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A new stability index for characterizing the colloidal gas aphrons dispersion
Accepted Manuscript Title: A new stability index for characterizing the colloidal gas aphrons dispersion Author: H. Sadeghialiabadi M.C. Amiri PII: DOI: Reference:
S0927-7757(15)00086-2 http://dx.doi.org/doi:10.1016/j.colsurfa.2015.01.058 COLSUA 19705
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
10-11-2014 22-1-2015 27-1-2015
Please cite this article as: H. Sadeghialiabadi, A new stability index for characterizing the colloidal gas aphrons dispersion, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2015), http://dx.doi.org/10.1016/j.colsurfa.2015.01.058 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.
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A new stability index for characterizing the colloidal gas aphrons dispersion
2
H. Sadeghialiabadi, M.C. Amiri1,
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Chemical Engineering Dept., Isfahan University of Technology, Isfahan, Iran
4 5 Abstract
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Aphrons are surfactant stabilized microbubbles with thick soapy shells. Stability is a key
8
feature of microbubbles. Colloidal gas aphrons (CGAs), with an average diameter of 50 μm,
9
offer particular advantages where the stability of microbubbles is of interest. Various factors
10
that affect on CGA stability such as surfactant type, concentration, and processing parameters
11
have been extensively studied. However, there is no simple and accurate stability index for
12
characterizing the stability of microbubbles dispersion. In this study, the stability of CGAs
13
dispersion has been examined based on the drainage curve by four stability indexes. The
14
surfactant of choice was nonyl phenol ethoxylate (NPE), a nonionic surfactant. The results
15
show that the one-tenth of drained liquid life (T0.1), the time elapsed when the drained liquid
16
from CGA dispersion reaches ten percent of its final height is the best indicator among the
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other stability indexes for characterizing the CGAs dispersion.
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Keywords: Colloidal gas aphrons; Stability indexes; One-tenth of drained liquid life index;
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Drainage curve
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Corresponding author: Email: Tel.: (+98)3133915615, Fax: (+98)3133912677. E-mail addresses: [email protected] (M.C. Amiri), [email protected] (H. Sadeghialiabadi)
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1. Introduction
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Colloidal gas aphrons (CGA) or aphrons for short, first described by Sebba in surface
3
phenomena literature, are surfactant stabilized gas microbubbles with diameters of the order
4
of µm. They have two main components: a spherical core filled with gas and a relatively thick
5
protective aqueous shell [1].
6
CGAs dispersion is generated by intense shearing force of a spinning disc in a surfactant
7
solution at high speeds of around 6500 rpm. Because the generated bubbles show some
8
colloidal properties, they are called colloidal gas aphrons (CGAs) or aphrons for short [1].
9
Aphrons appear to have an average diameter of about 50 μm and soapy shell of more than a
10
few μm in thickness. However, unresolved questions remain regarding the structure of
11
aphrons: nature and thickness of soapy shell, orientation of surfactant molecules at the gas–
12
liquid interface, and/or number of surfactant layers. The most widely accepted structure was
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suggested by Sebba as shown in Fig. 1.
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Fig.1. Proposed structure of a colloidal gas aphron by Sebba [2]
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CGAs have some unique properties: high interfacial area because of their small sizes, soapy
17
thick shell and high stability compared to the conventional foams, flow properties similar to
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those of water, gas content of 55 to 65%, make it the lightest compressible liquid at ordinary 2
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temperature and pressure conditions [3]. These features allow them to be pumped from the
2
generation place to the point of use without loss of their original structure.
3
Although the coalescence and shrinkage rate for aphrons are very low, the CGAs dispersion is
4
gradually separated into a clear liquid phase and a foam phase in which the aphrons are
5
inevitably crowded together more closely than the original dispersion. Details of clear solution
6
interface rise versus time (i.e. drainage curve) provide a very useful insight into the structure
7
of CGA dispersion. This is the basis of the method for the characterization of CGA
8
dispersions that has been developed by Amiri and Woodburn [1].
9
There are several applications of CGAs such as removal of organic components from wastes
10
[4, 5], removal of toxic wastes from soil [6-8], removal of fine particles from dispersion [4, 5],
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recovery of a wide variety of valuable materials ([4, 5, 9-11], clarification of suspensions [12],
12
protein recovery [13, 14], oil well drilling [15], recovery of gallic acid [16], and waste water
13
treatment [17]. A key property in the most applications of aphrons is their stability that is
14
characterized with various techniques.
15
The stability of a CGAs dispersion indicates its ability to resist changes in bubble size
16
distribution [12, 18]. However, measurement of the bubble size is not representative for some
17
reasons. First, aphrons with different diameters locate at different depth in a CGA dispersion
18
because of differences in their rising rate and therefore, the size of aphrons increases from
19
bottom to top. Second, shrinkage of aphrons may result in a smaller measured diameter than
20
the actual diameter (20). Thus sampling position and timing may significantly affect the
21
measurement results. Third, the limitations associated with an optical microscope make
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aphrons smaller than 10 microns difficult to be measured accurately. Jauregi et al. [19]
23
examined the stability and size distribution of aphrons by using microscopy connected to a
24
charge-coupled device (CCD) camera. Amiri and Woodburn [1] developed a macroscopic
25
method to study the stability of CGAs dispersion based on drainage curve.
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Various factors affecting the stability of CGAs including temperature, pressure, electrolyte
2
type, pH, concentration, type and structure of surfactant, and nanoparticle have been widely
3
investigated by other researchers [1, 9, 12, 20-29].
4
It has been generally accepted that the stable colloidal gas aphrons are difficult to form when
5
either concentration of surfactant (Cs) or time of aphron generation (Tg) is less than a
6
minimum value. Effects of Cs and Tg on the performance of CGAs have been extensively
7
studied and it is known that beyond a Cs and Tg threshold, the colloidal nature of generated
8
CGAs is independent of these two parameters [1, 5, 20].
9
However, studies on the effect of geometric specifications of aphron generator on the CGA
10
stability are limited. Lee et al. produced microbubbles of approximately 50 μm in a micro-
11
bubbler [30]. They found that a narrow bubble size distribution can be achieved by decreasing
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the threshold voltage.
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Amiri and Valsaraj investigated the influence of disc position in the surfactant solution on the
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separation efficiency in aphron flotation process [5]. They found that the highest separation
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efficiency in aphron flotation process is occurred when the spinning metal disc was positioned
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in an elevation of about 30% of the solution height from the bottom of the beaker [5]. This was a
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new finding that modified the Sebba’s idea that the produced surface wave is able to dissolve
18
enough air for complete CGA generation [31]. Sebba had recommended that the disc position
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should be 2cm below the surface of liquid [31].
20
In this study, the nonionic surfactant, Nonyl Phenol Ethoxylates (NPE), was used. This
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surfactant has a worldwide production of around 700,000 tons annually and is used in a wide
22
range of applications. Its main application is in industrial and institutional sectors (30%), and
23
household use (15%) as a cleaning agent [32, 33]. The remaining NPE is used in many
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industrial applications, e.g. as wetting agents, dispersants, emulsifiers, solubilizers, foaming
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agents and polymer stabilizers [34].
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The main objective of this work is to study the stability of CGAs dispersions with particular
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focus on the influence of disc size at various concentrations of surfactant and mixing times.
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2. Materials and methods
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2.1. Materials
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Pure water with a resistance of 18 MΩ cm at 25 0C was used. A nonionic surfactant, Nonyl
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Phenol Ethoxylate 20 (NPE20, Isfahan Copolymer Company), was examined. Chemical
7
structure of Nonyl Phenol Ethoxylate (NPE) is shown in Fig. 2. Table 1 shows the properties
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of NPE20 as reported by the supplier.
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Fig. 2. Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number
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of ethoxy units
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Table 1 Properties of NPE20 (supplier-reported)
2.2. Aphron Generator
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Fig. 3 shows the apparatus for aphron generation. This generator is similar to the one
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described by Sebba with minor changes in geometric specifications. Stirring rate was always
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fixed at 6500 rpm. Two concentrations of surfactant and three stirring times were examined.
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The size distribution of generated aphrons depends on the experimental conditions as shown
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in Figs. 4 and 5.
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Fig. 3. A plot of an aphron generator
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Fig. 4. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
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Fig. 5. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min.
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2.3. Drainage curve method
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Drainage curve is an established method to characterize CGAs dispersion. In this work, the
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drainage curve method was used to study the effect of disc diameter, surfactant concentration,
4
and mixing time on the CGAs performance. The method is based on determining the volume
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of drained liquid as a function of time in ambient conditions.
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Generated CGAs in each test were immediately transferred to a 0.5 liter measuring cylinder
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where the height of drained liquid (H) was recorded at various times.
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To plot the drainage curve, the dimensionless height of interface or normalized height
9
(H/H ∞ ) is drawn versus time. H ∞ is the ultimate height of CGA dispersion when the foam
10
completely collapses. All experiments in this work were performed at least in duplicate and
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the results are reported as mean values ± SD.
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2.4. Stability index
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Various stability indexes can be considered:
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a: A standard method for evaluation of conventional foam stability is called the time half life,
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T0.5. Measured half life in this case means the time elapsed when the drained liquid from CGA
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dispersion reaches its half of its final height.
