development to interpret the flow pattern and its transition in the cyclonic-static micro-bubble flotation column and other flotation devices. Most of the noninvasive technique is most suitable for the two-phase system. Few authors studied the
U
measurement of flow regime in the three-phase system using a non-invasive technique. More
N
detailed studies on three-phase flow regime and its transition required incorporating non-invasive technique at different dynamic and geometric variables. Steady flow and oscillatory flow pattern
A
can be incorporated to produce the bubbles in the flotation column. The latter one results in
M
enhanced gas dispersion, improved foam stability, improved phase holdup, and axial mixing [265]. Although plenty of flow regime studies are reported in the literature, it is observed that important
D
information concerning the flow regime transition is often unnoticed. In particular, gas holdup and
TE
bubble size, that is considered in flow regime correlation model are rarely incorporated. The future experiment should consider the important variables which greatly influences the flow regime maps for numerical analysis, therefore can enhance the comparability study and the validation of
EP
experimental results. Computational fluid dynamics technique also required to be more advanced
CC
that can predict the complex behavior of the individual phases in the flotation system.
4.2. Holdup characteristics
A
The accurate interpretation of gas holdup is important for the appropriate design, operation, and scale-up of the flotation systems in a wide range of industrial application. Many authors have described the experimental measurements technique for measurement of average and radial gas holdup profile. A number of techniques such as phase isolation, electrical resistance tomography, dynamic gas disengagement, pressure drop etc. are in use to measure the local gas holdup. There is a number of empirical correlation proposed by different authors to predict the radial gas holdup 50
but these correlations are not universally applicable to any flotation system at the wide range of geometric variable, kinematic variable and physical property of the system. It is due to the complex behavior of the flotation system; no fundamental equation is available which can interpret the radial gas holdup profile. Smaller bubble size is recommended for the high gas holdup in the flotation process. Smaller bubble size has high interfacial area facilitate improvement in the
SC RI PT
bubble-particle interaction efficiency, induction time as well as carrying capacity, which in turn enhances the flotation efficiency. Knowledge of radial and axial variation of gas holdup plays an important role in the design and analysis of the flotation systems. Radial variation in gas holdup causes a rise in pressure fluctuation because of which liquid recirculation takes place in the flotation system. This liquid recirculation directs the mixing rate and transport efficiency. Successful implementation of CFD is still an open challenge to understand the radial and axial gas
N
U
holdup characteristics of the flotation system.
A
4.3. Bubble size and its distribution
M
High interfacial area facilitated by small bubbles allows them to improve the bubble-particle collection efficiency [137]. Reduced bubble size results in better process efficiency due to
D
enhanced mass transfer across the gas-liquid interface [266]. The non-invasive technique like PIV
TE
can be used to predict the flow pattern of the phases, bubble and particle size and its distribution, rise velocity and instantaneous velocity vector of a bubble. So, current bubble size measurement technique needs to be more advanced in order to work in presence of a large number of bubbles as
EP
well as measure the bubble size in any part of the column. The probability of bubble-particle collision, attachment, and detachment depend on the appropriate bubble and particle size. There is
CC
lack of studies on bubble size, bubble coalescence, bubble-particle collision, attachment and detachment phenomena in the vertical and horizontal direction in presence of the solid particle.
A
During particle separation, the feed contains a range of particle size from ultrafine to coarse size. Therefore, a flotation system must be designed in such way to target ultrafine particles as well as coarse size particle.
4.4. Entrainment Characteristics
51
Entrainment significantly reduces the recovery efficiency of the flotation process. There is a lack of studies on entrainment characteristics based on the effect of operating variables, geometric variables and physical properties of the system. Different entrainment models developed by different investigators are valid for mechanical and column flotation system. Implementation of these models needs further validation. For instance, the model of Yiantos and Contreras [239]
SC RI PT
demonstrates only the effect of particle size on entrainment behavior, however numerous other factors such as solid concentration in the feed, range of particle size, slurry viscosity, feed flow rate, particle density, slurry density are also significant to entrainment. Hence it is essential to examine the effect of the other factors influencing the entrainment characteristics. A general comprehensive mechanistic entrainment model needs to be formulated which covers all other important variables. Developing a model based on the process variable and operating parameter to
U
estimate the flotation efficiency is a major challenge in industrial application.
