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Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion
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Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion R.Sh. Abiev ∗ , M.P. Vasilev St Petersburg State Institute of Technology (Technical University), Department of Optimization of Chemical and Biotechnological Equipment, Moskovskii pr. 26, 190013 Saint-Petersburg, Russia
a r t i c l e
i n f o
a b s t r a c t
Article history:
Hydrodynamics of pulsating flow type apparatus (PFA), namely droplet disintegration, was
Received 20 October 2015
investigated by use of theoretical approach and experimentally. Impact of several mecha-
Received in revised form 18
nisms on droplet sizes: Kelvin–Helmholtz instabilities, turbulence in the bulk of liquid and
February 2016
near walls of apparatus, dynamic and inertial mechanisms as well as high shear stresses
Accepted 8 March 2016
are studied. It was found that oil droplet sizes in water in PFA (mean diameter of 20 m
Available online xxx
and the maximum diameter of 35 m) are 1.8 times smaller than in the stirred tank with
Keywords:
rate. By other words, according to the Kolmogorov theory the stirred tank with Rushton tur-
Rushton turbine (maximum diameter about 70 m) at the same level of energy dissipation Oil/water dispersion
bine needs 4.5 times more dissipated energy to get the same sizes of droplets (1800 W/kg for
Emulsifying
Rushton turbine and 400 W/kg for PFA). Comparison of PFA with tubular turbulent apparatus
Energy dissipation rate
(baffled pipe) has shown similar advantages of PFA.
Pulsating flow type apparatus
It has been revealed that these effects attributed to the generally other mechanisms of
Turbulent dissipation
droplet dispersion in PFA compared with usual apparatuses like stirred tanks, where the
Flow instabilities
turbulence plays the main role in the droplet disintegration. Among these mechanisms are pulsations of velocity, acceleration and pressure, high shear stresses rate, and some instabilities. © 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Emulsification processes are widely used in the chemical and petro-
(jet mixers, agitators, rotary apparatus), centrifugal field, ultrasound and electromagnetic waves (including microwave), pressure pulsations and velocity. One of a new generation of equipment is the pulsating
chemical industry, for example in the products refining by removing aromatics from the gasoline by means of liquid extraction. In addition, emulsions are widely used in food products, cosmetics, pharmaceut-
flow type apparatus (PFA) (RF Patent, 2005) characterized with main
icals. Another field of industrial application of emulsions is their
actuator like piston.
use as a means for carrying of active compounds such as flavors, vitamins, antioxidants, nutraceuticals, phytochemicals, drugs, and chemicals within droplets. The introduction of these components
In recent decades, there has been a tendency to develop one of the promising areas of intensification of interphase transfer in heterogeneous media in mainly by the input of energy in the immediate vicinity
requires the use of suitable means for transferring the effective amount of the active ingredient in the desired location and effective, energy saving methods for disintegration of droplets is one of the
of the boundary between the phases (Dolinsky and Ivanitsky, 1997; Dolinsky and Nakorchevskii, 1997; Abiev, 2003a,b; Abiev and Galushko, 2013). Obviously, this method of energy conversion should lead to an
challenges. The most studied and applied in industrial practice are following physical impacts on heterogeneous media: powerful shear flows
increase in the efficiency of heat and mass transfer processes, which will be expressed, for example, by sharp increase in specific surface
∗
idea – generation of pulsations along the streamlines due to the special form of a longitudinal section of the apparatus without any mechanical
area of the dispersed phase at equal energy dissipation rate.
Corresponding author. Tel.: +7 812 494 92 76; fax: +7 812 494 92 76. E-mail address: [email protected] (R.Sh. Abiev) .
http://dx.doi.org/10.1016/j.cherd.2016.03.011 0263-8762/© 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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The main idea of the functioning of PFA is to create conditions to maximize the direct conversion of energy introduced into the apparatus, first, to the surface energy of the bubbles or droplets (in the process
7
7 3
PI1
PI2
drain
of dispersion), and secondly, to the kinetic energy of the relative motion of a continuous and dispersed phases to accelerate mass transfer processes, both on the surface of the bubbles or droplets, as well as within the volumes of continuous as dispersed phases. Dissipation of energy
6
FI
due to turbulence occurring at the same time is seen by us as a side effect; though it is inevitable, but partly controlled (Abiev and Galushko, 2013).
flow reactors) generated by mechanical piston are described (Harvey et al., 2003; Harvey and Stonestreet, 2002; Smith and Mackley, 2006; Gaidhani et al., 2005). It should be noted that baffled flow reactors – BFR (or baffled tubes) have generally other geometry and other principles of working (the baffles are necessary to generate turbulent vortices behind of them). Nevertheless, although they have significant differences from PFA, it should be mentioned that for the classification purposes BFR, PFA and TTA (see (Minsker et al., 2001; Danilov et al., 2011) for TTA – tubular turbulent apparatus) could be regarded as related apparatuses in contrast with usual batch reactors with stirrers, and even with wellknown static mixers having insertions of special form (e.g. Kenics Static Mixer). Some basic aspects of hydrodynamics of pulsating flow type apparatus has been studied both experimentally and theoretically in (Abiev and Galushko, 2013). At the same time the problems in droplets dispersion in PFA have not been studied yet. The aim of this work is an experimental and theoretical study of the quality of the emulsification process in the pulsating flow apparatus and comparison of the quality of dispersion for the PFA and other types of devices at the same level of energy dissipation rate. It was also necessary to investigate the effect of various devices by the characteristics of dispersion depending on the kinetic energy of the flow. The particular task was to identify how significant the role of turbulent eddies is in the process of splitting drops compared to other factors in the pulsating flow type apparatus.
2.
Experimental
A schematic of the pulsating flow type apparatus is shown in Fig. 1. The device can be used in chemical, petrochemical, pharmaceutical, food and other industries in the process of dispersing gas in a liquid, emulsifying (drops dispersion), with the concomitant heat and mass transfer processes like the dissolution of the solid phase (RF Patent, 1996; Abiev, 2012b), extraction (Vasilev and Abiev, 2014), the gas–liquid reactions (Galushko and Abiev, 2008) and absorption. Set out in Abiev and Galushko (2013), Abiev (2012a), the results of calculations of pressure, velocity and acceleration, as well as the distribution of the turbulent kinetic energy and dissipation of energy (for k- model) arising in pulsating flow
1 water
α
2
3
1
type apparatus suggests that there are conditions favorable for the dispersion of bubbles and drops in PFA. PFA consists of Venturi tubes disposed in series (Fig. 1), therefore the cross-section of apparatus is periodically varies along the axial coordinate of the apparatus, i.e. along direction of flow. Heterogeneous system, passing through portions PFA with varying cross-section, are excited by variations in velocity, acceleration and pressure change due to the variation of crosssection of the pipe having the shape of Venturi tubes elements. The oscillations role and other mechanisms will be discussed further in Sections 3.2 and 3.3. Experiments on the oil in water dispersion were performed at the set-up shown in Fig. 2. The water supplied from the tank 1 by a centrifugal pump 2 into the horizontal PFA 3 – a thickwalled glass tube consisted of ten elements of the “Venturi tube” (linear dimensions of the structural elements specified in Fig. 1 are: d = 9 mm, D = 20 mm, L1 = 15 mm, L2 = L4 = 10 mm, L3 = 50 mm, ˛ = 36◦ , ˇ = 11.5◦ ). The oil supply is performed in the point 4 upstream to the first diffuser through a check valve with a medical syringe of volume 20 ml. The sampling of oil-water mixture treated passing the through PFA has been performed by vessel 5 containing 5 ml pre-filled solution of surfactants; this was performed to avoid unnecessary coalescence of dispersed droplets during analysis of their sizes distribution. As the surfactant commercially available detergent ‘Fairy’ was used. Mixture flow rate was measured by electromagnetic mass flow meter 6 ‘VZLET ER ERSV-540M’ with a relative error of measurement ±2.0%, the pressure before and after the apparatus measured by a pressure gauges 7 ‘Elemer AIR-20/M2-DI’ with a relative error of measurement ±0.6%.
ux
L2
β
L3
ur
4
u
Ud
L1
5
oil 8
Fig. 2 – Draft of experimental set-up for oil droplets dispersion in water in pulsating flow type apparatus. 1 – feeding tank; 2 – pump; 3 – PFA; 4 – non-return valve; 5 – container to collect samples; 6 – mass flow meter; 7 – pressure gauges; 8 – flow rate control valves.
d
oil
8
2
Interest in the use of devices with periodically varying cross-section (PFA) or looking like that for use in chemical engineering has increased in recent years. In some studies investigations of the apparatus partly similar to PFA, but with additional oscillatory flow (oscillatory baffled
water
4
u
UD D
ux
L4
5
Fig. 1 – Schematic of Venturi tube element of PFA with typical dimensions. 1 – confuser; 2 – neck; 3 – diffuser; 4 – wide part of apparatus; 5 – oil feed point (for first element of PFA only); u – flow velocity vector, ur – radial velocity, ux – axial velocity. Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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mean droplet diameter averaged by volume
ımax
f (ık )ı3 dı =
ı30 = 0
k
ık+1
ık
f (ık )ı3 dı =
K
f (ık )
ı4k+1 − ı4k
k=1
4
,
(3)
and the mean Sauter diameter of the droplets: ı32 =
Fig. 3 – Example of microphotograph with oil droplets produced in PFA. Scale bar length is 1 mm (ı10 = 23 m).