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b: The one-tenth drained life can be considered as an indicator for evaluating the performance
18
of CGA dispersion. Therefore, a new stability index, one-tenth drained life, T0.1, is introduced:
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the time elapsed when the drained liquid from CGA dispersion reaches ten percent of its final
20
height.
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c: Initial slope of drainage curve can also be considered as an indicator for aphron size.
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Therefore, another stability index, initial slope was introduced: the slope of the best line fits
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three initial recorded drained volumes versus time.
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d: Linear slope of any drainage curve can also be considered as an indicator for aphron size.
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Therefore, another stability index, linear slope, was introduced: the slope of the linear section
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of drainage curve (including at least 8 points with coefficient of regression, R2, greater than
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99.9%)
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Measuring of all stability indexes have been demonstrated in Fig. 6 and the performance all
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indexes were examined in this work.
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Fig. 6. Graphical measurement of T0.5 , T0.1 , constant slope, and initial slope of a drainage curve
2.5 Surface tension measurement
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It was done using Processor Tensiometer K-12 version 5.05 Kruess GMBH- Hamburg, using
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Du Nouy ring. All measurements were carried out at room temperature (25±1)oC and each
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measurement test usually took about 10 minutes after preparing the samples. The tensiometer
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was calibrated by pure water every so often and all measurements were done by single method
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and in a semi-automatic mode
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3. Results
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The initial rising part of drainage curve is a good indicator of aphron bubble creaming rate
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[35]. Stokes’s law is a good approximate guide in predicting the rise up (creaming) of the
18
interface during CGA drainage. The rise velocity of a single aphron bubble depends on aphron
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size as follows:
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2 2 ⎛ g (ρF − ρ(r) ) r ⎞ u= ⎜ ⎟ ⎟ 9 ⎜⎝ μ ⎠
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where
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u= rise velocity
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g= gravitational acceleration
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ρ(r) = density of the aphron bubble of radius r
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r = radius of aphron
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ρF = density of fluid
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µ= dynamic viscosity of fluid
4 It should be noted that the density of an aphron bubble depends on its size according to
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1 1 Young–Laplace equation: ΔP = σ ( + ) where ΔP is the pressure difference across the r1 r2
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fluid interface, σ is the surface tension, and r1 and r2 are the principal radii of curvature. For
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a conventional bubble, the above formula becomes ΔP =
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consists of two spherical layers, it can be proved [2] that the Young-Laplace equation appears
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4σ . r
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The equation of state for an aphron bubble of radius r in a liquid at pressure P and temperature
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T can be written as:
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ΔP =
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where ρ(r) is the gas density in the aphron, M is the molecular weight of encapsulated air,
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and R is the universal gas constant. Rearranging the above equation gives:
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ρ(r) =
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ρ ( r ) = ρ (∞ ) + (
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where ρ(∞) is the density of the gas under normal conditions (temperature and pressure with
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a gas-liquid interface of zero curvature). Density of an aphron bubble increases with reduction
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in its radius and this leads to slower creaming rate in drainage curve. It should also be noted
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that the density of aphron bubble is always greater than ρ(r) because of its soapy shell.
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PM 4σM + RT rRT
4M σ )( ) RT r
(3)
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Furthermore, the following mathematical manipulation of creaming rate reveals that rising
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velocity of a aphron bubble is dependent on both the bubble size and surface tension. ⎛ ⎛ 4M σ ⎞ 2 ⎞ g ⎜ ρ F − ρ( ∞ ) − ( )( ) ⎟ r ⎟ 2 ⎞ ⎜ ⎛ g ρ − ρ (r) r ( ) 2 2 ⎝ 4M σ ⎞ 2 ⎞ RT r ⎠ ⎟ 2g ⎛ ⎛ F υ= ⎜ = ρ F − ρ( ∞ ) − ( )( ) ⎟ r ⎟ ⎟= ⎜ ⎜ ⎜ ⎟ 9⎜ 9 ⎝⎜ μ μ 9 μ RT r ⎠ ⎠ ⎟ ⎝ ⎝ ⎠ ⎜ ⎟ ⎝ ⎠ υ=
2g ⎛ ⎛ 4Mσ ⎞ ⎞ )⎟ r ⎟ ⎜ ⎜ (ρ F − ρ(∞))r − ( 9μ ⎝ ⎝ RT ⎠ ⎠
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It should be noticed that the importance of Equation (4) is that it shows when the surface
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tension remains constant, then, the creaming rate is a strong function of bubble size. However,
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this equation can not be used for calculating the creaming rate of CGAs as it describes the rise
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velocity of a single aphron bubble in an infinite liquid without any effect of the presence of
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neighboring bubbles. The effect of the local void fraction (gas phase fraction) on the drag
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force in aphron swarms is very complicated and beyond the scope of this work (37).
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In this work, a low surface active agent, NPE20 is used which can cause a little change in the
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surface tension when the concentration of surfactant is above 500 ppm as shown in Table 2.
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Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
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3.1. Effect of Disc Diameter
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Fig. 7 shows drainage curves of CGAs dispersions produced in the same conditions for
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different sizes of spinning disc when baffle position was set at L=28 mm.
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Fig. 7. Effect of spinning disc diameter on drainage curve for
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Fig. 7 clearly shows that more stable CGAs (consequently smaller bubbles) are generated
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when the diameter of spinning disc is large. This effect of disc diameter on the stability of
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generated CGAs is valid when the surfactant concentration increases from 750 ppm to 4000
Cs=750 ppm, Tg= 90 s
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ppm as shown in Fig. 8. As it was already discussed in Eq. 3, surfactant concentration affects
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the density of aphron bubbles. Equation (4) shows that both (ρ F − ρ(r) ) and r 2 can cause
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reduction in creaming flow. Decreasing in aphron size results in increasing the density of
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aphron and both terms (ρ F − ρ(r) ) and r 2 contribute in slowing down the creaming rate.
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Fig. 8. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 90 s
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Fig. 9 reveals that smaller bubble and consequently more stable CGAs are generated when the
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diameter of spinning disc is large even when the mixing time increases to 150 seconds.
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Fig. 9. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 150 s
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Comparing Figs. 10 and 9 shows increasing the surfactant concentration (from Cs=750 ppm to
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Cs=4000 ppm) can improve the stability of generated CGAs (smaller bubbles) for both
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spinning discs but slightly more for the large one. This improvement in the stability of
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generated CGAs for the large disc is due to availability of greater area for surfactant
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molecules at solid/liquid interface where they prefer to be accommodated.
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Fig. 10. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 150 s
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Fig. 11 shows that when the mixing time increases to 240 s, the large disc can generates more
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stable microbubbles in comparison to smaller disc.
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Fig. 11. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 240 s
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Comparing Figs. 11 and 12 reveals that when the surfactant concentration is sufficiently high,
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then the key role of spinning disc size is diminished and both drainage curves coincide with
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each other. This phenomenon can be explained as follows:
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For producing new surfaces (smaller bubbles), a certain amount of energy is required (as work
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of spinning shaft), but surfactant molecules can reduce the amount of required work by
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reducing the surface tension of aqueous phase. Therefore, it can be imagined when surfactant
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concentration is sufficiently high, then the smaller size disc is also able to supply the threshold
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required energy.
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Fig. 12. Effect of spinning disc diameter on drainage curve for
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Cs=4000 ppm, Tg= 240 s
12 4. Discussion
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The developed rise velocity of microbubbles in this work, Equation 4, shows that creaming
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rate, a critical issue for stability of microbubbles, depends on both the bubble size and surface
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tension. However, the low surface active agent used here, NPE20, can cause a little change in
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the surface tension of aqueous phase. To demonstrate the negligible effect of surface tension
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in the range of surfactant concentrations arisen in this study, the theoretical rise velocities of a
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100 µm aphron bubble are calculated and shown in Fig.13a. The actual rise velocity is of
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course lower than the theoretical value because of friction in aphrons swarm. Fig. 13b shows
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that the rise velocity of aphron bubbles for a given surface tension is strongly dependent on
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their sizes. Therefore, it is reasonable to assume any change in creaming rate in this work is
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due to the size of bubbles.
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Fig. 13a. Change in rise velocity of a 100 μm aphron bubble versus surface tension
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Fig. 13b. Calculated rise velocity versus aphron size for a constant surface tension of 45 mN/m
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In the experiments, the effect of spinning disc diameter on the characteristics of generated
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microbubbles has been investigated in various surfactant concentrations and mixing times.
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Increasing in disc diameter enhances the availability of greater area for accommodating the
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surfactant molecules at solid/liquid interface in addition to promoting the turbulency.
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Increasing the turbulency and interfacial area facilitate the formation of microbubbles.
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Furthermore, mixing operation must supply enough energy to the system for producing new
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surfaces (as bubbles) and surfactant molecules can reduce the amount of required energy by
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decreasing the surface tension of aqueous phase. Hence, mixing time, surfactant
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concentration, and spinning disc size may play roles in the size of generated colloidal gas
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aphrons in addition to baffle position that affects on turbulency progress. Nonetheless, for
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conciseness of discussion, only one baffle position has been reported in this work. To
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quantify the effects of various parameters, a collection of experimental conditions and results
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based on the presented drainage curves is summarized in Table 3.
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Any referred selected parameter can play a role in the stability of generated microbubbles.