N
4.5. Mixing characteristics
A
Mixing characteristics is important for the modeling, design, and optimization of the flotation
M
processes. The intensity of mixing can be helpful to understand the degree of homogeneity of phases and is used to increase the transport efficiency of any system. Many authors have reported
D
considerable work on analysis of mixing characteristics using axial dispersion model but there is
TE
the scarcity of research work based on radial dispersion of the phases. Physical properties of the system greatly influence the mixing intensity. However, detail studies are required to analyze the effect of the flow pattern and physical properties on the mixing mechanism. Computation fluid
CC
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EP
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TE
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true distribution of flotation rate constants, Int J Miner Process 58 (2000) 145-166. [264] R.K. Tuteja, D.J. Spottiswood, V.N. Misras, Mathematical models of the column flotation process a review, Miner Eng 7 (1994) 1459-1472.
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D
M
A
51 (2011) 1864-1877.
75
M
A
N
U
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Figures:
A
CC
EP
TE
D
Fig. 1. Schematic diagram of FCSMC [27].
76
Downcomer Feed
Air inlet Nozzle Free Jet
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Plunging Jet
Mixing Zone
Recirculating Eddy
Pipe Flow Zone
Concentrate
Disengagement Zone
A
Tailings
N
U
Pulp Mixture
Cell
A
CC
EP
TE
D
M
Fig. 2. Schematic diagram of Jameson cell [54].
77
N
U
SC RI PT
Fig. 3. Schematic of flow regime map [85].
A
CC
EP
TE
D
M
A
Fig. 4. Plot of drift flux vs gas holdup applying Wallis [97].
Fig. 5. Schematic of photographic technique and BSD fitting in the air-water system.
78
Acquisition
Seeding
Flow
Illumination
Imaging
Storing
Enhancement
Quantization Interrogation
Correlation
Sampling
Estimation
N
U
Selection
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Pixelization
Analysis
M
A
Result
A
CC
EP
TE
D
Fig. 6. Steps of PIV technique.
79
Validation
Tables:
Table 1: Some correlations for gas holdup measurement. Author
dp db
ug usl
0.08
0.02
Shukla et al. [108]
H dc
Cs sl
0.433
Rel 1 Cs 0.594
0.3
d pore db
0.008
Bhunia et al. [105]
2.25
Abdulrahman [109]
1.196
1.16
d pore ds
2.86 0.264
A
CC
EP
TE
d g 2.2 Fr 1.07 Ar 0.84Eo 0.19 s dc
s 0.108
11
D
d g 0.085 c hr
p sl
Kumar and Khanna [107]
0.235
U
0.2
Pr 2 l ul
N
g 244.6 Re
p sl
0.02 g
2.46
0.820
A
g 290.69 Re
db d p
1.07 g
ug ul
M
1.09
ud g 3.60 10 l l c l 7
SC RI PT
Gas holdup correlation
80
Anastasiou et al. [110]
Table 2: Bubble generation techniques. Flotation technique/device
Bubble generation system
Bubble size range (m)
Sebba [77], Jauregi and Varley [142] Bennet [143]
Gas aphrons
Mechanical agitation or gas aspiration nozzle
10-100
Induced air flotation (IAF) Nozzle Flotation
Mechanical agitation
700-1500*