Experiments were carried out in the range of liquid flow rates QL = 0.56/2.24 m3 /h (9.33/37.3 l/min), the velocity at the throat wherein was in the range Ud = 2.45/9.79 m/s. We used sunflower oil as the dispersed phase, tap water as the continuous phase. Oil volumetric flow rate was set 1% of the water flow rate. The physical properties of the emulsion components are given below. Water
ı330 ı220
,
(4)
where k is the interval number, K – total number of intervals. At a flow rate QL = 0.5 m3 /h arithmetic mean oil droplet diameter was ı10 = 255.8 m, whereas the flow rate QL = 2.24 m3 /h, it was equal ı10 = 21.1 m. The calculation results for droplet diameters at flow rates of continuous phase QL = 0.56/2.24 m3 /h are shown in Table 1. In this paper, we propose to estimate the efficiency of the energy spend to the formation of droplets and preservation against coalescence determined by the formula E =
W . W0
(5)
The energy introduced into the apparatus W0 (spent by pump to supply the fluid through PFA W0PFA and energy necessary to rotate liquid and generate eddies in the stirred tank with Rushton turbine W0RT ), for PFA is defined as
Density (1 )
1000 kg/m3
Dynamic viscosity (1 )
1 × 10−3 Pa s
W0PFA = P · QL · s .
Density (2 )
925 kg/m3
Dynamic viscosity (2 )
56 × 10−3 Pa s
where s is residence time of emulsion in PFA. The pressure drop along the length of PFA was measured in experiments as a difference:
Interfacial tension ()
32 mN/m
(6)
Sunflower oil
P = P1 − P2 , Estimation of drop size was performed by means of microphotographs obtained using a microscope MBS-9 (the overall magnification was 56-fold) equipped with a SLR camera Nikon D3100 SLR with Zoom NIKKOR 18-55 mm f/3.5-5.6G AF-S VR DX lens, resolution of photographs was 4608 × 3072 (14.2 million) pixels. At each microphotograph several arbitrary frames with oil drops were selected (see Fig. 3), the sample size in this case was 110/220 drops. Photo processing was carried out using the CAD program Kompas-3D TM (Russia).
(7)
where P1 is the pressure at the inlet of PFA, and P2 is the pressure at the outlet of the PFA. Energy dissipation rate, required to disperse droplets at given liquid flow rate is usually characterized by specific energy dissipation rate εm , W/kg (see Table 2): ε=
P · QL , m
(8)
3.
Results and discussion
where m is the mass of liquid contained in the volume of PFA. The energy spends W necessary to prepare emulsions for PFA is defined as
3.1. costs
Estimation of the mean droplet size and energy
WPFA = N · s
Mean droplet sizes were calculated by Eqs. (1)–(4). The arithmetic mean diameter of the droplets is given by:
ı10 =
ıf (ı)dı.
(1)
(9)
Power N, necessary to create new surface of drops in PFA can be estimated as the energy spent directly to the preparation of the emulsion, N=
E , t
(10)
where E is the energy required to create new surface: The mean diameter of the droplets averaged by surface
ımax
f (ık )ı2 dı =
ı20 = 0
k
E = · S, ık+1
ık
f (ık )ı2 dı =
K k=1
f (ık )
ı3k+1 − ı3k 3 (2)
(11)
where t is the time interval during which this energy is consumed, is the interfacial tension (in this case at the interface of oil and water), S is the change in the interphase area.
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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Table 1 – Arithmetic mean, the mean for the square and volume of droplet diameters and Sauter mean diameter at different flow rates in PFA. QL , m3 /h P, kPa ı10 , m ı20 , m ı30 , m ı32 , m
0.56 16.7 259.15 277.47 292.99 326.67
0.72 26.7 118.10 131.02 144.23 174.79
0.91 41.5 95.83 102.86 111.32 130.40
1.12 55.3 81.34 90.18 98.95 119.13
1.31 80.6 47.23 54.11 60.62 76.08
1.55 122.4 42.18 45.14 48.18 54.88
1.66 126.0 34.62 37.29 40.02 46.08
1.77 140.5 39.77 41.30 42.63 45.41
1.84 150.5 34.84 36.21 37.85 41.36
1.99 173.8 35.20 36.04 37.53 40.69
2.04 185.0 34.48 35.57 37.02 40.09
2.14 187.7 30.66 31.43 33.20 37.03
2.24 210.9 23.01 23.30 24.56 27.29
Table 2 – Droplet sizes obtained by experiment and calculated by dispersion models. QL , m3 /h
, W/kg
Ud , m/s
0.56 0.72 0.91 1.12 1.31 1.55 1.66 1.77 1.84 1.99 2.04 2.14 2.24
2.45 3.15 3.98 4.89 5.72 6.77 7.25 7.73 8.04 8.69 8.91 9.35 9.79
7.87 16.18 31.8 52.1 88.86 159.68 176.06 209.33 233.1 291.13 317.68 338.02 397.66
The calculated droplets diameter, ı m
Drops obtained in PFA ı10 , m
ımax , m
Kelvin–Helmholtz instability
Turbulent mechanism
Dynamic mechanism
Shear mechanism
259.15 118.1 95.83 81.34 47.23 42.18 34.62 39.77 34.84 35.2 34.48 30.66 23.01
460 254.4 204 186 129.16 80.6 72 58.3 63.58 55 50 40 35.7
69.98 42.34 26.50 17.50 12.79 9.14 7.96 7.01 6.48 5.54 5.27 4.79 4.37
447.70 331.10 250.00 194.90 161.50 131.90 121.50 112.50 107.40 97.76 94.90 89.60 84.82
25.15 15.22 9.53 6.29 4.60 3.28 2.86 2.52 2.33 1.99 1.90 1.72 1.57
71.34 55.48 43.90 35.67 30.49 25.77 24.06 22.57 21.71 20.07 19.58 18.67 17.83
The interphase area for any state of emulsion is defined as Si = ni · · ı2i
· S = · 6 · qoil · t
S = Se − Ss = (ne ı2e − ns ı2s )
ıe
−
1 ıs
(18)
ne · · ı2e − ns · · ı2s S = . t t
(14)
The volumetric flow rate of oil qoil [m3 /s] can be expressed as follows 3 ns · · ı3s ne · · ı3e n · ıi ni · Vi = i · = = t t 6 6t 6t
(15)
where Vi is the volume of oil flowing through the volume of unit (one ‘Venturi pipe/tube’ is specified here as a ‘unit’/‘element’) for the same period of time t. It is assumed that all drops in the unit have at the start size of the ıs dispersed to a size ıe at the end of the unit (indices: e – end; s – start). Expressing the ni /t from Eq. (15) and substituting it into (14) we have found power N as follows: ns 6 · qoil = t · ı3s
The initial size of the drops introduced into the apparatus through a syringe with a needle (see Fig. 2) defined by the equation
ıs =
3
6 · Vs ,
(19)
(13)
Then, the rate of the new surface per time unit is
where VS is the volume of one drop formed by injection by a syringe into a tube. It has been experimentally revealed (experiment was conducted five times) that the injection 1 ml of oil into the cylindrical pipe results in formation of droplets with the same size. The initial amount n0 droplets injected into the PFA was 60 pieces and a syringe volume was 20 ml, hence the volume of one drop of V0 = 0.33 ml. Experimentally determined diameter of the oil droplets detached from the tube was ı0e = 9 mm. Estimated same droplet diameter ı0r determined by the formula (19) was 8.6 mm. For further calculations the initial droplet diameter was set as ı0 = ı0r = 8.6 mm. At water flow rate QL = 2.24 m3 /h (and oil flow rate of 1% of the water flow rate) arithmetic mean oil droplet diameter after passing through PFA was ı10 = 23 m, whereas the maximum droplet size was ımax = 35 m (see Table 2). However, due to the lack of accurate information about the optimal numbers of the Venturi tube we did not take into account energy consumption in each element (see Fig. 4).