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Table 3 can be examined for cross effects of various parameters. For example, it is expected
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that the effect of disc size is more prominent when surface tension is higher, as higher surface
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tension makes bubble generation unfavorable while higher disc size improves bubble
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formation.
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Table 3 Summary of the experimental conditions and results
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Fig. 7 demonstrates the effect of disc diameter when the surfactant concentration and mixing
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time are low while Fig. 8 shows the effect of disc diameter under the same conditions when
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the surfactant concentration is high. Detailed analysis of the data in table 3 for these figures is
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listed below.
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The first two rows (belongs to Fig. 7) show that under the same conditions, large disc in
26
comparison with small one produces more stable microbubbles (T0.5 index of 361 seconds 12
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instead of 211 seconds with a difference of 150 seconds). The T0.1 index supports this result
2
(127 s instead of 31 s). As lower slope represents smaller bubbles, hence, the initial slope
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index also supports this result (0.0017 mm/s instead of 0.0025 mm/s). On the other hand, the
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linear slope index does not support this outcome.
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The rows 3 and 4 (belongs to Fig. 8) also show the better performance of large disc with a T0.5
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index of 312 s instead of 281 s and a difference of 31 s when the surfactant concentration is
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4000ppm. Therefore, performance of large disc is more prominent (with a difference of 150 s
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instead of 31 s) when the concentration of surfactant is low (surface tension is high).
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The T0.1 index also supports this result (with a difference of 96 s for higher surface tension
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instead of 38 s for lower surface tension).
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The initial slope and the linear slope indexes are unable to detect such a fine discrimination.
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Fig. 11 demonstrates the effect of disc diameter when the surfactant concentration is low but
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mixing time is highest. Comparing rows 9 and 10 shows that under these conditions the
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performance of large disc is better than the small disc (309 s instead of 267 s) based on T0.5
15
index. Initial slope index as well as T0.1 index support this result (102 s instead of 86 s)
16
although linear slope index does not show this difference.
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To appreciate the role of mixing time, Fig. 7 (mixing time of 90 s) and Fig. 11 (mixing time of
18
240 s) should be compared. T0.5 index is 211 s for small disc when mixing time is 90 s instead
19
of 267 s when mixing time is 240 s. The corresponding values for large disc are 361s instead
20
of 309 s. The similar result is found using T0.1 index: 31 s when mixing time is 90 s instead of
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86 s when mixing time is 240 s for the small disc but 127 s instead of 102 s for the large disc.
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These results show that the role of mixing time is constructive only for the small size disc and
23
not for the large disc. This result that the large disc generates slightly less stable microbubbles
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at higher mixing time is odd even though both stability indexes indicate it. One possible
25
explanation may be the generation of more nano size bubbles at higher mixing time that can
26
not be detected in clear drained liquid phase (38).
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Comparing rows 5 and 6 (Fig. 9) with rows 7 and 8 (Fig. 10) reveals that when mixing time is
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150 seconds, T0.5 index shows a difference of 306-231=75 s when surfactant concentration is
3
750 ppm instead of 319-270= 49 s when surfactant concentration is 4000 ppm. Therefore, half
4
life index shows that the performance of large disc is more prominent when surfactant
5
concentration is low at moderate mixing time.
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Analyzing the data obtained from Figs. 9 and 10 based on the T0.1 index shows that when
7
surfactant concentration is 750 ppm, the time difference is 114-78= 36 s instead of 111-61=50
8
s when surfactant concentration is 4000 ppm. Therefore, the T0.1 index predicts that more
9
stable microbubbles are generated at highest surfactant concentration but with moderate
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mixing time.
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Fig. 12 demonstrates the effect of disc diameter when the surfactant concentration and mixing
12
time are both high. Comparing rows 11 and 12 shows that under these conditions the
13
performance of large and small discs are the same based on half-life index (214 s), i.e. the
14
effect of disc size is negligible when surfactant concentration and mixing time are high
15
enough. However, T0.1 index indicates that the large disc has a slightly better performance
16
than the small one (78 instead of 71 seconds). This comparison reveals that T0.1 index is a
17
better stability indicator than half-life index. Both initial slope index and linear slope index do
18
not support this result.
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5. Conclusions
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Four possible stability indexes (half-life time, one-tenth drained liquid life, initial slope, and
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linear slope of drainage curve) have been considered for analyzing the performance of CGAs
23
dispersion. The ability of each of these stability indexes has been examined in various mixing
24
times for aphron generation and surfactant concentrations with two spinning disc diameters. It
25
was found that the one-tenth drained liquid life is the most suitable for characterizing the
26
CGAs dispersion. In other words, the time elapsed when the drained liquid from CGA 14
Page 14 of 29
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dispersion reaches ten percent of its final height, T0.1, can predict more accurately than the
2
lengthy half-life time the performance of CGAs dispersion.
3
Acknowledgement
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The authors wish to acknowledge and appreciate the research deputy in Isfahan University of
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Technology for the financial support of this work.
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[1] M.C. Amiri, E. Woodburn, A method for the characterisation of colloidal gas aphron dispersions, Chemical engineering research & design, 68 (1990) 154-160. [2] F. Sebba, Foams and biliquid foams-aphrons, Wiley New York, 1987. [3] J.A. Attia, I.M. McKinley, D. Moreno-Magana, L. Pilon, Convective heat transfer in foams under laminar flow in pipes and tube bundles, International Journal of Heat and Mass Transfer, 55 (2012) 7823-7831. [4] M.A. Hashim, B.S. Gupta, The application of colloidal gas aphrons in the recovery of fine cellulose fibres from paper mill wastewater, Bioresource technology, 64 (1998) 199-204. [5] M.C. Amiri, K. Valsaraj, Effect of gas transfer on separation of whey protein with aphron flotation, Separation and purification technology, 35 (2004) 161-167. [6] R.R. Kommalapati, K.T. Valsaraj, W.D. Constant, D. Roy, Soil flushing using colloidal gas aphron suspensions generated from a plant-based surfactant, Journal of Hazardous materials, 60 (1998) 73-87. [7] S. Basu, P. Malpani, Removal of methyl orange and methylene blue dye from water using Colloidal Gas Aphron-effect of processes parameters, Separation Science and Technology, 36 (2001) 2997-3013. [8] D. Roy, K. Valsaraj, W. Constant, M. Darji, Removal of hazardous oily waste from a soil matrix using surfactants and colloidal gas aphron suspensions under different flow conditions, Journal of Hazardous materials, 38 (1994) 127-144. [9] P. Jauregi, S. Gilmour, J. Varley, Characterisation of colloidal gas aphrons for subsequent use for protein recovery, The Chemical Engineering Journal and The Biochemical Engineering Journal, 65 (1997) 1-11. [10] M.C. Amiri, Separation of ultra-fine sulphur particles from NTA dispersion by aphron flotation, International Journal of Engineering, 3 (1990) 148-153. [11] M.C. Amiri, Jalali, Ability of Aphron Flotation in Whey Treatment, Iranian journal of Chemistry & Chemical Engineering, 12 (1993). [12] M.B. Subramaniam, N. Blakebrough, M.A. Hashim, Clarification of suspensions by colloidal gas aphrons, Journal of Chemical Technology and Biotechnology, 48 (1990) 41-60. [13] M. Noble, A. Brown, P. Jauregi, A. Kaul, J. Varley, Protein recovery using gas–liquid dispersions, Journal of Chromatography B: Biomedical Sciences and Applications, 711 (1998) 31-43. [14] E. Fuda, P. Jauregi, D. Pyle, Recovery of lactoferrin and lactoperoxidase from sweet whey using colloidal gas aphrons (CGAs) generated from an anionic surfactant, AOT, Biotechnology progress, 20 (2004) 514-525. [15] F.B. Growcock, A. Belkin, M. Fosdick, M. Irving, B. O'Connor, T. Brookey, Recent advances in aphron drilling fluids, in: IADC/SPE Drilling Conference, Society of Petroleum Engineers, 2006. [16] D. Cosgrove, Ultrasound contrast agents: an overview, European journal of radiology, 60 (2006) 324-330. [17] D. Roy, K. Valsaraj, S. Kottai, Separation of organic dyes from wastewater by using colloidal gas aphrons, Separation science and technology, 27 (1992) 573-588. [18] K. Matsushita, A. Mollah, D. Stuckey, C. Del Cerro, A. Bailey, Predispersed solvent extraction of dilute products using colloidal gas aphrons and colloidal liquid aphrons: aphron preparation, stability and size, Colloids and surfaces, 69 (1992) 65-72. [19] P. Jauregi, G.R. Mitchell, J. Varley, Colloidal gas aphrons (CGA): dispersion and structural features, AIChE journal, 46 (2000) 24-36. [20] P. Chaphalkar, K. Valsaraj, D. Roy, A study of the size distribution and stability of colloidal gas aphrons using a particle size analyzer, Separation science and technology, 28 (1993) 1287-1302.
