Electrical conductivity as a novel technique for characterization of colloidal gas aphrons (CGA)

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Colloids and Surfaces A: Physicochem. Eng. Aspects 317 (2008) 262–269

Electrical conductivity as a novel technique for characterization of colloidal gas aphrons (CGA) M. Moshkelani, M.C. Amiri ∗ Department of Chemical Engineering, Isfahan University of Technology, Isfahan, Iran Received 2 July 2007; received in revised form 22 September 2007; accepted 24 October 2007 Available online 21 December 2007

Abstract Colloidal gas aphron (CGA) characterization demands further investigation for exploring its potential ability in separation processes. In this paper, both integrated and differentiated electrical conductivity (EC) of CGA dispersion was measured and compared with surfactant concentration. They confirm each other well. The range of concentration of anionic surfactant for producing CGA was chosen from below the critical micelle concentration (CMC) up to above it. EC technique results in differentiating three separate stages compared with two stages in conventional aphron drainage method. The experimental results show that EC data is a good indicator for probing and characterizing the CGA dispersion. The most interesting aspect of EC results is that EC data (an intensive property) follows fairly well the cumulative drainage volume (an extensive property). © 2007 Elsevier B.V. All rights reserved. Keywords: Colloidal gas aphron; Integrated; Differentiated; Electrical conductivity; Drainage stages

1. Introduction Colloidal gas aphrons (CGAs), which first were introduced by Sebba [1], are spherical bubbles with gaseous core inside and are surrounded by multilayer of surfactant molecules. CGA bubbles are enough stable to be transferred by peristaltic pump to the point of use and performing a successful flotation of tiny particles. These unique characteristics make CGA to be used in various fields such as firefighting [2], separation technologies [2–28], bioengineering [2,29–36], well bore drilling [37–45], and recently tissue engineering [46]. Drainage is a popular method for characterization of CGA dispersion. In this technique, the variation of drained liquid volume with time is measured. This measurements results in a drainage curve mainly composed of two distinct stages as reported by some researchers [3,47–49]. The first stage accounts for removal of more than 90% of bulk liquid. The second stage through which foam films gradually rupture and bubbles collapse is slow due to capillary pressure control and plateau border suction. There are a number of studies simulating microscopic foam drainage since

∗

Corresponding author. Tel.: +98 311 3915615; fax: +98 311 3912677. E-mail addresses: [email protected] (M. Moshkelani), [email protected] (M.C. Amiri). 0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.10.034

1965. However, there are two major categorized distinctions for simulation. Leonard and Lemlich [50] assumed that viscous losses occurred only in plateau borders rather than junctions. But Koehler et al. [51] developed a model for viscous losses occurring at junctions. In Table 1 the models and relevant assumptions are summarized. Unfortunately the second stage although is very time taking, is not informative and useful for characterization of CGA dispersion in conventional drainage measurement. In this paper an alternative method, EC probing, was introduced to achieve a better understanding of this process. 2. Theory A brief history of researches on the theory of CGA suspension drainage has been addressed in Table 2. The theory of drainage is based on this fact that as a result of creaming, the CGA is separated into a clear water region and froth. In the froth phase the bubbles are crowded together more than they were in the original dispersion and become polyhedral foams finally. Fig. 1 shows the morphology of aphron bubbles during drainage process with time. It illustrates how spherical bubbles change into polyhedral foams. Changes in cumulative drained volume versus time were measured by many researchers. Amiri and Woodburn took some illustrative photos of CGA drainage

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Table 1 Mathematical models of microscopic drainage Researchers

Proposed model

Leonard and Lemlich [50] Koehler et al. [51]

∂α ∂τ

+

∂α ∂τ

+

∂ ∂τ ∂ ∂ξ





α2 −

√ α ∂α 2 ∂ξ

α3/2 −



 1 ∂α

2 ∂ξ

Assumptions = 0,

= 0,

α= α=

A , Z02 A , Z02

ξ= ξ=

Z Z0 , Z Z0 ,

τ= τ=

t t0 t t0

Foam is monodisperse and dry, neglect liquid in the film and junctions, stokes flow, no inertia, Surfactants with low shear viscosity, plug flow in plateau borders, shearing flow in junctions,