(16a) Es=σ·Ss
ne 6 · qoil = t · ı3e S = 6 · qoil t
1
(12)
where ni is the initial or final number of drops, ıi is the initial or final droplet diameter, i = s is the initial state; i = e is the final state. Change of the interphase area for one act of dispersing
qoil =
N=
Ee=σ·Se
(16b)
1 ıe
−
1 ıs
(17)
Fig. 4 – Scheme of energy flows to determine the efficiency of the PFA.
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A comparative analysis of energy consumption by formation and keeping drops surface in PFA and in the stirrer tank with Rushton turbine has been performed. As a criteria for comparison the maximum droplet size ımax , obtained after processing in apparatus PFA (see Fig. 6) was chosen. Energy spends necessary for dispersing droplets of oil in water with a maximum size of 35 m in PFA were ε = 400 W/kg, while the minimum power consumption for the production of such drops in the stirred tank with Rushton turbine was estimated as ε = 1800 W/kg. The energy spent for emulsification by means of turbulent eddies generated with Rushton turbine is W0RT = ε · m · mix
(20)
where mix is the mixing time of liquid in the stirred tank with Rushton turbine. Both external energies W0 for PFA and tank with Rushton turbine were calculated taking into account the equal mass of liquid located in PFA and in the tank, this mass was taken equal to the mass of liquid in PFA m = 0.33 kg. Energy necessary to create new surface of drops in the stirred tank with Rushton turbine was defined as WRT = · (Se − Ss )
(21)
According to our calculations, the efficiency of the energy for the formation and maintenance of drops in PFA is EPFA = 0.025%. Such low value EPFA can be attributed to a small volume ratio of oil to water, qoil /QL = 1%. For extended volume ratio of oil and assuming that the drops have a hexagonal packing, the volume fraction of oil in water could be up to qoil /QL = 30%; for this case efficiency of PFA could be assessed as EPFA = 0.025 · 30 = 0.75%. The latter value characterizes quite high energy transformation efficiency in PFA, but this has to be proven experimentally. For mixer with Rushton turbine we obtained the estimated value of the efficiency coefficient ERT = 3 · 10−4 %, which is 84.5 times less than in the pulsating flow type apparatus. If we compare these apparatuses with equal performance then the volume of the stirrer vessel will increase and the ratio of the efficiencies will be even more different. This is due to the fact that the preparation of the emulsion in the stirrer vessel significantly greater than in PFA. This is an indirect confirmation of the fact that the turbulent mechanism of liquids’ dispersion is not dominant in PFA. In this connection different mechanisms of dispersion in PFA to identify prevailing one were analyzed. To determine the degree of influence of one or another mechanism for dispersion of oil droplets in water in PFA pulsating droplet sizes in the following well-known models were calculated (Abiev, 2006): Kelvin–Helmholtz instability; droplets dispersion in the turbulent fluid flow (Kolmogorov); dynamic mechanism of drops’ dispersion (Levich); the shear emulsification mechanism (Ghopal).
3.2. Assessment of the impact of the various mechanisms of dispersion on the droplet size in PFA To determine the degree of influence of one or another mechanism for dispersion of oil droplets in water in the pulsating flow type apparatus droplet sizes by use the following wellknown models (Abiev, 2006) was calculated:
1) Kelvin–Helmholtz instability. Instability arises as a result of the formation of surface waves in the longitudinal motion of two immiscible liquids with respect to the interface. The droplet size is calculated by the following formula: ıv =
2 (1 + 2 ) 1 2 (vL )
(22)
2
where is the interfacial tension, 1 , 2 are the densities of water and oil, respectively, L is the linear velocity of the fluid at the narrowest part of the throat ( L = Ud ). 2) Dispersion of droplets in the turbulent fluid flow. According to the theory of homogeneous and isotropic turbulence developed by Kolmogorov, dispersion of drops in a turbulent flow occurs due to pulsations, the scale of which is larger compared to the inner scale of turbulence:
ıT = 2 · L2/5 ·
kf ·
3/5 √ ·
2 , U6/5
(23)
where L is the characteristic size of the unit, here L = d, kf is the coefficient of resistance for the flow circumfluent to drops, kf = 0.5, is the continuous fluid density, U is the characteristic superficial fluid velocity in the throat of apparatus (U = Ud ). 3) Dynamic mechanism of drops dispersion. According to the theory of Levich (Abiev, 2006), the motion of a continuous medium due to the continuity of the tangential stresses on the surface of the drop causes the motion of the fluid inside it, having rotational, and possibly turbulent, while inside there is a dynamic pressure, directed from the inside out. If the pressure exceeds the capillary forces holding the drop, the drop should burst. Droplet diameter for the dispersing mechanism is calculated by the formula:
ıD =
3
6 2 · . kf (2 · )1/3 · U2 2 1
(24)
4) The shear emulsification mechanism. Dispersion of droplets under the influence of shear flows deforming liquid sphere is calculated as follows: ıG =
4· p
p = 4G · 1 ·
(25) 192 + 161 · cos(2ϕ), 162 + 161
(26)
where G is the shear rate, 1 , 2 – dynamic viscosities of water and oil, respectively, ϕ is the angle between the principal axis of the prolate spheroid and the vertical axis. The results of calculations on the droplet size dispersion models, as well as droplet sizes obtained experimentally in the pulsating flow type apparatus are shown in Table 2. As can be seen from the graph in Fig. 5, for small flow rates, approximately less than 1.1 m3 /s (and therefore small energy dissipation rates) predominant mechanism of dispersion of oil droplets in water is turbulent mechanism, but at higher flow rates the droplet size decreases and becomes closer to the shear, dynamic mechanism and the model of Kelvin–Helmholtz. Diameter ratio of drops calculated according to the mechanism of turbulent dispersion with droplets calculated by other models are presented in Table 3.
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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500 450 400
Turbulent mechanism
Shear mechanism
Experiment: δmax
Kelvin-Helmholtz instability
Experiment: δ10
Dynamic mechanism
350
δ, μm
300 250 200 150 100 50 0 0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
QL, m³/h Fig. 5 – Graph of the calculated and experimental size of the oil droplets of the mixture. Table 3 – The ratio of the diameters of the drops dispersed by turbulent mechanism to the droplet size calculated by other dispersion models. QL , m3 /h
0.56
0.72
0.91
1.12
1.31
1.55
1.66
1.77
1.84
1.99
2.04
2.14
2.24
ıT ıV
6.40
7.82
9.43
11.14
12.63
14.44
15.26
16.06
16.57
17.64
17.99
18.70
19.39
ıT ıD
17.35
21.20
25.57
30.20
34.24
39.14
41.35
43.54
44.92
47.83
48.79
50.68
52.59
ıT ıG
6.28
5.97
5.69
5.46
5.30
5.12
5.05
4.98
4.95
4.87
4.85
4.80
4.76
Traditional ways (described in the literature as usual principles) of intensification of processes in heterogeneous media are based primarily on the concept of locally isotropic turbulence of Kolmogorov. According to this concept a crucial role in the implementation of the heat and mass transfer between dispersed and continuous media and dispersion of bubbles and droplets belongs to pulsation components of the velocity and stresses of the turbulent flow. In this theory, the level of intensification is directly related to the turbulent velocity fluctuations. However, the use of turbulence as a tool to improve the efficiency of processes requires additional energy spends and consequently reduces the efficiency of the apparatuses (see Section 3.1), since most of the energy is transformed into the energy of turbulent eddies and then dissipated in the volume of the continuous phase and on the walls of the apparatus. Comparison of the degree of dispersion of oil in the pulsating flow type apparatus with different types of dispersing apparatuses in a wide range of specific energy consumption during preparation of the emulsion is shown in Fig. 6 which is a replica of the diagram proposed by Dolinsky (Dolinsky and Ivanitsky, 1997) and adopted from (Davies, 1987) with addition of experimental points for PFA found in this work. At Fig. 6 there are two corridors: the upper one corresponds to the traditional apparatuses where the energy transformed into useful work (here – into new surface of droplets) not very effective. The lower corridor corresponds to ‘smart’ devices characterized with much smaller sizes of droplets at the same energy dissipation rate. It was revealed that the behavior of experimental points for PFA obtained experimentally depends on the energy dissipation rate. At low energy dissipation rates energy consumption for the preparation of fine emulsion in PFA is comparable to static
mixers at the same droplet size. In the field of higher energy dissipation rates maximum size of the oil droplets in water in PFA is 1.8 times less than lower limit of traditional dispersing apparatus according to diagram (see Fig. 6). Similar droplet diameter can be obtained in a tank with mechanical stirrers (Rushton turbine and other), in which the energy input is 4.5 times higher. Thus, in experiments performed in this work is revealed that droplets dispersed in PFA are finer in comparison with other types of apparatuses at the same energy dissipation rate. By other words, the experimental points move from the upper corridor toward to the lower. Hence, at high energy input PFA could demonstrate its belonging to class of high-performance apparatuses (lower corridor). In addition, PFA has other advantages: (1) PFA is compact; (2) has a 14–16 smaller hydraulic resistance as compared with similar (at first glance) devices such as TTA; (3) contains no dead space; (4) tubular shape ensures the continuity of the process, thereby higher productivity can be achieved. All this allows us to recommend it for extended use in industrial practice.