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2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
References
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[21] J. Cardoso, L. Spinelli, V. Monteiro, R. Lomba, E. Lucas, Influence of polymer and surfactant on the aphrons characteristics: Evaluation of fluid invasion controlling, eXPRESS Polymer Letters, 4 (2010) 474-479. [22] N. Bjorndalen, E. Kuru, Stability of Microbubble-Based Drilling Fluids Under Downhole Conditions, Journal of Canadian Petroleum Technology, 47 (2006). [23] S.V. Save, V.G. Pangarkar, Characterisation of colloidal gas aphrons, Chemical Engineering Communications, 127 (1994) 35-54. [24] D. Myers, Surfaces, Interfaces and Colloids: Principles and Applications. 1991, in, Weinheim, VCH Publishers, 1990. [25] H. Sadeghialiabadi, Performance evaluation of Colloidal Gas Aphrons (CGAs) generated by mixing nanoparticles and surfactant materials. Ph.D Thesis, in: Department of Chemical Engineering, Isfahan University of Technology (IUT), Isfahan, 2014. [26] S. Zhang, Q. Lan, Q. Liu, J. Xu, D. Sun, Aqueous foams stabilized by Laponite and CTAB, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 317 (2008) 406413. [27] T.N. Hunter, E.J. Wanless, G.J. Jameson, R.J. Pugh, Non-ionic surfactant interactions with hydrophobic nanoparticles: Impact on foam stability, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 347 (2009) 81-89. [28] M. Amiri, H. Sadeghialiabadi, Evaluating the Stability of Colloidal Gas Aphrons in the Presence of Montmorillonite Nanoparticles, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 457 (2014) 212-219. [29] J. Boos, W. Drenckhan, C. Stubenrauch, Protocol for studying aqueous foams stabilized by surfactant mixtures, Journal of Surfactants and Detergents, 16 (2013) 1-12. [30] S. Lee, W. Sutomo, C. Liu, E. Loth, Micro-fabricated electrolytic micro-bubblers, International journal of multiphase flow, 31 (2005) 706-722. [31] F. Sebba, Improved generator for micron-sized bubbles, Chemistry and Industry, (1985) 91-92. [32] G.-G. Ying, B. Williams, R. Kookana, Environmental fate of alkylphenols and alkylphenol ethoxylates—a review, Environment International, 28 (2002) 215-226. [33] T.P. Knepper, J.L. Berna, Surfactants: properties, production, and environmental aspects, Analysis and fate of surfactants in the aquatic environment. Elsevier, Amsterdam, The Netherlands, (2003) 1-50. [34] J.B. Plomley, P.W. Crozier, V.Y. Taguchi, Characterization of nonyl phenol ethoxylates in sewage treatment plants by combined precursor ion scanning and multiple reaction monitoring, Journal of Chromatography A, 854 (1999) 245-257. [35] M. Moshkelani, M.C. Amiri, Electrical conductivity as a novel technique for characterization of colloidal gas aphrons (CGA), Colloids and Surfaces A: Physicochemical and Engineering Aspects, 317 (2008) 262-269.
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17
Page 17 of 29
1 2
Tables Captions: Table 1 Properties of NPE20 (supplier-reported)
4
Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
5
Table 3 Summary of the experimental conditions and results
ip t
3
7
us
Table 1 Properties of NPE20 (supplier-report) Cloud Point (0C)
73-76 5-7
Hydroxyl No.
an
pH
49-52
1.06-1.08
M
Specific gravity@25 0C
110-130
MW(g/mole)
1079-1145
Hydrophilic-lipophilic balance (HLB)
15.4-16.3
Water Content (%)
0.5 MAX
d
Viscosity (cP)@25 0C
9
Ac ce pt e
8
cr
6
Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
Concentration of NPE 20
50
100
500
1000
2000
2500
3000
51.87
49.32
44.28
43.75
44.07
43.09
43.14
(ppm)
γ (mN/m)
10 11 12 13 14 18
Page 18 of 29
1 2 3
Table 3 Summary of the experimental conditions and results
No.
Tg (s)
T 0.5 (s)
T 0.1 (s)
(ppm)
Initial
Linear
slope
slope
(mm/s)
(mm/s)
37.5
750
90
211
31
0.0025
0.0017
2
59.5
750
90
361
127
0.0008
0.0017
3
37.5
4000
90
281
78
0.0011
0.0022
4
59.5
4000
90
312
116
5
37.5
750
150
231
78
6
59.5
750
150
306
7
37.5
4000
150
270
8
59.5
4000
150
319
9
37.5
750
240
10
59.5
750
240
11
37.5
4000
240
12
59.5
4000
240
us
cr
1
0.0024
0.0014
0.0030
an
0.0010
0.0011
0.0025
61
0.0015
0.0021
111
0.0009
0.0023
267
86
0.0012
0.0023
309
102
0.0009
0.0023
214
71
0.0016
0.0035
214
78
0.0017
0.0035
d
M
114
Ac ce pt e
4 5 6 7 8 9 10
Cs
Fig.
ip t
D (mm)
7 8 9
10 11 12
D, Cs, and Tg correspond to disk diameter, surfactant concentration, and mixing time respectively T 0.5: the time elapsed when the drained liquid from CGA dispersion reaches its fifty percent of its final height T 0.1: the time elapsed when the drained liquid from CGA dispersion reaches its ten percent of its final height. Initial slope: the slope of the best fit through the three data points in the beginning of drainage curve Linear slope: the slope of the linear section of drainage curve (including at least 6 points with R2 greater than 99.9%)
19
Page 19 of 29
1
Figures Captions:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Fig. 1 Proposed structure of a colloidal gas aphron by Sebba [2]. Fig. 2 Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number of ethoxy units.
19 20
Fig. 13a Change in rise velocity of a 100 μm aphron bubble versus surface tension
Fig. 4 A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
ip t
Fig. 5 A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min. Fig. 6 Graphical measurement of T0.5, T0.1 and constant slope and initial slope of a drainage curve graphically
cr
Fig. 7 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 90s
Fig. 8 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 90s
us
Fig. 9 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg = 150s
Fig. 10 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 150s Fig. 11 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg = 240s
an
Fig. 12 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 240s
d
M
Fig. 13b Calculated rise velocity versus aphron size for a constant surface tension of 45mN/m
Ac ce pt e
21 22 23 24
Fig. 3 A plot of an aphron generator
25 26 27 28
Fig. 1 Proposed structure of a colloidal gas aphron by Sebba [2]
20
Page 20 of 29
1
2
Fig. 2. Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number
3
of ethoxy units
ip t
4 5
7 8 9
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cr
6
Fig. 3. A plot of an aphron generator
10
21
Page 21 of 29
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an 5
Fig. 4. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
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2 3 4
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1
22
Page 22 of 29
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1
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Fig. 5. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min.
Ac ce pt e
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2 3 4
5 6
Fig. 6. Graphical measurement of T0.5 , T0.1, constant slope,
23
Page 23 of 29
1
and initial slope of a drainage curve
2
8 9
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Fig. 7. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 90 s
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4 5 6 7
M
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cr
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3
Fig. 8. Effect of spinning disc diameter on drainage curve for
24
Page 24 of 29
Cs=4000 ppm, Tg= 90 s
M
Fig. 9. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 150 s
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3 4 5
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1 2
6 7 8
Fig. 10. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 150 s
25
Page 25 of 29
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1
Fig. 11. Effect of spinning disc diameter on drainage curve for
3 4
Cs=750 ppm, Tg= 240 s
d Ac ce pt e
5
M
2
6 7
Fig. 12. Effect of spinning disc diameter on drainage curve for
26
Page 26 of 29
Cs=4000 ppm, Tg= 240 s
Fig. 13a. Change in rise velocity of a 100 μm aphron bubble versus surface tension
an
3 4 5
us
cr
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1 2
7 8 9 10
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M
6
Fig. 13b. Calculated rise velocity versus aphron size for a constant surface tension of 45 mN/m
11 12
27
Page 27 of 29
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Graphical Abstract
3
28
Page 28 of 29
Highlights
2
• Stability index is a key feature of colloidal gas aphrons (CGAs).
3
•
There is no simple and accurate stability index for CGAs dispersion.
4
•
Four stability indexes for CGAs dispersion have been compared.
5
•
When the drained liquid from CGA reaches 10% of its final height was called T0.1.
6
•
The one-tenth of drained liquid life,T0.1, has found the desirable stability index.
ip t
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8
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Page 29 of 29
S0927-7757(15)00086-2 http://dx.doi.org/doi:10.1016/j.colsurfa.2015.01.058 COLSUA 19705
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
10-11-2014 22-1-2015 27-1-2015
Please cite this article as: H. Sadeghialiabadi, A new stability index for characterizing the colloidal gas aphrons dispersion, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2015), http://dx.doi.org/10.1016/j.colsurfa.2015.01.058 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.
1
A new stability index for characterizing the colloidal gas aphrons dispersion
2
H. Sadeghialiabadi, M.C. Amiri1,
3
Chemical Engineering Dept., Isfahan University of Technology, Isfahan, Iran
4 5 Abstract
7
Aphrons are surfactant stabilized microbubbles with thick soapy shells. Stability is a key
8
feature of microbubbles. Colloidal gas aphrons (CGAs), with an average diameter of 50 μm,
9
offer particular advantages where the stability of microbubbles is of interest. Various factors
10
that affect on CGA stability such as surfactant type, concentration, and processing parameters
11
have been extensively studied. However, there is no simple and accurate stability index for
12
characterizing the stability of microbubbles dispersion. In this study, the stability of CGAs
13
dispersion has been examined based on the drainage curve by four stability indexes. The
14
surfactant of choice was nonyl phenol ethoxylate (NPE), a nonionic surfactant. The results
15
show that the one-tenth of drained liquid life (T0.1), the time elapsed when the drained liquid
16
from CGA dispersion reaches ten percent of its final height is the best indicator among the
17
other stability indexes for characterizing the CGAs dispersion.