A: plateau border cross sectional area at position x = (0, 0, z) and time t.

in measuring cylinder at various times. They show clearly both the drained liquid volume increases and also how CGA structure deforms by proceeding the drainage time. Two stages for CGA drainage were conventionally distinguishable as macroscopic stage in which the rising velocity of interface is conspicuous and specified by Stocks (or modified Stocks) law, and microscopic stage. Although the first stage is clear very well, the second stage, which proceeds for more than 90% of total drainage process time, is very sluggish and non differentiable. Therefore, useful practical information is available only for first stage of drainage. However, the most imperative specifications of CGA dispersion emerge at final period of drainage in which bubbles collapse. This problem is due to the fact that amount of entrapped liquid in shell (disperse phase), is extremely low in comparison with bulk liquid (continues phase). Therefore, volume measurements (as an extensive parameter) could not be an informative indicator for final stage of drainage process as it would be bound to large errors. It is a matter of fact that an intensive parameter should be sought for describing this phenomenon. We anticipated that water in CGA dispersion or drained water has different characterization due to different amount of surfactant ion and micelle particles. That is in the initial CGA dispersion three different water solutions can be distinguished: (1) pure water solution; (2) soapy water mainly in the shell;

(3) water with surfactant molecules in presence or absence of micelle.

We also believed in that EC is a good differentiator for these various solutions. Morphology data such as Fig. 1 illustrates that during drainage the composition of drained solutions change with time. There is no doubt that EC for these solutions are not the same. Therefore, we should expect a strong correlation between drainage and EC measurement. As soapy shell of bubble is a host for surfactant molecule, we devised that concentration of surfactant in continues phase (bulk) or dispersion phase (shell of bubble) can dictate the progress of aphron drainage. The movement of surfactant molecule from shell side into bulk indicates the bubble coalescence or rupture, the topmost controller in drainage process. Therefore, it was decided to measure surfactant concentration to follow drainage process. Two different approaches can be made to measure the surfactant concentration. This can be carried out by measuring either electrical conductivity or Sodium (surfactant head) concentration. Both measurements have been done and it was found that the results well confirm each other. Both integrated and differentiated EC measurements have been done. It was found that integrated EC data is much similar to conventional drainage method, but differentiated EC data show the instantly progress of drainage process.

Fig. 1. Morphological illustration of CGA dispersion during drainage time (s): left: 10, middle 300 and right 600 [56].

264

Table 2 Summery of studies on CGA drainage Studied parameter

Drainage velocity/rate

Conclusion

Amiri and Woodburn [47]

pH, volume fraction of aphron

Experiment: 0.0002–0.117 (mm/s), calculation: 0.018–0.199 (mm/s)

Chaphalkar et al. [52]

τ d a , surfactant type and Cb

Save and Pangarkar [53]

pH, stirring time, surfactant and salt concentration, viscosity, impeller clearance, additives, enzyme, polymer, electrolytes effects

Inner core of aphrons (±35 ␮m) rising with a shell thickness of 0.75 ␮m. Stability of aphron is strongly dependent on pH. Drainage velocity is not sensitive to surfactant concentration, but bubble stability is sensitive to surfactant addition. Increasing in surfactant concentration and ionic strength, reduce the mean diameter size of bubbles (with size range of 30–300 ␮m) Systematic studies on system properties and operating variables on CGA characteristics have brought out. Hass and Johnson’s model can be adapted to describe CGA drainage.

w(t, Z0 ) = L0 (t0 , Z0 ) CT



t−t0 0 (t−t0 )+1

ρg 32μ

×

4 πnk2

×

Jauregi et al. [17]

Surfactant and salt concentration, stirring time, Tc , pH

Jauregi and Varley [54]

Stirring time, protein recovery, pH, stirrer speed

Jauregi et al. [55]

Surfactant and salt C, stirring time, T, pH

Jarudilokkul [20]

Stirring time, pH, rpm, NaCl C, protein recovery

Yan et al. [48]

Surfactant concentration and type, T

Vt = Vmax knt+t n

Bhatia et al. [49]

Surfactant concentration, stirring speed, air hold up, stirring time, mixing of two oppositely charged CGAs

ln

a c

Drainage time. Concentration. Temperature.