3.3. Checking the possibility of resonant oscillations of drops in PFA Using the formula of Rayleigh (27), we determined the eigen frequencies of the n-modes of drops with diameter ı. The calculation results of natural frequency oscillations are presented in Table 4.
fn =
1 · 2·
8 · (n − 1) · n · (n + 1)(n + 2) · [(n + 1) · 2 + n · 1 ] · ı
(27)
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7
Fig. 6 – Comparison of energy spends in the preparation of emulsions PFA and other devices.
Table 4 – Eigen frequencies of the oil droplets. ı, m n 2 3 4 5
20
50
75
100
fn, Hz 6.383 × 104 1.205 × 105 1.839 × 105 2.54 × 105
1.615 × 104 3.048 × 104 4.653 × 104 6.427 × 104
8.79 × 103 1.659 × 104 2.533 × 104 3.498 × 104
5.709 × 103 1.078 × 104 1.645 × 104 2.272 × 104
Pulsation frequency was calculated as reciprocal of residence time T1 in one unit of Venturi tubes with volume V1 , i.e. f =
1 QL = . T1 V1
(28)
In the pulsating flow type apparatus for flow rates of continuous fluid QL = 0.56/2.24 m3 /h pulsation frequency was in the range of f = 9.82/39.28 Hz, well below the eigen frequency of drops, and thus the resonance effect under the experimental conditions did not arise. Nevertheless, even at such frequencies pulsations could play significant role in process intensification in the inner volume of droplets, allowing to distribute substance in the drops better than at usual flow around at constant flow velocities. This effect has to be proven in the future works.
4.
Conclusion and future work
One of the main results of our investigation is better energy transformation in pulsating flow type apparatus compared to one of the benchmarks in mixing and dispersion processes – stirred tank with Rushton turbine. Maximum droplet size could be used as an indicator of energy transformation efficiency in any kind of devices for droplets/bubbles dispersion, as the measurements technique for the size of droplets is more feasible and provides more reliable results compared with measurements of bubbles’ sizes. It was found that oil in water emulsion with a maximum droplet size 1.8 times smaller than that in conventional
dispersing apparatuses like stirred tanks could be produced. Comparison of energy spend according to Davies–Dolinsky diagram (Fig. 6) showed that the energy required to disperse oil droplets in water to a maximum size of 35 m in PFA is only 400 W/kg, while the minimum power consumption for producing of drops in conventional mixing devices (stirred tanks) is 1800 W/kg. Thus, PFA can continuously produce fine emulsions; dissipated energy is 4.5 times less than in the existing apparatuses. A comparative analysis of energy consumption for the formation of drops and their preservation against coalescence in PFA and in the stirred tank with Rushton turbine was performed by means of Eq. (5) as a criterion of energy efficiency. If the volume of apparatuses and a droplets size to use as a basis for comparison, it was found that the efficiency of energy for the formation and preservation of droplets in PFA is 84.5 times higher than in stirred tank with Rushton turbine. If we compare these apparatuses with equal performance then the volume of the stirred tank will increase and the ratio of the efficiencies will be even more different. This is due to the fact that the preparation of the emulsion in the stirred tank significantly greater than in PFA. Analysis of main impacts on the droplets size has showed that turbulence is the predominant mechanism of the oil droplets dispersed in water only at low energy dissipation rate (ε < 90 W/kg), and with increasing the energy supplied to the apparatus (ε > 100 W/kg) the droplet size decreases and approaches the values calculated by equations for the shear, dynamic mechanism and model of Kelvin–Helmholtz. This indicates that in PFA are conditions arising allowing to create more complex flow organization compared to turbulent eddies and turbulence plays just a side role. Traditional points of view to process intensification in heterogeneous media based primarily on the concept of locally isotropic turbulence. According to this concept a determinant role in the dispersion of bubbles and droplets belongs to pulsation components of the velocity and stresses of turbulent flow. However, the use of turbulence as a means of increasing
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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the efficiency of apparatuses involves extra energy costs and consequently reduces the efficiency of the apparatus. In this paper it is shown that the energy spent for turbulence generation in stirred tank for producing a dispersion of oil droplets in water of with maximal size of about 35 m is 84.5 times higher than that necessary for PFA. Further research is aimed to expand the range of continuous phase velocities (and to increase energy dissipation rate) in order to check the trajectory of points on Fig. 6. If they will approach the lower corridor at the plot on Fig. 6, this will confirm further development of non-turbulent mechanisms of disintegration and decay of the role of turbulence. Similar behavior has been found earlier and very well known, e.g. for coiled pipes where turbulence is suppressed by organized secondary flows, or for convergent tubes, where acceleration of velocity on the one hand increase the stability of flow, and on the other hand the density of energy is also increases in the throat (just like in the neck of the PFA). The other way to improve the effectiveness of disintegration of droplets is the introduction of a third phase (gas), which may serve as an additional way to increase the degree of emulsification and mass transfer in both phases of liquid–liquid systems. Besides, it is necessary in further works to perform detailed analysis of “life” of droplets during their way along different parts of PFA, taking into account the different impacts on the droplet surface and volume. This will allow to specify more accurately distribution of impacts within PFA volume, making possible to use the multiblock model conjugated with population balance method similar to those which was applied to stirred tank by Alopaeus et al. (1999).
References A device for processing fluids capillary-porous particles. RF Patent No 2 064 319. Byull. Izobret. No. 10, 1996. Abiev, R.Sh., 2003a. The flow of homogeneous incompressible fluid in a tube with a periodically varying cross-section. J. Chem. Oil Mech. Eng. 1, 6–10 (in Russian). Abiev, R.Sh., 2003b. The study of gas–liquid flow in a pipe with a periodically varying cross-section. Chem. Ind. 80, 600–607 (in Russian). Abiev, R.Sh., 2006. Theoretical Foundation of Energy and Resource Saving in Chemical Technologies. VVM Publ., St. Petersburg (in Russian). Abiev, R.S., 2012a. New concept of energy-efficient and resource-saving apparatuses for mixing and conjugated
processes. In: Proceedings of 14th European Conferences on Mixing, 09–14 September, Warsaw, pp. 13–18. Abiev, R.Sh., 2012b. Intensification of industrial wastewater treatment in the pulsating flow type apparatus. Bull. St. Petersb. Technol. Univ. 13 (39), 82–86 (in Russian). Abiev, R.Sh., Galushko, A.S., 2013. Hydrodynamics of pulsating flow type apparatus: simulation and experiments. Chem. Eng. J. 229, 285–295. Alopaeus, V., Koskinen, J., Keskinen, K.I., 1999. Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 1 Description and qualitative validation of the model. Chem. Eng. Sci. 54, 5887–5899. Danilov, Yu.M., Mukhametzyanova, A.G., Deberdeev, R.Ya., Berlin, A.A., 2011. Estimating the efficiency of mixing of liquid components in small tubular turbulent apparatuses. Theor. Found. Chem. Eng. 45, 81–84. Davies, J.T., 1987. A physical interpretation of drop sizes in homogenizers and agitated tanks, including the dispersion of viscous oils. Chem. Eng. Sci. 42, 1671–1676. Dolinsky, A.A., Ivanitsky, G.K., 1997. Principles for the development of new energy-saving technologies and equipment based on discrete-pulse energy input. Ind. Heat Eng. 19, 13–25 (in Russian). Dolinsky, A.A., Nakorchevskii, A.I., 1997. Optimization principles of mass transfer technology based on discrete-pulse energy input. Ind. Heat Eng. 19, 5–9 (in Russian). Gaidhani, H.K., McNeil, B., Ni, X., 2005. Fermentation of pullulan using an oscillatory baffled fermenter. Chem. Eng. Res. Des. 6A, 640–645. Galushko, A.S., Abiev, R.Sh., 2008. The study of hydrodynamics of gas–liquid mixture in the pulsating flow type apparatus. Bull. Kazan Technol. Univ. 6, 199–205 (in Russian). Harvey, A., Stonestreet, P., 2002. A mixing-based design methodology for continuous oscillatory flow reactors. Trans IChemE Part A Chem. Eng. Res. Des. 80, 31–44. Harvey, A.P., Mackley, M.R., Seliger, T., 2003. Process intensification of biodiesel production using a continuous oscillatory flow reactor. J. Chem. Technol. Biotechnol. 78, 338–341. Minsker, K.S., Zakharov, V.P., Berlin, Al.Al., Takhavutdinov, R.G., 2001. Turbulent mixing of liquid flows in divergent-convergent tubular continuous-flow apparatuses. Dokl. Chem. 381, 336–339. Method of intensification of reactions and mass-exchange processes in the heterogeneous systems and the apparatus for its realization. RF Patent No 2 264 847. Bull. No. 33, 2005. Smith, K.B., Mackley, M.R., 2006. An experimental investigation into the scale-up of oscillatory flow mixing in baffled tubes. Chem. Eng. Res. Des. 11A, 1001–1011. Vasilev, M.P., Abiev, R.Sh., 2014. Research of processes dispersion and extraction of arenes in the pulsation flow type apparatus. Chem. Ind. (2), 70–77 (in Russian).