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18 19
Keywords: Colloidal gas aphrons; Stability indexes; One-tenth of drained liquid life index;
20
Drainage curve
21 22 23 24 25 26 1
Corresponding author: Email: Tel.: (+98)3133915615, Fax: (+98)3133912677. E-mail addresses: [email protected] (M.C. Amiri), [email protected] (H. Sadeghialiabadi)
1
Page 1 of 29
1. Introduction
2
Colloidal gas aphrons (CGA) or aphrons for short, first described by Sebba in surface
3
phenomena literature, are surfactant stabilized gas microbubbles with diameters of the order
4
of µm. They have two main components: a spherical core filled with gas and a relatively thick
5
protective aqueous shell [1].
6
CGAs dispersion is generated by intense shearing force of a spinning disc in a surfactant
7
solution at high speeds of around 6500 rpm. Because the generated bubbles show some
8
colloidal properties, they are called colloidal gas aphrons (CGAs) or aphrons for short [1].
9
Aphrons appear to have an average diameter of about 50 μm and soapy shell of more than a
10
few μm in thickness. However, unresolved questions remain regarding the structure of
11
aphrons: nature and thickness of soapy shell, orientation of surfactant molecules at the gas–
12
liquid interface, and/or number of surfactant layers. The most widely accepted structure was
13
suggested by Sebba as shown in Fig. 1.
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1
14 15
Fig.1. Proposed structure of a colloidal gas aphron by Sebba [2]
16
CGAs have some unique properties: high interfacial area because of their small sizes, soapy
17
thick shell and high stability compared to the conventional foams, flow properties similar to
18
those of water, gas content of 55 to 65%, make it the lightest compressible liquid at ordinary 2
Page 2 of 29
temperature and pressure conditions [3]. These features allow them to be pumped from the
2
generation place to the point of use without loss of their original structure.
3
Although the coalescence and shrinkage rate for aphrons are very low, the CGAs dispersion is
4
gradually separated into a clear liquid phase and a foam phase in which the aphrons are
5
inevitably crowded together more closely than the original dispersion. Details of clear solution
6
interface rise versus time (i.e. drainage curve) provide a very useful insight into the structure
7
of CGA dispersion. This is the basis of the method for the characterization of CGA
8
dispersions that has been developed by Amiri and Woodburn [1].
9
There are several applications of CGAs such as removal of organic components from wastes
10
[4, 5], removal of toxic wastes from soil [6-8], removal of fine particles from dispersion [4, 5],
11
recovery of a wide variety of valuable materials ([4, 5, 9-11], clarification of suspensions [12],
12
protein recovery [13, 14], oil well drilling [15], recovery of gallic acid [16], and waste water
13
treatment [17]. A key property in the most applications of aphrons is their stability that is
14
characterized with various techniques.
15
The stability of a CGAs dispersion indicates its ability to resist changes in bubble size
16
distribution [12, 18]. However, measurement of the bubble size is not representative for some
17
reasons. First, aphrons with different diameters locate at different depth in a CGA dispersion
18
because of differences in their rising rate and therefore, the size of aphrons increases from
19
bottom to top. Second, shrinkage of aphrons may result in a smaller measured diameter than
20
the actual diameter (20). Thus sampling position and timing may significantly affect the
21
measurement results. Third, the limitations associated with an optical microscope make
22
aphrons smaller than 10 microns difficult to be measured accurately. Jauregi et al. [19]
23
examined the stability and size distribution of aphrons by using microscopy connected to a
24
charge-coupled device (CCD) camera. Amiri and Woodburn [1] developed a macroscopic
25
method to study the stability of CGAs dispersion based on drainage curve.
Ac ce pt e
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3
Page 3 of 29
Various factors affecting the stability of CGAs including temperature, pressure, electrolyte
2
type, pH, concentration, type and structure of surfactant, and nanoparticle have been widely
3
investigated by other researchers [1, 9, 12, 20-29].
4
It has been generally accepted that the stable colloidal gas aphrons are difficult to form when
5
either concentration of surfactant (Cs) or time of aphron generation (Tg) is less than a
6
minimum value. Effects of Cs and Tg on the performance of CGAs have been extensively
7
studied and it is known that beyond a Cs and Tg threshold, the colloidal nature of generated
8
CGAs is independent of these two parameters [1, 5, 20].
9
However, studies on the effect of geometric specifications of aphron generator on the CGA
10
stability are limited. Lee et al. produced microbubbles of approximately 50 μm in a micro-
11
bubbler [30]. They found that a narrow bubble size distribution can be achieved by decreasing
12
the threshold voltage.
13
Amiri and Valsaraj investigated the influence of disc position in the surfactant solution on the
14
separation efficiency in aphron flotation process [5]. They found that the highest separation
15
efficiency in aphron flotation process is occurred when the spinning metal disc was positioned
16
in an elevation of about 30% of the solution height from the bottom of the beaker [5]. This was a
17
new finding that modified the Sebba’s idea that the produced surface wave is able to dissolve
18
enough air for complete CGA generation [31]. Sebba had recommended that the disc position
19
should be 2cm below the surface of liquid [31].
20
In this study, the nonionic surfactant, Nonyl Phenol Ethoxylates (NPE), was used. This
21
surfactant has a worldwide production of around 700,000 tons annually and is used in a wide
22
range of applications. Its main application is in industrial and institutional sectors (30%), and
23
household use (15%) as a cleaning agent [32, 33]. The remaining NPE is used in many
24
industrial applications, e.g. as wetting agents, dispersants, emulsifiers, solubilizers, foaming
25
agents and polymer stabilizers [34].
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Page 4 of 29
The main objective of this work is to study the stability of CGAs dispersions with particular
2
focus on the influence of disc size at various concentrations of surfactant and mixing times.
3
2. Materials and methods
4
2.1. Materials
5
Pure water with a resistance of 18 MΩ cm at 25 0C was used. A nonionic surfactant, Nonyl
6
Phenol Ethoxylate 20 (NPE20, Isfahan Copolymer Company), was examined. Chemical
7
structure of Nonyl Phenol Ethoxylate (NPE) is shown in Fig. 2. Table 1 shows the properties
8
of NPE20 as reported by the supplier.
9
an
us
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1
Fig. 2. Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number
11
of ethoxy units
M
10
12
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Table 1 Properties of NPE20 (supplier-reported)
2.2. Aphron Generator
14
Fig. 3 shows the apparatus for aphron generation. This generator is similar to the one
15
described by Sebba with minor changes in geometric specifications. Stirring rate was always
16
fixed at 6500 rpm. Two concentrations of surfactant and three stirring times were examined.
17
The size distribution of generated aphrons depends on the experimental conditions as shown
18
in Figs. 4 and 5.
19
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13
Fig. 3. A plot of an aphron generator
20 21 22 23
Fig. 4. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
24 25 26
Fig. 5. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min.
5
Page 5 of 29
2.3. Drainage curve method
2
Drainage curve is an established method to characterize CGAs dispersion. In this work, the
3
drainage curve method was used to study the effect of disc diameter, surfactant concentration,
4
and mixing time on the CGAs performance. The method is based on determining the volume
5
of drained liquid as a function of time in ambient conditions.
6
Generated CGAs in each test were immediately transferred to a 0.5 liter measuring cylinder
7
where the height of drained liquid (H) was recorded at various times.
8
To plot the drainage curve, the dimensionless height of interface or normalized height
9
(H/H ∞ ) is drawn versus time. H ∞ is the ultimate height of CGA dispersion when the foam
10
completely collapses. All experiments in this work were performed at least in duplicate and
11
the results are reported as mean values ± SD.
12
2.4. Stability index
13
Various stability indexes can be considered:
14
a: A standard method for evaluation of conventional foam stability is called the time half life,
15
T0.5. Measured half life in this case means the time elapsed when the drained liquid from CGA
16
dispersion reaches its half of its final height.
17
b: The one-tenth drained life can be considered as an indicator for evaluating the performance
18
of CGA dispersion. Therefore, a new stability index, one-tenth drained life, T0.1, is introduced:
19
the time elapsed when the drained liquid from CGA dispersion reaches ten percent of its final
20
height.
21
c: Initial slope of drainage curve can also be considered as an indicator for aphron size.
22
Therefore, another stability index, initial slope was introduced: the slope of the best line fits
23
three initial recorded drained volumes versus time.
24
d: Linear slope of any drainage curve can also be considered as an indicator for aphron size.
25
Therefore, another stability index, linear slope, was introduced: the slope of the linear section
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Page 6 of 29
1
of drainage curve (including at least 8 points with coefficient of regression, R2, greater than
2
99.9%)
3
Measuring of all stability indexes have been demonstrated in Fig. 6 and the performance all
4
indexes were examined in this work.