,

CT0 =

1/2

× L(t0 , Z0 )

Prediction of liquid drainage rate in order to predict apron diameter

n



b

4 Hd2

VT0 −VL VT0



= −mtd

Determining of air hold-up and τ d . increasing in gas hold up, decreases required power for CGA generation. Stirring speed and pH had little effect on separation parameters. Surfactant and protein initial concentration are important factors in separation. Optimum protein recovery was 95% without loss of lysozyme activity. Electron microscopy and X-ray diffraction indicates existence of multilayer surfactant shell. Save and Pangarkar’s model best fits with experimental data. Increasing stirring time and surfactant concentration increases the stability, but the latter decreases separation. pH should be such that electrostatic interactions favor separation Mathematical model describes CGA drainage. Two independent mechanisms identified drainage rate. Developing of an empirical correlation for air hold up and stirring time. Validating first order model for drainage rate with experiment. Size distribution observation with population balance model.

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Researchers

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3. Experimental procedure Different concentrations of sodium dodecyl sulfate (SDS), an anionic surfactant (FSA, England), was used to produce CGA according to the method proposed by Sebba [2]. EC of differentiated and integrated samples of clear solution and continues phase was measured by using pH/EC Meter C732 (Belgium). For measurements of integrated EC, the probe position was fixed at the bottom of the cylinder and the variations were recorded versus time. For differentiated tests, the drained clear solutions were separated periodically according to progress of drainage. The data for mother solutions (the initial surfactant solution before producing CGA) were measured as well. Two different methods of atomic absorption (Buck Scientific GP 210, USA) and flame photometer (Sherwood 410, Germany) were applied to measure surfactant concentration (Sodium ion). It was found that flame photometer results are reproducible and more reliable than atomic absorption measurements. More details of experimental procedure and measurements are shown in Fig. 2. Integrated EC measurement was recorded continuously but differentiated EC was recorded batchwise. In order to minimize the errors of EC measurements the following points were considered: (a) Only the range of concentration with a linear calibration curve was chosen. (b) Variations of EC of each sample with time were followed and the equilibrium time (te ) for having reproducible EC was determined. These data guided us to set a default time for each EC reading. (c) For each sample, three tests were done but the average was reported. The acceptable ratio of standard deviation to mean value was less than 6%.

Fig. 2. Arrangement of experimental design. (a) A photograph of apparatus, (b) a schematic diagram of testing procedure.

ber corresponds to the sequential sampling time from the start of drainage. As is reflected in the figure, in comparison with conventional drainage mechanism, differentiated EC approach depicts following three stages for the mechanism:

4. Results and discussion Fig. 3 illustrates differentiated EC of CGA dispersion which was produced at CMC of SDS in distilled water. For differentiated EC measurement, samples of drained water were isolated and measured at different time intervals. The sample num-

1. Initial low EC stage, in which mostly the electrical conductivity of continues phase rather than dispersed phase is sensed. 2. Constant EC stage, in which the electrical conductivity of a mixture of liquid content of plateau border and contin-

Fig. 3. CGA drainage stages using EC technique.