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Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion R.Sh. Abiev ∗ , M.P. Vasilev St Petersburg State Institute of Technology (Technical University), Department of Optimization of Chemical and Biotechnological Equipment, Moskovskii pr. 26, 190013 Saint-Petersburg, Russia
a r t i c l e
i n f o
a b s t r a c t
Article history:
Hydrodynamics of pulsating flow type apparatus (PFA), namely droplet disintegration, was
Received 20 October 2015
investigated by use of theoretical approach and experimentally. Impact of several mecha-
Received in revised form 18
nisms on droplet sizes: Kelvin–Helmholtz instabilities, turbulence in the bulk of liquid and
February 2016
near walls of apparatus, dynamic and inertial mechanisms as well as high shear stresses
Accepted 8 March 2016
are studied. It was found that oil droplet sizes in water in PFA (mean diameter of 20 m
Available online xxx
and the maximum diameter of 35 m) are 1.8 times smaller than in the stirred tank with
Keywords:
rate. By other words, according to the Kolmogorov theory the stirred tank with Rushton tur-
Rushton turbine (maximum diameter about 70 m) at the same level of energy dissipation Oil/water dispersion
bine needs 4.5 times more dissipated energy to get the same sizes of droplets (1800 W/kg for
Emulsifying
Rushton turbine and 400 W/kg for PFA). Comparison of PFA with tubular turbulent apparatus
Energy dissipation rate
(baffled pipe) has shown similar advantages of PFA.
Pulsating flow type apparatus
It has been revealed that these effects attributed to the generally other mechanisms of
Turbulent dissipation
droplet dispersion in PFA compared with usual apparatuses like stirred tanks, where the
Flow instabilities
turbulence plays the main role in the droplet disintegration. Among these mechanisms are pulsations of velocity, acceleration and pressure, high shear stresses rate, and some instabilities. © 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Emulsification processes are widely used in the chemical and petro-
(jet mixers, agitators, rotary apparatus), centrifugal field, ultrasound and electromagnetic waves (including microwave), pressure pulsations and velocity. One of a new generation of equipment is the pulsating
chemical industry, for example in the products refining by removing aromatics from the gasoline by means of liquid extraction. In addition, emulsions are widely used in food products, cosmetics, pharmaceut-
flow type apparatus (PFA) (RF Patent, 2005) characterized with main
icals. Another field of industrial application of emulsions is their
actuator like piston.
use as a means for carrying of active compounds such as flavors, vitamins, antioxidants, nutraceuticals, phytochemicals, drugs, and chemicals within droplets. The introduction of these components
In recent decades, there has been a tendency to develop one of the promising areas of intensification of interphase transfer in heterogeneous media in mainly by the input of energy in the immediate vicinity
requires the use of suitable means for transferring the effective amount of the active ingredient in the desired location and effective, energy saving methods for disintegration of droplets is one of the
of the boundary between the phases (Dolinsky and Ivanitsky, 1997; Dolinsky and Nakorchevskii, 1997; Abiev, 2003a,b; Abiev and Galushko, 2013). Obviously, this method of energy conversion should lead to an
challenges. The most studied and applied in industrial practice are following physical impacts on heterogeneous media: powerful shear flows
increase in the efficiency of heat and mass transfer processes, which will be expressed, for example, by sharp increase in specific surface
∗
idea – generation of pulsations along the streamlines due to the special form of a longitudinal section of the apparatus without any mechanical
area of the dispersed phase at equal energy dissipation rate.
Corresponding author. Tel.: +7 812 494 92 76; fax: +7 812 494 92 76. E-mail address: [email protected] (R.Sh. Abiev) .
http://dx.doi.org/10.1016/j.cherd.2016.03.011 0263-8762/© 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
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The main idea of the functioning of PFA is to create conditions to maximize the direct conversion of energy introduced into the apparatus, first, to the surface energy of the bubbles or droplets (in the process
7
7 3
PI1
PI2
drain
of dispersion), and secondly, to the kinetic energy of the relative motion of a continuous and dispersed phases to accelerate mass transfer processes, both on the surface of the bubbles or droplets, as well as within the volumes of continuous as dispersed phases. Dissipation of energy
6
FI
due to turbulence occurring at the same time is seen by us as a side effect; though it is inevitable, but partly controlled (Abiev and Galushko, 2013).
flow reactors) generated by mechanical piston are described (Harvey et al., 2003; Harvey and Stonestreet, 2002; Smith and Mackley, 2006; Gaidhani et al., 2005). It should be noted that baffled flow reactors – BFR (or baffled tubes) have generally other geometry and other principles of working (the baffles are necessary to generate turbulent vortices behind of them). Nevertheless, although they have significant differences from PFA, it should be mentioned that for the classification purposes BFR, PFA and TTA (see (Minsker et al., 2001; Danilov et al., 2011) for TTA – tubular turbulent apparatus) could be regarded as related apparatuses in contrast with usual batch reactors with stirrers, and even with wellknown static mixers having insertions of special form (e.g. Kenics Static Mixer). Some basic aspects of hydrodynamics of pulsating flow type apparatus has been studied both experimentally and theoretically in (Abiev and Galushko, 2013). At the same time the problems in droplets dispersion in PFA have not been studied yet. The aim of this work is an experimental and theoretical study of the quality of the emulsification process in the pulsating flow apparatus and comparison of the quality of dispersion for the PFA and other types of devices at the same level of energy dissipation rate. It was also necessary to investigate the effect of various devices by the characteristics of dispersion depending on the kinetic energy of the flow. The particular task was to identify how significant the role of turbulent eddies is in the process of splitting drops compared to other factors in the pulsating flow type apparatus.
2.