6 7
Fig. 6. Graphical measurement of T0.5 , T0.1 , constant slope, and initial slope of a drainage curve
2.5 Surface tension measurement
us
9
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8
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5
It was done using Processor Tensiometer K-12 version 5.05 Kruess GMBH- Hamburg, using
11
Du Nouy ring. All measurements were carried out at room temperature (25±1)oC and each
12
measurement test usually took about 10 minutes after preparing the samples. The tensiometer
13
was calibrated by pure water every so often and all measurements were done by single method
14
and in a semi-automatic mode
15
3. Results
16
The initial rising part of drainage curve is a good indicator of aphron bubble creaming rate
17
[35]. Stokes’s law is a good approximate guide in predicting the rise up (creaming) of the
18
interface during CGA drainage. The rise velocity of a single aphron bubble depends on aphron
19
size as follows:
20
2 2 ⎛ g (ρF − ρ(r) ) r ⎞ u= ⎜ ⎟ ⎟ 9 ⎜⎝ μ ⎠
21
where
22
u= rise velocity
23
g= gravitational acceleration
24
ρ(r) = density of the aphron bubble of radius r
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(1)
7
Page 7 of 29
1
r = radius of aphron
2
ρF = density of fluid
3
µ= dynamic viscosity of fluid
4 It should be noted that the density of an aphron bubble depends on its size according to
6
1 1 Young–Laplace equation: ΔP = σ ( + ) where ΔP is the pressure difference across the r1 r2
7
fluid interface, σ is the surface tension, and r1 and r2 are the principal radii of curvature. For
8
a conventional bubble, the above formula becomes ΔP =
9
consists of two spherical layers, it can be proved [2] that the Young-Laplace equation appears
cr
ip t
5
an
us
2σ . But as the shell of aphron r
4σ . r
as ΔP =
11
The equation of state for an aphron bubble of radius r in a liquid at pressure P and temperature
12
T can be written as:
13
ΔP =
14
where ρ(r) is the gas density in the aphron, M is the molecular weight of encapsulated air,
15
and R is the universal gas constant. Rearranging the above equation gives:
16
ρ(r) =
17
ρ ( r ) = ρ (∞ ) + (
18
where ρ(∞) is the density of the gas under normal conditions (temperature and pressure with
19
a gas-liquid interface of zero curvature). Density of an aphron bubble increases with reduction
20
in its radius and this leads to slower creaming rate in drainage curve. It should also be noted
21
that the density of aphron bubble is always greater than ρ(r) because of its soapy shell.
Ac ce pt e
4σ 4σ R ⇒P+ = T ρ (r) r r M
d
M
10
(2)
PM 4σM + RT rRT
4M σ )( ) RT r
(3)
8
Page 8 of 29
1
Furthermore, the following mathematical manipulation of creaming rate reveals that rising
2
velocity of a aphron bubble is dependent on both the bubble size and surface tension. ⎛ ⎛ 4M σ ⎞ 2 ⎞ g ⎜ ρ F − ρ( ∞ ) − ( )( ) ⎟ r ⎟ 2 ⎞ ⎜ ⎛ g ρ − ρ (r) r ( ) 2 2 ⎝ 4M σ ⎞ 2 ⎞ RT r ⎠ ⎟ 2g ⎛ ⎛ F υ= ⎜ = ρ F − ρ( ∞ ) − ( )( ) ⎟ r ⎟ ⎟= ⎜ ⎜ ⎜ ⎟ 9⎜ 9 ⎝⎜ μ μ 9 μ RT r ⎠ ⎠ ⎟ ⎝ ⎝ ⎠ ⎜ ⎟ ⎝ ⎠ υ=
2g ⎛ ⎛ 4Mσ ⎞ ⎞ )⎟ r ⎟ ⎜ ⎜ (ρ F − ρ(∞))r − ( 9μ ⎝ ⎝ RT ⎠ ⎠
( 4)
ip t
3
cr
4
It should be noticed that the importance of Equation (4) is that it shows when the surface
6
tension remains constant, then, the creaming rate is a strong function of bubble size. However,
7
this equation can not be used for calculating the creaming rate of CGAs as it describes the rise
8
velocity of a single aphron bubble in an infinite liquid without any effect of the presence of
9
neighboring bubbles. The effect of the local void fraction (gas phase fraction) on the drag
M
an
us
5
force in aphron swarms is very complicated and beyond the scope of this work (37).
11
In this work, a low surface active agent, NPE20 is used which can cause a little change in the
12
surface tension when the concentration of surfactant is above 500 ppm as shown in Table 2.
Ac ce pt e
13
d
10
Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
14
3.1. Effect of Disc Diameter
15
Fig. 7 shows drainage curves of CGAs dispersions produced in the same conditions for
16
different sizes of spinning disc when baffle position was set at L=28 mm.
17 18 19 20
Fig. 7. Effect of spinning disc diameter on drainage curve for
21
Fig. 7 clearly shows that more stable CGAs (consequently smaller bubbles) are generated
22
when the diameter of spinning disc is large. This effect of disc diameter on the stability of
23
generated CGAs is valid when the surfactant concentration increases from 750 ppm to 4000
Cs=750 ppm, Tg= 90 s
9
Page 9 of 29
ppm as shown in Fig. 8. As it was already discussed in Eq. 3, surfactant concentration affects
2
the density of aphron bubbles. Equation (4) shows that both (ρ F − ρ(r) ) and r 2 can cause
3
reduction in creaming flow. Decreasing in aphron size results in increasing the density of
4
aphron and both terms (ρ F − ρ(r) ) and r 2 contribute in slowing down the creaming rate.
5 6
Fig. 8. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 90 s
cr
7
ip t
1
Fig. 9 reveals that smaller bubble and consequently more stable CGAs are generated when the
9
diameter of spinning disc is large even when the mixing time increases to 150 seconds.
us
8
13
Fig. 9. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 150 s
M
11 12
an
10
Comparing Figs. 10 and 9 shows increasing the surfactant concentration (from Cs=750 ppm to
15
Cs=4000 ppm) can improve the stability of generated CGAs (smaller bubbles) for both
16
spinning discs but slightly more for the large one. This improvement in the stability of
17
generated CGAs for the large disc is due to availability of greater area for surfactant
18
molecules at solid/liquid interface where they prefer to be accommodated.
20 21 22
Ac ce pt e
19
d
14
Fig. 10. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 150 s
23
Fig. 11 shows that when the mixing time increases to 240 s, the large disc can generates more
24
stable microbubbles in comparison to smaller disc.
25 26
Fig. 11. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 240 s
27 10
Page 10 of 29
Comparing Figs. 11 and 12 reveals that when the surfactant concentration is sufficiently high,
2
then the key role of spinning disc size is diminished and both drainage curves coincide with
3
each other. This phenomenon can be explained as follows:
4
For producing new surfaces (smaller bubbles), a certain amount of energy is required (as work
5
of spinning shaft), but surfactant molecules can reduce the amount of required work by
6
reducing the surface tension of aqueous phase. Therefore, it can be imagined when surfactant
7
concentration is sufficiently high, then the smaller size disc is also able to supply the threshold
8
required energy.
9 10 11
us
cr
ip t
1
Fig. 12. Effect of spinning disc diameter on drainage curve for
an
Cs=4000 ppm, Tg= 240 s
12 4. Discussion
14
The developed rise velocity of microbubbles in this work, Equation 4, shows that creaming
15
rate, a critical issue for stability of microbubbles, depends on both the bubble size and surface
16
tension. However, the low surface active agent used here, NPE20, can cause a little change in
17
the surface tension of aqueous phase. To demonstrate the negligible effect of surface tension
18
in the range of surfactant concentrations arisen in this study, the theoretical rise velocities of a
19
100 µm aphron bubble are calculated and shown in Fig.13a. The actual rise velocity is of
20
course lower than the theoretical value because of friction in aphrons swarm. Fig. 13b shows
21
that the rise velocity of aphron bubbles for a given surface tension is strongly dependent on
22
their sizes. Therefore, it is reasonable to assume any change in creaming rate in this work is
23
due to the size of bubbles.
Ac ce pt e
d
M
13
24 25
Fig. 13a. Change in rise velocity of a 100 μm aphron bubble versus surface tension
26 27 28
Fig. 13b. Calculated rise velocity versus aphron size for a constant surface tension of 45 mN/m
11
Page 11 of 29
In the experiments, the effect of spinning disc diameter on the characteristics of generated
2
microbubbles has been investigated in various surfactant concentrations and mixing times.
3
Increasing in disc diameter enhances the availability of greater area for accommodating the
4
surfactant molecules at solid/liquid interface in addition to promoting the turbulency.
5
Increasing the turbulency and interfacial area facilitate the formation of microbubbles.
6
Furthermore, mixing operation must supply enough energy to the system for producing new
7
surfaces (as bubbles) and surfactant molecules can reduce the amount of required energy by
8
decreasing the surface tension of aqueous phase. Hence, mixing time, surfactant
9
concentration, and spinning disc size may play roles in the size of generated colloidal gas
10
aphrons in addition to baffle position that affects on turbulency progress. Nonetheless, for
11
conciseness of discussion, only one baffle position has been reported in this work. To
12
quantify the effects of various parameters, a collection of experimental conditions and results
13
based on the presented drainage curves is summarized in Table 3.
14
Any referred selected parameter can play a role in the stability of generated microbubbles.