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Fig. 4. Changes in EC of clear solution with time for different SDS concentrations.

ues water phase is sensed. As the EC of continues phase is not very different from EC of liquid content of plateau border, therefore the EC of the mixed liquid remains roughly constant. 3. Final rising EC stage, in which mostly the electrical conductivity of soapy liquid (shell liquid) is sensed. As can be expected in this stage, the final samples have the highest EC. Based on this theory it is not difficult to grasp that these three stages should be observed clearly in concentration of surfactant at CMC. At concentrations lower or upper than CMC the difference between EC of continues phase and disperse phase is not enough to show these stages sharply. Fig. 4 illustrates EC variation versus time for integrated measurements. The variation trend is the same for different concentrations of SDS and looked like the behavior of drained water volume with time (Fig. 5). The EC data curve for CMC lasts more than other concentrations. This is due to more stable CGA dispersion. This phenomenon, more stable CGA at CMC, was reported by other researchers [48,49]. The differentiated EC for various concentrations of SDS surfactant are shown in Fig. 6. To appreciate the importance of differentiated method, the EC data for first and final samples

Table 3 Electrical conductivity (␮s/cm) data of different samples at different concentrations (mM) of SDS Concentration

First sample EC

Final sample EC

Mother solution EC

0.5 3 6 8.1 10 12

53.7 269 563 654 850 964

76.4 386 686 943 956 1033

66.9 316 597 797 889 998

and also mother solutions for different concentrations of SDS are recorded in Table 3. It is seen that there are meaningful difference between EC data of various samples, i.e. the range of data is well enough wide for differentiation. These data support our theory that differentiated EC can be a paramount factor to identify drainage progress. The interesting point in Table 3 is that the EC of first sample (the drained liquid at initial period) is less than EC of mother solution. This reveals the fact that surfactant molecules prefer to accumulate in shell of bubbles. This conclusion is also correct for interpreting the highest EC in final samples.

Fig. 5. Cumulative volume of drained liquid for different SDS concentrations.

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Fig. 6. EC of differentiated samples for various SDS concentrations.

The EC of initial samples seems enough high to conclude that continues phase in CGA dispersion is never empty of surfactant molecules. The source for these high EC in initial samples can be due to: (a) the existence of free surfactant molecules, as Gibbs equation dictates for sharing of surfactant molecules between interface and bulk phase; (b) the existence of tiny bubbles in clear solution. We detected these tiny bubbles as shown Fig. 7. This finding supports the idea that the shell of aphron bubble is porous that looks like a turbulent fluidized bed (more details of this phenomenon appears in further communication). Fig. 8 shows the surfactant (Na+ ) concentrations of different samples and their EC data are shown in Fig. 6. The Na+ concentration was measured by flame photometer method. Comparing Figs. 6 and 8 reveal that both EC data and surfactant concentration measurements have the same trend. Fig. 9 shows change of surfactant concentration versus EC in various samples. The linear relation between surfactant concentration and EC confirms the fact that they are equivalent

Fig. 7. A micrograph of CGA bubbles generated from Triton X-405 solution at surfactant concentration of 20.24 g in 1 l of water.

Fig. 8. Na+ concentrations of various samples.

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Fig. 9. Na+ concentrations vs. EC measurement of various samples.

parameters. For this reason, electrical conductivity can be considered as a novel technique for characterization of colloidal gas aphrons (CGA). 5. Conclusions • Major data in this work was reported based on EC measurements as electrical conductivity is an intensive and easy test for low concentration measurement. • An interesting point is that the integrated EC data (an intensive property) follows fairly well the cumulative volume data (an extensive property). • It was found that differentiated electrical conductivity of drained solution of CGA is a good indicator for following the drainage progress. Therefore, a novel technique for characterization of colloidal gas aphrons (CGA) based on EC measurements was introduced in this paper. • The main advantage of this technique is that three clear stages, rather than two stages in conventional method, can be identified. Acknowledgement Isfahan University of Technology is gratefully acknowledged for financial support of this project. References [1] F. Sebba, An unexpected colloid system, J. Colloidal Interface Sci. 35 (1971) 643–646. [2] F. Sebba, Foams and Biliquid Foams, 1st ed., Wiley, Chichester, UK, 1987. [3] M.C. Amiri, Separation of ultra-fine sulphur particles from NTA dispersion by aphron flotation, J. Eng. Islamic Republic of Iran 3 (3 and 4) (1990) 148–153. [4] D.L. Michelson, D.A. Wallis, F. Sebba, The use of aphron techniques for treating hazardous wastes, in: World congress III of Chemical Engineering, vol. 3, Tokyo, Japan, Sept, 1986, pp. 592–595. [5] D.L. Michelson, K.W. Ruettimann, K.R. Hunter, F. Sebba, Use of predisposed solvents extraction/flotation techniques for removal of hazardous organics from contaminated waters, Chem. Eng. Comm. 49 (1986) 155–163.