Gas aspiration nozzle to draw air into recycled water Sparger of porous stainless steel or ceramic Gas aspiration nozzle to draw air into recycled water in a down comer Electrolysis of diluted aqueous solutions (H2 and O2 bubbles) Injection of water/air mixture through static mixtures Reducing water pressure which is supersaturated at high pressure via needle valve. Reducing water pressure which is supersaturated at high pressure Electrolysis of diluted aqueous conducting solution at electrodes (Bubble generation takes place on electrode). Gas-water circulation method followed by coupling of palladium electrode with ultrasonication Stirring Surfactant solution at high speed Air injection system or Mechanical agitator Ultrasonication of mixed surfactant solution upon mixing of octafluoropropan gas at regular interval. Supersaturated water passes through the nozzle (pressure reduction)
400-800*
Yianatos et al. [144] Jameson and Manlapig [56], Clayton et al. [57] Zouboulis et al. [145,146] Yoon et al. [147]
Column Flotation
Lazaridis et al. [46]
Dissolved air flotation (DAF)
Edzwald [148], Couto et al. [149] Hosny [33]
Dissolved air flotation (DAF) Electroflotation (EF)
D
TE
EP
Jauregi et al. [65]
Colloidal Gas Aphrons Induced air flotation (IAF) Ultrasonication
CC
Ultrasonication
A
Oeffinger and Wheatley [151]
Takahashi et al. [152]
M
Microcel Flotation
Dissolved air flotation (DAF)
N
Electroflotation
Kim et al. [150]
Rubio et al. [39]
U
Jet flotation
A
Bennet [143]
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Author
81
0.0067-0.0012 100-600
20-40* 400* 30-100
10-100 40* 20
0.3-0.5
37-115.6 700-1500 0.4-0.7
5-40
Sarkar et al. [31] Kim et al. [153]
Chegeni et al. [154]
Electroflotation (EF) Dissolved air flotation (DAF) Column flotation
Hydrogen bubbles generated on platinum wire electrode. Reducing water pressure which is supersaturated at high pressure via nozzle. Sparger
15-23 19.2-54.2
800-2000
A
CC
EP
TE
D
M
A
N
U
SC RI PT
*represents mean bubble size
82
Table 3: Different techniques to measure bubble size distribution. Bubble size range (m)
Image analysis
Bubble sampling Bubble features generation methods Viewing box Orifice plate
Image analysis
Flat cell
Porous plate
75-655
Drift flux analysis
Calculated by measuring gas velocity and gas holdup Photographs captured after placing rectangular view box around the column filled with water
Ventury static mixer
420-900*
Yianatos et al. [144]
Image analysis (Zeiss digitizer)
Porous stainless steel or ceramic sparger
0.0067-0.0012*
O’Connor et al. [158]
Porous plate
O’Connor and Mills [158]
Refractive index of bubble and slurry (due to change in light intensity)
300-2000
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Unno and Inoue [155] Ahmed and Jameson [156] Dobby et al. [157]
U
Methods
Drift flux analysis
Rijk et al. [160]
Image analysis
Tucker et al. [161]
Porous plate
Biswal et al. [162]
Optical
Rykaart and Haarhof [163]
Image analysis
A
M
Drawing bubbles into a capillary tube Bubbles drawn into capillary under vacuum and transform its shape close spherical to cylindrical Calculated by measuring gas velocity and gas holdup Cuvette cell
Porous plate
1620-3340*
Sintered disc
0.261-0.290* (2-phase system) 0.261-0.291* (3-phase system)
Porous tube
320-770*
D
TE
EP
CC
Yoon [159]
A
N
Author
Dissolved air flotation Drawing bubbles Induced air into a capillary flotation tube Drawing bubbles Synthetic filter into a capillary cloth tube Measuring Dissolved air module (with air flotation filter) 83
10-300 390-2230*
300-2000 29-77*
Filippov et al. [166]
Drift flux analysis
Chen et al. [167]