15
Table 3 can be examined for cross effects of various parameters. For example, it is expected
16
that the effect of disc size is more prominent when surface tension is higher, as higher surface
17
tension makes bubble generation unfavorable while higher disc size improves bubble
18
formation.
20
cr
us
an
M
d
Ac ce pt e
19
ip t
1
Table 3 Summary of the experimental conditions and results
21
Fig. 7 demonstrates the effect of disc diameter when the surfactant concentration and mixing
22
time are low while Fig. 8 shows the effect of disc diameter under the same conditions when
23
the surfactant concentration is high. Detailed analysis of the data in table 3 for these figures is
24
listed below.
25
The first two rows (belongs to Fig. 7) show that under the same conditions, large disc in
26
comparison with small one produces more stable microbubbles (T0.5 index of 361 seconds 12
Page 12 of 29
instead of 211 seconds with a difference of 150 seconds). The T0.1 index supports this result
2
(127 s instead of 31 s). As lower slope represents smaller bubbles, hence, the initial slope
3
index also supports this result (0.0017 mm/s instead of 0.0025 mm/s). On the other hand, the
4
linear slope index does not support this outcome.
5
The rows 3 and 4 (belongs to Fig. 8) also show the better performance of large disc with a T0.5
6
index of 312 s instead of 281 s and a difference of 31 s when the surfactant concentration is
7
4000ppm. Therefore, performance of large disc is more prominent (with a difference of 150 s
8
instead of 31 s) when the concentration of surfactant is low (surface tension is high).
9
The T0.1 index also supports this result (with a difference of 96 s for higher surface tension
us
cr
ip t
1
instead of 38 s for lower surface tension).
11
The initial slope and the linear slope indexes are unable to detect such a fine discrimination.
12
Fig. 11 demonstrates the effect of disc diameter when the surfactant concentration is low but
13
mixing time is highest. Comparing rows 9 and 10 shows that under these conditions the
14
performance of large disc is better than the small disc (309 s instead of 267 s) based on T0.5
15
index. Initial slope index as well as T0.1 index support this result (102 s instead of 86 s)
16
although linear slope index does not show this difference.
17
To appreciate the role of mixing time, Fig. 7 (mixing time of 90 s) and Fig. 11 (mixing time of
18
240 s) should be compared. T0.5 index is 211 s for small disc when mixing time is 90 s instead
19
of 267 s when mixing time is 240 s. The corresponding values for large disc are 361s instead
20
of 309 s. The similar result is found using T0.1 index: 31 s when mixing time is 90 s instead of
21
86 s when mixing time is 240 s for the small disc but 127 s instead of 102 s for the large disc.
22
These results show that the role of mixing time is constructive only for the small size disc and
23
not for the large disc. This result that the large disc generates slightly less stable microbubbles
24
at higher mixing time is odd even though both stability indexes indicate it. One possible
25
explanation may be the generation of more nano size bubbles at higher mixing time that can
26
not be detected in clear drained liquid phase (38).
Ac ce pt e
d
M
an
10
13
Page 13 of 29
Comparing rows 5 and 6 (Fig. 9) with rows 7 and 8 (Fig. 10) reveals that when mixing time is
2
150 seconds, T0.5 index shows a difference of 306-231=75 s when surfactant concentration is
3
750 ppm instead of 319-270= 49 s when surfactant concentration is 4000 ppm. Therefore, half
4
life index shows that the performance of large disc is more prominent when surfactant
5
concentration is low at moderate mixing time.
6
Analyzing the data obtained from Figs. 9 and 10 based on the T0.1 index shows that when
7
surfactant concentration is 750 ppm, the time difference is 114-78= 36 s instead of 111-61=50
8
s when surfactant concentration is 4000 ppm. Therefore, the T0.1 index predicts that more
9
stable microbubbles are generated at highest surfactant concentration but with moderate
us
cr
ip t
1
mixing time.
11
Fig. 12 demonstrates the effect of disc diameter when the surfactant concentration and mixing
12
time are both high. Comparing rows 11 and 12 shows that under these conditions the
13
performance of large and small discs are the same based on half-life index (214 s), i.e. the
14
effect of disc size is negligible when surfactant concentration and mixing time are high
15
enough. However, T0.1 index indicates that the large disc has a slightly better performance
16
than the small one (78 instead of 71 seconds). This comparison reveals that T0.1 index is a
17
better stability indicator than half-life index. Both initial slope index and linear slope index do
18
not support this result.
M
d
Ac ce pt e
19
an
10
20
5. Conclusions
21
Four possible stability indexes (half-life time, one-tenth drained liquid life, initial slope, and
22
linear slope of drainage curve) have been considered for analyzing the performance of CGAs
23
dispersion. The ability of each of these stability indexes has been examined in various mixing
24
times for aphron generation and surfactant concentrations with two spinning disc diameters. It
25
was found that the one-tenth drained liquid life is the most suitable for characterizing the
26
CGAs dispersion. In other words, the time elapsed when the drained liquid from CGA 14
Page 14 of 29
1
dispersion reaches ten percent of its final height, T0.1, can predict more accurately than the
2
lengthy half-life time the performance of CGAs dispersion.
3
Acknowledgement
5
The authors wish to acknowledge and appreciate the research deputy in Isfahan University of
6
Technology for the financial support of this work.
7
cr
8
us
an
9
14 15 16 17 18
d
13
Ac ce pt e
12
M
10 11
ip t
4
19 20 21 22
15
Page 15 of 29
M
an
us
cr
ip t
[1] M.C. Amiri, E. Woodburn, A method for the characterisation of colloidal gas aphron dispersions, Chemical engineering research & design, 68 (1990) 154-160. [2] F. Sebba, Foams and biliquid foams-aphrons, Wiley New York, 1987. [3] J.A. Attia, I.M. McKinley, D. Moreno-Magana, L. Pilon, Convective heat transfer in foams under laminar flow in pipes and tube bundles, International Journal of Heat and Mass Transfer, 55 (2012) 7823-7831. [4] M.A. Hashim, B.S. Gupta, The application of colloidal gas aphrons in the recovery of fine cellulose fibres from paper mill wastewater, Bioresource technology, 64 (1998) 199-204. [5] M.C. Amiri, K. Valsaraj, Effect of gas transfer on separation of whey protein with aphron flotation, Separation and purification technology, 35 (2004) 161-167. [6] R.R. Kommalapati, K.T. Valsaraj, W.D. Constant, D. Roy, Soil flushing using colloidal gas aphron suspensions generated from a plant-based surfactant, Journal of Hazardous materials, 60 (1998) 73-87. [7] S. Basu, P. Malpani, Removal of methyl orange and methylene blue dye from water using Colloidal Gas Aphron-effect of processes parameters, Separation Science and Technology, 36 (2001) 2997-3013. [8] D. Roy, K. Valsaraj, W. Constant, M. Darji, Removal of hazardous oily waste from a soil matrix using surfactants and colloidal gas aphron suspensions under different flow conditions, Journal of Hazardous materials, 38 (1994) 127-144. [9] P. Jauregi, S. Gilmour, J. Varley, Characterisation of colloidal gas aphrons for subsequent use for protein recovery, The Chemical Engineering Journal and The Biochemical Engineering Journal, 65 (1997) 1-11. [10] M.C. Amiri, Separation of ultra-fine sulphur particles from NTA dispersion by aphron flotation, International Journal of Engineering, 3 (1990) 148-153. [11] M.C. Amiri, Jalali, Ability of Aphron Flotation in Whey Treatment, Iranian journal of Chemistry & Chemical Engineering, 12 (1993). [12] M.B. Subramaniam, N. Blakebrough, M.A. Hashim, Clarification of suspensions by colloidal gas aphrons, Journal of Chemical Technology and Biotechnology, 48 (1990) 41-60. [13] M. Noble, A. Brown, P. Jauregi, A. Kaul, J. Varley, Protein recovery using gas–liquid dispersions, Journal of Chromatography B: Biomedical Sciences and Applications, 711 (1998) 31-43. [14] E. Fuda, P. Jauregi, D. Pyle, Recovery of lactoferrin and lactoperoxidase from sweet whey using colloidal gas aphrons (CGAs) generated from an anionic surfactant, AOT, Biotechnology progress, 20 (2004) 514-525. [15] F.B. Growcock, A. Belkin, M. Fosdick, M. Irving, B. O'Connor, T. Brookey, Recent advances in aphron drilling fluids, in: IADC/SPE Drilling Conference, Society of Petroleum Engineers, 2006. [16] D. Cosgrove, Ultrasound contrast agents: an overview, European journal of radiology, 60 (2006) 324-330. [17] D. Roy, K. Valsaraj, S. Kottai, Separation of organic dyes from wastewater by using colloidal gas aphrons, Separation science and technology, 27 (1992) 573-588. [18] K. Matsushita, A. Mollah, D. Stuckey, C. Del Cerro, A. Bailey, Predispersed solvent extraction of dilute products using colloidal gas aphrons and colloidal liquid aphrons: aphron preparation, stability and size, Colloids and surfaces, 69 (1992) 65-72. [19] P. Jauregi, G.R. Mitchell, J. Varley, Colloidal gas aphrons (CGA): dispersion and structural features, AIChE journal, 46 (2000) 24-36. [20] P. Chaphalkar, K. Valsaraj, D. Roy, A study of the size distribution and stability of colloidal gas aphrons using a particle size analyzer, Separation science and technology, 28 (1993) 1287-1302.