Experimental
A schematic of the pulsating flow type apparatus is shown in Fig. 1. The device can be used in chemical, petrochemical, pharmaceutical, food and other industries in the process of dispersing gas in a liquid, emulsifying (drops dispersion), with the concomitant heat and mass transfer processes like the dissolution of the solid phase (RF Patent, 1996; Abiev, 2012b), extraction (Vasilev and Abiev, 2014), the gas–liquid reactions (Galushko and Abiev, 2008) and absorption. Set out in Abiev and Galushko (2013), Abiev (2012a), the results of calculations of pressure, velocity and acceleration, as well as the distribution of the turbulent kinetic energy and dissipation of energy (for k- model) arising in pulsating flow
1 water
α
2
3
1
type apparatus suggests that there are conditions favorable for the dispersion of bubbles and drops in PFA. PFA consists of Venturi tubes disposed in series (Fig. 1), therefore the cross-section of apparatus is periodically varies along the axial coordinate of the apparatus, i.e. along direction of flow. Heterogeneous system, passing through portions PFA with varying cross-section, are excited by variations in velocity, acceleration and pressure change due to the variation of crosssection of the pipe having the shape of Venturi tubes elements. The oscillations role and other mechanisms will be discussed further in Sections 3.2 and 3.3. Experiments on the oil in water dispersion were performed at the set-up shown in Fig. 2. The water supplied from the tank 1 by a centrifugal pump 2 into the horizontal PFA 3 – a thickwalled glass tube consisted of ten elements of the “Venturi tube” (linear dimensions of the structural elements specified in Fig. 1 are: d = 9 mm, D = 20 mm, L1 = 15 mm, L2 = L4 = 10 mm, L3 = 50 mm, ˛ = 36◦ , ˇ = 11.5◦ ). The oil supply is performed in the point 4 upstream to the first diffuser through a check valve with a medical syringe of volume 20 ml. The sampling of oil-water mixture treated passing the through PFA has been performed by vessel 5 containing 5 ml pre-filled solution of surfactants; this was performed to avoid unnecessary coalescence of dispersed droplets during analysis of their sizes distribution. As the surfactant commercially available detergent ‘Fairy’ was used. Mixture flow rate was measured by electromagnetic mass flow meter 6 ‘VZLET ER ERSV-540M’ with a relative error of measurement ±2.0%, the pressure before and after the apparatus measured by a pressure gauges 7 ‘Elemer AIR-20/M2-DI’ with a relative error of measurement ±0.6%.
ux
L2
β
L3
ur
4
u
Ud
L1
5
oil 8
Fig. 2 – Draft of experimental set-up for oil droplets dispersion in water in pulsating flow type apparatus. 1 – feeding tank; 2 – pump; 3 – PFA; 4 – non-return valve; 5 – container to collect samples; 6 – mass flow meter; 7 – pressure gauges; 8 – flow rate control valves.
d
oil
8
2
Interest in the use of devices with periodically varying cross-section (PFA) or looking like that for use in chemical engineering has increased in recent years. In some studies investigations of the apparatus partly similar to PFA, but with additional oscillatory flow (oscillatory baffled
water
4
u
UD D
ux
L4
5
Fig. 1 – Schematic of Venturi tube element of PFA with typical dimensions. 1 – confuser; 2 – neck; 3 – diffuser; 4 – wide part of apparatus; 5 – oil feed point (for first element of PFA only); u – flow velocity vector, ur – radial velocity, ux – axial velocity. Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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mean droplet diameter averaged by volume
ımax
f (ık )ı3 dı =
ı30 = 0
k
ık+1
ık
f (ık )ı3 dı =
K
f (ık )
ı4k+1 − ı4k
k=1
4
,
(3)
and the mean Sauter diameter of the droplets: ı32 =
Fig. 3 – Example of microphotograph with oil droplets produced in PFA. Scale bar length is 1 mm (ı10 = 23 m).
Experiments were carried out in the range of liquid flow rates QL = 0.56/2.24 m3 /h (9.33/37.3 l/min), the velocity at the throat wherein was in the range Ud = 2.45/9.79 m/s. We used sunflower oil as the dispersed phase, tap water as the continuous phase. Oil volumetric flow rate was set 1% of the water flow rate. The physical properties of the emulsion components are given below. Water
ı330 ı220
,
(4)
where k is the interval number, K – total number of intervals. At a flow rate QL = 0.5 m3 /h arithmetic mean oil droplet diameter was ı10 = 255.8 m, whereas the flow rate QL = 2.24 m3 /h, it was equal ı10 = 21.1 m. The calculation results for droplet diameters at flow rates of continuous phase QL = 0.56/2.24 m3 /h are shown in Table 1. In this paper, we propose to estimate the efficiency of the energy spend to the formation of droplets and preservation against coalescence determined by the formula E =
W . W0
(5)
The energy introduced into the apparatus W0 (spent by pump to supply the fluid through PFA W0PFA and energy necessary to rotate liquid and generate eddies in the stirred tank with Rushton turbine W0RT ), for PFA is defined as
Density (1 )
1000 kg/m3
Dynamic viscosity (1 )
1 × 10−3 Pa s
W0PFA = P · QL · s .
Density (2 )
925 kg/m3
Dynamic viscosity (2 )
56 × 10−3 Pa s
where s is residence time of emulsion in PFA. The pressure drop along the length of PFA was measured in experiments as a difference:
Interfacial tension ()
32 mN/m
(6)
Sunflower oil
P = P1 − P2 , Estimation of drop size was performed by means of microphotographs obtained using a microscope MBS-9 (the overall magnification was 56-fold) equipped with a SLR camera Nikon D3100 SLR with Zoom NIKKOR 18-55 mm f/3.5-5.6G AF-S VR DX lens, resolution of photographs was 4608 × 3072 (14.2 million) pixels. At each microphotograph several arbitrary frames with oil drops were selected (see Fig. 3), the sample size in this case was 110/220 drops. Photo processing was carried out using the CAD program Kompas-3D TM (Russia).
(7)
where P1 is the pressure at the inlet of PFA, and P2 is the pressure at the outlet of the PFA. Energy dissipation rate, required to disperse droplets at given liquid flow rate is usually characterized by specific energy dissipation rate εm , W/kg (see Table 2): ε=
P · QL , m
(8)
3.
Results and discussion
where m is the mass of liquid contained in the volume of PFA. The energy spends W necessary to prepare emulsions for PFA is defined as
3.1. costs
Estimation of the mean droplet size and energy
WPFA = N · s
Mean droplet sizes were calculated by Eqs. (1)–(4). The arithmetic mean diameter of the droplets is given by:
ı10 =
ıf (ı)dı.
(1)
(9)
Power N, necessary to create new surface of drops in PFA can be estimated as the energy spent directly to the preparation of the emulsion, N=
E , t
(10)
where E is the energy required to create new surface: The mean diameter of the droplets averaged by surface
ımax
f (ık )ı2 dı =
ı20 = 0
k
E = · S, ık+1
ık
f (ık )ı2 dı =
K k=1
f (ık )
ı3k+1 − ı3k 3 (2)
(11)
where t is the time interval during which this energy is consumed, is the interfacial tension (in this case at the interface of oil and water), S is the change in the interphase area.
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Table 1 – Arithmetic mean, the mean for the square and volume of droplet diameters and Sauter mean diameter at different flow rates in PFA. QL , m3 /h P, kPa ı10 , m ı20 , m ı30 , m ı32 , m
0.56 16.7 259.15 277.47 292.99 326.67
0.72 26.7 118.10 131.02 144.23 174.79
0.91 41.5 95.83 102.86 111.32 130.40
1.12 55.3 81.34 90.18 98.95 119.13
1.31 80.6 47.23 54.11 60.62 76.08
1.55 122.4 42.18 45.14 48.18 54.88
1.66 126.0 34.62 37.29 40.02 46.08
1.77 140.5 39.77 41.30 42.63 45.41
1.84 150.5 34.84 36.21 37.85 41.36
1.99 173.8 35.20 36.04 37.53 40.69
2.04 185.0 34.48 35.57 37.02 40.09
2.14 187.7 30.66 31.43 33.20 37.03
2.24 210.9 23.01 23.30 24.56 27.29
Table 2 – Droplet sizes obtained by experiment and calculated by dispersion models. QL , m3 /h
, W/kg
Ud , m/s
0.56 0.72 0.91 1.12 1.31 1.55 1.66 1.77 1.84 1.99 2.04 2.14 2.24
2.45 3.15 3.98 4.89 5.72 6.77 7.25 7.73 8.04 8.69 8.91 9.35 9.79
7.87 16.18 31.8 52.1 88.86 159.68 176.06 209.33 233.1 291.13 317.68 338.02 397.66
The calculated droplets diameter, ı m
Drops obtained in PFA ı10 , m
ımax , m
Kelvin–Helmholtz instability
Turbulent mechanism
Dynamic mechanism
Shear mechanism
259.15 118.1 95.83 81.34 47.23 42.18 34.62 39.77 34.84 35.2 34.48 30.66 23.01
460 254.4 204 186 129.16 80.6 72 58.3 63.58 55 50 40 35.7
69.98 42.34 26.50 17.50 12.79 9.14 7.96 7.01 6.48 5.54 5.27 4.79 4.37
447.70 331.10 250.00 194.90 161.50 131.90 121.50 112.50 107.40 97.76 94.90 89.60 84.82
25.15 15.22 9.53 6.29 4.60 3.28 2.86 2.52 2.33 1.99 1.90 1.72 1.57
71.34 55.48 43.90 35.67 30.49 25.77 24.06 22.57 21.71 20.07 19.58 18.67 17.83
The interphase area for any state of emulsion is defined as Si = ni · · ı2i
· S = · 6 · qoil · t
S = Se − Ss = (ne ı2e − ns ı2s )
ıe
−
1 ıs
(18)
ne · · ı2e − ns · · ı2s S = . t t
(14)
The volumetric flow rate of oil qoil [m3 /s] can be expressed as follows 3 ns · · ı3s ne · · ı3e n · ıi ni · Vi = i · = = t t 6 6t 6t
(15)
where Vi is the volume of oil flowing through the volume of unit (one ‘Venturi pipe/tube’ is specified here as a ‘unit’/‘element’) for the same period of time t. It is assumed that all drops in the unit have at the start size of the ıs dispersed to a size ıe at the end of the unit (indices: e – end; s – start). Expressing the ni /t from Eq. (15) and substituting it into (14) we have found power N as follows: ns 6 · qoil = t · ı3s
The initial size of the drops introduced into the apparatus through a syringe with a needle (see Fig. 2) defined by the equation
ıs =
3
6 · Vs ,
(19)
(13)
Then, the rate of the new surface per time unit is
where VS is the volume of one drop formed by injection by a syringe into a tube. It has been experimentally revealed (experiment was conducted five times) that the injection 1 ml of oil into the cylindrical pipe results in formation of droplets with the same size. The initial amount n0 droplets injected into the PFA was 60 pieces and a syringe volume was 20 ml, hence the volume of one drop of V0 = 0.33 ml. Experimentally determined diameter of the oil droplets detached from the tube was ı0e = 9 mm. Estimated same droplet diameter ı0r determined by the formula (19) was 8.6 mm. For further calculations the initial droplet diameter was set as ı0 = ı0r = 8.6 mm. At water flow rate QL = 2.24 m3 /h (and oil flow rate of 1% of the water flow rate) arithmetic mean oil droplet diameter after passing through PFA was ı10 = 23 m, whereas the maximum droplet size was ımax = 35 m (see Table 2). However, due to the lack of accurate information about the optimal numbers of the Venturi tube we did not take into account energy consumption in each element (see Fig. 4).