Image analysis
Chen et al. [167] Zhou et al. [168], Grau and Heiskanen [169] Han et al. [170]
Image analysis Image analysis
Han et al. [170]
Optical (opticalsensor Image processing
Perforated plate
3700-4100*
Drawing bubbles into a capillary tube Calculated by measuring gas velocity and gas holdup Bubble viewer
Induced air flotation
530-1450*
Ventury static mixer
350-1100*
Bubble viewer Viewing chamber
Electroresistivity Particle counters
A
A
CC
EP
TE
D
*Mean bubble diameter (µm)
Induced air flotation Porous plate Induced air flotation
350-1750
Dissolved air flotation DAF Electroflotation Induced air flotation Dissolved air flotation
13-96
N
Particle counters (laser) Bubbles drawn into column (Special viewing chamber)
M
Rodrigues and Rubio [171]
Optical fibre
84
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Optical (optical sensor) Porous plate
U
Saberi et al. [164] Gorain et al. [165]
400-1200 1500-3600*
15-85 15-65 250-1500* 33-37.5*
Table 4: List of correlation for estimation of carrying capacity. Correlations
Espinosa-Gomez et al. [215]
Cm 0.068d80 p
Finch and dobby [177]
C A 0.05d80 p
Patwardhan and Honker [216]
C A n p d 3p p u g d b3
Patwardhan and Honker [216]
0.542 0.2 3 C A 522.54d 50 (n p d 50 p d b3 )usg
A
CC
EP
TE
D
M
A
N
U
SC RI PT
Author
85
Table 5: Models of probability of collision [261]. Model name
model
Langmuir-Blodgett model Sutherland model
PcLB (ks /(0.2 k )) 2 , where ks is the stoke’s number
Gaudin model
Pc 1.5(d p / db ) 2
Flint-Howarth
Pc (v p /(v p vb ))
Anfruns-Kitchener
Pc ((1 d p db ) 2 /(1 (v p / vb ))) (v p / vb ) 2 c0 /(1 (d p db )) 2
Weber-Paddock model
Pcg sin 2 m (1 d p / db ) 2 (v p / vb ) ; collision efficiency due to
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Pc 3(d p / db )
interceptional effect
Pc 1.5(d p / db ) 2 ; Reb < 1
N
Yoon-Luttrell model
U
gravitational effect Pc (1 (2 /(1 37 / Reb0.85 )))(d p / db ) ; collision efficiency due to
Pc 3(d p / db ) ; at potential flow condition
A
Pc (d p / db ) 2 (1.5 (4 Reb0.72/ 15)) ; at intermediate flow condition Pc 2 c /((1 v p / vb )vb Reb2 ) ; collision efficiency due to
M
Schulze model
interceptional effect
D
Pc (1 /(1 v p / vb ))(1 d p / db ) 2 )(k s /( ks a))b ; collision efficiency
A
CC
EP
TE
due to inertial effect
86
Table 6: Flotation kinetic models.
4a exp( Pe / 2) R 1 2 2 (1 a ) exp( aPe / 2 (1 a )) exp( aPe / 2) Pe 4 K a Pe * R R (1 exp( Kt ))
Model Finch and dobby model, based on axial dispersion, R is overall recovery, Rc is collection zone recovery, Rf is froth zone recovery VPI model
SC RI PT
Model equation 100 Rc R f R 1 Rc R f Rc
0.5
First order model, R denotes recovery at time t, R* represents maximum flotation recovery at infinite time, K is rate constsnt First order model, Rectangular distribution of flotatiblities
N
U
(1 exp( Kt )) R R * 1 kt
1 R R* 1 1 t / K
A M D
kt R R * m (1 Kt ) ln(1 Kt ) R R* 1 Kt
Fully mixed model
R (1 z )(1 e Kt ) z (1 e K t )
TE
EP
1 e Kt 2e Kt / 2 R R * 1 ( Kt / 2) 2 2
Second order model, Rectangular distribution of flotatiblities Three parameter model, fast (K) and slow K* flotatiblities Three parameter model, gamma distribution
*
a R R* 1 P at
Gas or solid adsorption model
Two parameter form, Triangular distribution 2nd order kinetic model
A
CC
R* K t R 1 R * Kt
87