d
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
References
Ac ce pt e
1
16
Page 16 of 29
41
d
M
an
us
cr
ip t
[21] J. Cardoso, L. Spinelli, V. Monteiro, R. Lomba, E. Lucas, Influence of polymer and surfactant on the aphrons characteristics: Evaluation of fluid invasion controlling, eXPRESS Polymer Letters, 4 (2010) 474-479. [22] N. Bjorndalen, E. Kuru, Stability of Microbubble-Based Drilling Fluids Under Downhole Conditions, Journal of Canadian Petroleum Technology, 47 (2006). [23] S.V. Save, V.G. Pangarkar, Characterisation of colloidal gas aphrons, Chemical Engineering Communications, 127 (1994) 35-54. [24] D. Myers, Surfaces, Interfaces and Colloids: Principles and Applications. 1991, in, Weinheim, VCH Publishers, 1990. [25] H. Sadeghialiabadi, Performance evaluation of Colloidal Gas Aphrons (CGAs) generated by mixing nanoparticles and surfactant materials. Ph.D Thesis, in: Department of Chemical Engineering, Isfahan University of Technology (IUT), Isfahan, 2014. [26] S. Zhang, Q. Lan, Q. Liu, J. Xu, D. Sun, Aqueous foams stabilized by Laponite and CTAB, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 317 (2008) 406413. [27] T.N. Hunter, E.J. Wanless, G.J. Jameson, R.J. Pugh, Non-ionic surfactant interactions with hydrophobic nanoparticles: Impact on foam stability, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 347 (2009) 81-89. [28] M. Amiri, H. Sadeghialiabadi, Evaluating the Stability of Colloidal Gas Aphrons in the Presence of Montmorillonite Nanoparticles, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 457 (2014) 212-219. [29] J. Boos, W. Drenckhan, C. Stubenrauch, Protocol for studying aqueous foams stabilized by surfactant mixtures, Journal of Surfactants and Detergents, 16 (2013) 1-12. [30] S. Lee, W. Sutomo, C. Liu, E. Loth, Micro-fabricated electrolytic micro-bubblers, International journal of multiphase flow, 31 (2005) 706-722. [31] F. Sebba, Improved generator for micron-sized bubbles, Chemistry and Industry, (1985) 91-92. [32] G.-G. Ying, B. Williams, R. Kookana, Environmental fate of alkylphenols and alkylphenol ethoxylates—a review, Environment International, 28 (2002) 215-226. [33] T.P. Knepper, J.L. Berna, Surfactants: properties, production, and environmental aspects, Analysis and fate of surfactants in the aquatic environment. Elsevier, Amsterdam, The Netherlands, (2003) 1-50. [34] J.B. Plomley, P.W. Crozier, V.Y. Taguchi, Characterization of nonyl phenol ethoxylates in sewage treatment plants by combined precursor ion scanning and multiple reaction monitoring, Journal of Chromatography A, 854 (1999) 245-257. [35] M. Moshkelani, M.C. Amiri, Electrical conductivity as a novel technique for characterization of colloidal gas aphrons (CGA), Colloids and Surfaces A: Physicochemical and Engineering Aspects, 317 (2008) 262-269.
Ac ce pt e
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
17
Page 17 of 29
1 2
Tables Captions: Table 1 Properties of NPE20 (supplier-reported)
4
Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
5
Table 3 Summary of the experimental conditions and results
ip t
3
7
us
Table 1 Properties of NPE20 (supplier-report) Cloud Point (0C)
73-76 5-7
Hydroxyl No.
an
pH
49-52
1.06-1.08
M
Specific gravity@25 0C
110-130
MW(g/mole)
1079-1145
Hydrophilic-lipophilic balance (HLB)
15.4-16.3
Water Content (%)
0.5 MAX
d
Viscosity (cP)@25 0C
9
Ac ce pt e
8
cr
6
Table 2 Effect of concentration of NPE20 surfactant on the surface tension of water
Concentration of NPE 20
50
100
500
1000
2000
2500
3000
51.87
49.32
44.28
43.75
44.07
43.09
43.14
(ppm)
γ (mN/m)
10 11 12 13 14 18
Page 18 of 29
1 2 3
Table 3 Summary of the experimental conditions and results
No.
Tg (s)
T 0.5 (s)
T 0.1 (s)
(ppm)
Initial
Linear
slope
slope
(mm/s)
(mm/s)
37.5
750
90
211
31
0.0025
0.0017
2
59.5
750
90
361
127
0.0008
0.0017
3
37.5
4000
90
281
78
0.0011
0.0022
4
59.5
4000
90
312
116
5
37.5
750
150
231
78
6
59.5
750
150
306
7
37.5
4000
150
270
8
59.5
4000
150
319
9
37.5
750
240
10
59.5
750
240
11
37.5
4000
240
12
59.5
4000
240
us
cr
1
0.0024
0.0014
0.0030
an
0.0010
0.0011
0.0025
61
0.0015
0.0021
111
0.0009
0.0023
267
86
0.0012
0.0023
309
102
0.0009
0.0023
214
71
0.0016
0.0035
214
78
0.0017
0.0035
d
M
114
Ac ce pt e
4 5 6 7 8 9 10
Cs
Fig.
ip t
D (mm)
7 8 9
10 11 12
D, Cs, and Tg correspond to disk diameter, surfactant concentration, and mixing time respectively T 0.5: the time elapsed when the drained liquid from CGA dispersion reaches its fifty percent of its final height T 0.1: the time elapsed when the drained liquid from CGA dispersion reaches its ten percent of its final height. Initial slope: the slope of the best fit through the three data points in the beginning of drainage curve Linear slope: the slope of the linear section of drainage curve (including at least 6 points with R2 greater than 99.9%)
19
Page 19 of 29
1
Figures Captions:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Fig. 1 Proposed structure of a colloidal gas aphron by Sebba [2]. Fig. 2 Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number of ethoxy units.
19 20
Fig. 13a Change in rise velocity of a 100 μm aphron bubble versus surface tension
Fig. 4 A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
ip t
Fig. 5 A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min. Fig. 6 Graphical measurement of T0.5, T0.1 and constant slope and initial slope of a drainage curve graphically
cr
Fig. 7 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 90s
Fig. 8 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 90s
us
Fig. 9 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg = 150s
Fig. 10 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 150s Fig. 11 Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg = 240s
an
Fig. 12 Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg = 240s
d
M
Fig. 13b Calculated rise velocity versus aphron size for a constant surface tension of 45mN/m
Ac ce pt e
21 22 23 24
Fig. 3 A plot of an aphron generator
25 26 27 28
Fig. 1 Proposed structure of a colloidal gas aphron by Sebba [2]
20
Page 20 of 29
1
2
Fig. 2. Chemical structure of Nonyl Phenol Ethoxylate, (NPE-n), n is an average of 20 and denoting the number
3
of ethoxy units
ip t
4 5
7 8 9
Ac ce pt e
d
M
an
us
cr
6
Fig. 3. A plot of an aphron generator
10
21
Page 21 of 29
ip t cr us M
an 5
Fig. 4. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.62 mole/liter and mixing time = 5min.
d
2 3 4
Ac ce pt e
1
22
Page 22 of 29
ip t cr us an
1
M
Fig. 5. A micrograph of generated colloidal gas aphrons surfactant concentration = 0.94 mole/liter and mixing time = 5min.
Ac ce pt e
d
2 3 4
5 6
Fig. 6. Graphical measurement of T0.5 , T0.1, constant slope,
23
Page 23 of 29
1
and initial slope of a drainage curve
2
8 9
d
Fig. 7. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 90 s
Ac ce pt e
4 5 6 7
M
an
us
cr
ip t
3
Fig. 8. Effect of spinning disc diameter on drainage curve for
24
Page 24 of 29
Cs=4000 ppm, Tg= 90 s
M
Fig. 9. Effect of spinning disc diameter on drainage curve for Cs=750 ppm, Tg= 150 s
Ac ce pt e
d
3 4 5
an
us
cr
ip t
1 2
6 7 8
Fig. 10. Effect of spinning disc diameter on drainage curve for Cs=4000 ppm, Tg= 150 s
25
Page 25 of 29
ip t cr us an
1
Fig. 11. Effect of spinning disc diameter on drainage curve for
3 4
Cs=750 ppm, Tg= 240 s
d Ac ce pt e
5
M
2
6 7
Fig. 12. Effect of spinning disc diameter on drainage curve for
26
Page 26 of 29
Cs=4000 ppm, Tg= 240 s
Fig. 13a. Change in rise velocity of a 100 μm aphron bubble versus surface tension
an
3 4 5
us
cr
ip t
1 2
7 8 9 10
Ac ce pt e
d
M
6
Fig. 13b. Calculated rise velocity versus aphron size for a constant surface tension of 45 mN/m
11 12
27
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Graphical Abstract
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Highlights
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• Stability index is a key feature of colloidal gas aphrons (CGAs).
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There is no simple and accurate stability index for CGAs dispersion.
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Four stability indexes for CGAs dispersion have been compared.
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When the drained liquid from CGA reaches 10% of its final height was called T0.1.
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The one-tenth of drained liquid life,T0.1, has found the desirable stability index.
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