(16a) Es=σ·Ss
ne 6 · qoil = t · ı3e S = 6 · qoil t
1
(12)
where ni is the initial or final number of drops, ıi is the initial or final droplet diameter, i = s is the initial state; i = e is the final state. Change of the interphase area for one act of dispersing
qoil =
N=
Ee=σ·Se
(16b)
1 ıe
−
1 ıs
(17)
Fig. 4 – Scheme of energy flows to determine the efficiency of the PFA.
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A comparative analysis of energy consumption by formation and keeping drops surface in PFA and in the stirrer tank with Rushton turbine has been performed. As a criteria for comparison the maximum droplet size ımax , obtained after processing in apparatus PFA (see Fig. 6) was chosen. Energy spends necessary for dispersing droplets of oil in water with a maximum size of 35 m in PFA were ε = 400 W/kg, while the minimum power consumption for the production of such drops in the stirred tank with Rushton turbine was estimated as ε = 1800 W/kg. The energy spent for emulsification by means of turbulent eddies generated with Rushton turbine is W0RT = ε · m · mix
(20)
where mix is the mixing time of liquid in the stirred tank with Rushton turbine. Both external energies W0 for PFA and tank with Rushton turbine were calculated taking into account the equal mass of liquid located in PFA and in the tank, this mass was taken equal to the mass of liquid in PFA m = 0.33 kg. Energy necessary to create new surface of drops in the stirred tank with Rushton turbine was defined as WRT = · (Se − Ss )
(21)
According to our calculations, the efficiency of the energy for the formation and maintenance of drops in PFA is EPFA = 0.025%. Such low value EPFA can be attributed to a small volume ratio of oil to water, qoil /QL = 1%. For extended volume ratio of oil and assuming that the drops have a hexagonal packing, the volume fraction of oil in water could be up to qoil /QL = 30%; for this case efficiency of PFA could be assessed as EPFA = 0.025 · 30 = 0.75%. The latter value characterizes quite high energy transformation efficiency in PFA, but this has to be proven experimentally. For mixer with Rushton turbine we obtained the estimated value of the efficiency coefficient ERT = 3 · 10−4 %, which is 84.5 times less than in the pulsating flow type apparatus. If we compare these apparatuses with equal performance then the volume of the stirrer vessel will increase and the ratio of the efficiencies will be even more different. This is due to the fact that the preparation of the emulsion in the stirrer vessel significantly greater than in PFA. This is an indirect confirmation of the fact that the turbulent mechanism of liquids’ dispersion is not dominant in PFA. In this connection different mechanisms of dispersion in PFA to identify prevailing one were analyzed. To determine the degree of influence of one or another mechanism for dispersion of oil droplets in water in PFA pulsating droplet sizes in the following well-known models were calculated (Abiev, 2006): Kelvin–Helmholtz instability; droplets dispersion in the turbulent fluid flow (Kolmogorov); dynamic mechanism of drops’ dispersion (Levich); the shear emulsification mechanism (Ghopal).
3.2. Assessment of the impact of the various mechanisms of dispersion on the droplet size in PFA To determine the degree of influence of one or another mechanism for dispersion of oil droplets in water in the pulsating flow type apparatus droplet sizes by use the following wellknown models (Abiev, 2006) was calculated:
1) Kelvin–Helmholtz instability. Instability arises as a result of the formation of surface waves in the longitudinal motion of two immiscible liquids with respect to the interface. The droplet size is calculated by the following formula: ıv =
2 (1 + 2 ) 1 2 (vL )
(22)
2
where is the interfacial tension, 1 , 2 are the densities of water and oil, respectively, L is the linear velocity of the fluid at the narrowest part of the throat ( L = Ud ). 2) Dispersion of droplets in the turbulent fluid flow. According to the theory of homogeneous and isotropic turbulence developed by Kolmogorov, dispersion of drops in a turbulent flow occurs due to pulsations, the scale of which is larger compared to the inner scale of turbulence:
ıT = 2 · L2/5 ·
kf ·
3/5 √ ·
2 , U6/5
(23)
where L is the characteristic size of the unit, here L = d, kf is the coefficient of resistance for the flow circumfluent to drops, kf = 0.5, is the continuous fluid density, U is the characteristic superficial fluid velocity in the throat of apparatus (U = Ud ). 3) Dynamic mechanism of drops dispersion. According to the theory of Levich (Abiev, 2006), the motion of a continuous medium due to the continuity of the tangential stresses on the surface of the drop causes the motion of the fluid inside it, having rotational, and possibly turbulent, while inside there is a dynamic pressure, directed from the inside out. If the pressure exceeds the capillary forces holding the drop, the drop should burst. Droplet diameter for the dispersing mechanism is calculated by the formula:
ıD =
3
6 2 · . kf (2 · )1/3 · U2 2 1
(24)
4) The shear emulsification mechanism. Dispersion of droplets under the influence of shear flows deforming liquid sphere is calculated as follows: ıG =
4· p
p = 4G · 1 ·
(25) 192 + 161 · cos(2ϕ), 162 + 161
(26)
where G is the shear rate, 1 , 2 – dynamic viscosities of water and oil, respectively, ϕ is the angle between the principal axis of the prolate spheroid and the vertical axis. The results of calculations on the droplet size dispersion models, as well as droplet sizes obtained experimentally in the pulsating flow type apparatus are shown in Table 2. As can be seen from the graph in Fig. 5, for small flow rates, approximately less than 1.1 m3 /s (and therefore small energy dissipation rates) predominant mechanism of dispersion of oil droplets in water is turbulent mechanism, but at higher flow rates the droplet size decreases and becomes closer to the shear, dynamic mechanism and the model of Kelvin–Helmholtz. Diameter ratio of drops calculated according to the mechanism of turbulent dispersion with droplets calculated by other models are presented in Table 3.
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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500 450 400
Turbulent mechanism
Shear mechanism
Experiment: δmax
Kelvin-Helmholtz instability
Experiment: δ10
Dynamic mechanism
350
δ, μm
300 250 200 150 100 50 0 0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
QL, m³/h Fig. 5 – Graph of the calculated and experimental size of the oil droplets of the mixture. Table 3 – The ratio of the diameters of the drops dispersed by turbulent mechanism to the droplet size calculated by other dispersion models. QL , m3 /h
0.56
0.72
0.91
1.12
1.31
1.55
1.66
1.77
1.84
1.99
2.04
2.14
2.24
ıT ıV
6.40
7.82
9.43
11.14
12.63
14.44
15.26
16.06
16.57
17.64
17.99
18.70
19.39
ıT ıD
17.35
21.20
25.57
30.20
34.24
39.14
41.35
43.54
44.92
47.83
48.79
50.68
52.59
ıT ıG
6.28
5.97
5.69
5.46
5.30
5.12
5.05
4.98
4.95
4.87
4.85
4.80
4.76
Traditional ways (described in the literature as usual principles) of intensification of processes in heterogeneous media are based primarily on the concept of locally isotropic turbulence of Kolmogorov. According to this concept a crucial role in the implementation of the heat and mass transfer between dispersed and continuous media and dispersion of bubbles and droplets belongs to pulsation components of the velocity and stresses of the turbulent flow. In this theory, the level of intensification is directly related to the turbulent velocity fluctuations. However, the use of turbulence as a tool to improve the efficiency of processes requires additional energy spends and consequently reduces the efficiency of the apparatuses (see Section 3.1), since most of the energy is transformed into the energy of turbulent eddies and then dissipated in the volume of the continuous phase and on the walls of the apparatus. Comparison of the degree of dispersion of oil in the pulsating flow type apparatus with different types of dispersing apparatuses in a wide range of specific energy consumption during preparation of the emulsion is shown in Fig. 6 which is a replica of the diagram proposed by Dolinsky (Dolinsky and Ivanitsky, 1997) and adopted from (Davies, 1987) with addition of experimental points for PFA found in this work. At Fig. 6 there are two corridors: the upper one corresponds to the traditional apparatuses where the energy transformed into useful work (here – into new surface of droplets) not very effective. The lower corridor corresponds to ‘smart’ devices characterized with much smaller sizes of droplets at the same energy dissipation rate. It was revealed that the behavior of experimental points for PFA obtained experimentally depends on the energy dissipation rate. At low energy dissipation rates energy consumption for the preparation of fine emulsion in PFA is comparable to static
mixers at the same droplet size. In the field of higher energy dissipation rates maximum size of the oil droplets in water in PFA is 1.8 times less than lower limit of traditional dispersing apparatus according to diagram (see Fig. 6). Similar droplet diameter can be obtained in a tank with mechanical stirrers (Rushton turbine and other), in which the energy input is 4.5 times higher. Thus, in experiments performed in this work is revealed that droplets dispersed in PFA are finer in comparison with other types of apparatuses at the same energy dissipation rate. By other words, the experimental points move from the upper corridor toward to the lower. Hence, at high energy input PFA could demonstrate its belonging to class of high-performance apparatuses (lower corridor). In addition, PFA has other advantages: (1) PFA is compact; (2) has a 14–16 smaller hydraulic resistance as compared with similar (at first glance) devices such as TTA; (3) contains no dead space; (4) tubular shape ensures the continuity of the process, thereby higher productivity can be achieved. All this allows us to recommend it for extended use in industrial practice.
3.3. Checking the possibility of resonant oscillations of drops in PFA Using the formula of Rayleigh (27), we determined the eigen frequencies of the n-modes of drops with diameter ı. The calculation results of natural frequency oscillations are presented in Table 4.
fn =
1 · 2·
8 · (n − 1) · n · (n + 1)(n + 2) · [(n + 1) · 2 + n · 1 ] · ı
(27)
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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Fig. 6 – Comparison of energy spends in the preparation of emulsions PFA and other devices.
Table 4 – Eigen frequencies of the oil droplets. ı, m n 2 3 4 5
20
50
75
100
fn, Hz 6.383 × 104 1.205 × 105 1.839 × 105 2.54 × 105
1.615 × 104 3.048 × 104 4.653 × 104 6.427 × 104
8.79 × 103 1.659 × 104 2.533 × 104 3.498 × 104
5.709 × 103 1.078 × 104 1.645 × 104 2.272 × 104
Pulsation frequency was calculated as reciprocal of residence time T1 in one unit of Venturi tubes with volume V1 , i.e. f =
1 QL = . T1 V1
(28)
In the pulsating flow type apparatus for flow rates of continuous fluid QL = 0.56/2.24 m3 /h pulsation frequency was in the range of f = 9.82/39.28 Hz, well below the eigen frequency of drops, and thus the resonance effect under the experimental conditions did not arise. Nevertheless, even at such frequencies pulsations could play significant role in process intensification in the inner volume of droplets, allowing to distribute substance in the drops better than at usual flow around at constant flow velocities. This effect has to be proven in the future works.
4.
Conclusion and future work
One of the main results of our investigation is better energy transformation in pulsating flow type apparatus compared to one of the benchmarks in mixing and dispersion processes – stirred tank with Rushton turbine. Maximum droplet size could be used as an indicator of energy transformation efficiency in any kind of devices for droplets/bubbles dispersion, as the measurements technique for the size of droplets is more feasible and provides more reliable results compared with measurements of bubbles’ sizes. It was found that oil in water emulsion with a maximum droplet size 1.8 times smaller than that in conventional
dispersing apparatuses like stirred tanks could be produced. Comparison of energy spend according to Davies–Dolinsky diagram (Fig. 6) showed that the energy required to disperse oil droplets in water to a maximum size of 35 m in PFA is only 400 W/kg, while the minimum power consumption for producing of drops in conventional mixing devices (stirred tanks) is 1800 W/kg. Thus, PFA can continuously produce fine emulsions; dissipated energy is 4.5 times less than in the existing apparatuses. A comparative analysis of energy consumption for the formation of drops and their preservation against coalescence in PFA and in the stirred tank with Rushton turbine was performed by means of Eq. (5) as a criterion of energy efficiency. If the volume of apparatuses and a droplets size to use as a basis for comparison, it was found that the efficiency of energy for the formation and preservation of droplets in PFA is 84.5 times higher than in stirred tank with Rushton turbine. If we compare these apparatuses with equal performance then the volume of the stirred tank will increase and the ratio of the efficiencies will be even more different. This is due to the fact that the preparation of the emulsion in the stirred tank significantly greater than in PFA. Analysis of main impacts on the droplets size has showed that turbulence is the predominant mechanism of the oil droplets dispersed in water only at low energy dissipation rate (ε < 90 W/kg), and with increasing the energy supplied to the apparatus (ε > 100 W/kg) the droplet size decreases and approaches the values calculated by equations for the shear, dynamic mechanism and model of Kelvin–Helmholtz. This indicates that in PFA are conditions arising allowing to create more complex flow organization compared to turbulent eddies and turbulence plays just a side role. Traditional points of view to process intensification in heterogeneous media based primarily on the concept of locally isotropic turbulence. According to this concept a determinant role in the dispersion of bubbles and droplets belongs to pulsation components of the velocity and stresses of turbulent flow. However, the use of turbulence as a means of increasing
Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011
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the efficiency of apparatuses involves extra energy costs and consequently reduces the efficiency of the apparatus. In this paper it is shown that the energy spent for turbulence generation in stirred tank for producing a dispersion of oil droplets in water of with maximal size of about 35 m is 84.5 times higher than that necessary for PFA. Further research is aimed to expand the range of continuous phase velocities (and to increase energy dissipation rate) in order to check the trajectory of points on Fig. 6. If they will approach the lower corridor at the plot on Fig. 6, this will confirm further development of non-turbulent mechanisms of disintegration and decay of the role of turbulence. Similar behavior has been found earlier and very well known, e.g. for coiled pipes where turbulence is suppressed by organized secondary flows, or for convergent tubes, where acceleration of velocity on the one hand increase the stability of flow, and on the other hand the density of energy is also increases in the throat (just like in the neck of the PFA). The other way to improve the effectiveness of disintegration of droplets is the introduction of a third phase (gas), which may serve as an additional way to increase the degree of emulsification and mass transfer in both phases of liquid–liquid systems. Besides, it is necessary in further works to perform detailed analysis of “life” of droplets during their way along different parts of PFA, taking into account the different impacts on the droplet surface and volume. This will allow to specify more accurately distribution of impacts within PFA volume, making possible to use the multiblock model conjugated with population balance method similar to those which was applied to stirred tank by Alopaeus et al. (1999).
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Please cite this article in press as: Abiev, R.Sh., Vasilev, M.P., Pulsating flow type apparatus: Energy dissipation rate and droplets dispersion. Chem. Eng. Res. Des. (2016), http://dx.doi.org/10.1016/j.cherd.2016.03.011