[6] D.L. Michelson, J.W. Longe, T.A. Smith, J.A. Suggs, A micro bubble dispersion in water—what role in industrial waste treatment? in: Proceeding of Mid-Atlantic Industrial Waste Water and Hazardous Materials Conference, 1988, pp. 13–30. [7] D. Roy, K.T. Valsaraj, S.A. Kottai, Separation of organic dyes from wastewater by using colloidal gas aphrons Sep. Sci. Technol. 27 (1992) 573–588. [8] Y.Y. Huang, Y.D. Wang, G.H. Wu, Y.Y. Dai, Separation of organic dyes from water by colloidal gas aphrons, Tsinghua Sci. Technol. 7 (2002) 46–51. [9] M.A. Hashim, S.B. Gupta, S.V. Kumar, R. Lim, C.C. Tan, Effect of air to solid ratio in the clarification of yeast by colloidal gas aphrons, J. Chem. Technol. Biotechnol. 71 (1998) 335–339. [10] E.H.A. Mansur, Y.D. Wang, Y.Y. Dai, Separation of fine particles by using colloidal gas aphrons, Chin. J. Chem. Eng. 12 (2004) 286–289. [11] D. Roy, K.T. Valsaraj, W.D. Constant, M. Darji, Removal of hazardous oily waste from a soil matrix using surfactants and colloidal gas aphron suspensions under different flow conditions, J. Hazard. Mater. 38 (1) (1994) 127–144. [12] S. Ciriello, S.M. Barnett, F.J. Deluise, Removal of heavy metals from aqueous solutions using micro gas dispersion, Sep. Sci. Technol. 17 (1982) 521–534. [13] J.J. Cilliers, D. Bradshaw, The flotation of fine pyrite using colloidal gas aphrons, Miner. J. Eng. 9 (1996) 235–241. [14] Y.D. Wang, H.Z. Wen, Y.Y. Dai, Flotation of Cu(II) by colloidal gas aphrons (CGA), J. Chem. Ind. Eng. (China) 52 (2001) 266–269. [15] Z.Y. Guan, F.X. Ding, N.J. Yuan, Application of loop flotation separation approach in treatment of waste water containing Cu(II), J. Tsinghua Univ. Sci. Technol. 39 (1999) 114–117. [16] P. Jauregi, J. Varley, Lysozyme separation by colloidal gas aphrons, Prog. Colloid Polym. Sci. 100 (1996) 362–367. [17] P. Jauregi, S. Gilmour, J. Varley, Characterization of colloidal gas aphrons for subsequent use for protein recovery, Chem. Eng. J. 65 (1997) 1–11. [18] M. Noble, A. Brown, A. Jauregi, P. Kaul, J. Varley, Protein recovery using gas–-liquid dispersions, J. Chromatogr. B 711 (1998) 31–43. [19] M.C. Amiri, K.T. Valsaraj, Effect of gas transfer on separation of whey protein with aphron flotation, Sep. Purif. Technol. 35 (2004) 161–167. [20] S. Jarudilokkul, K. Rungphetcharat, V. Boonamnuayvitaya, Protein separation by colloidal gas aphrons using non-ionic surfactant, Sep. Purif. Technol. 35 (2004) 23–29. [21] M. Caballero, R. Cela, J.A. Perez-bustamentze, Studies on the use of colloidal gas aphrons in coflotation and solvent-sublation processes. A comparison with the conventional technique, Sep. Sci. Technol. 24 (9 and 10) (1989) 629–640. [22] E.T. Woodburn, D.J. Robbins, J.B. Stockton, Separating ultra fine coal particles by froth flotation process, Filter. Sep. 24 (2) (1987) 92–96.

M. Moshkelani, M.C. Amiri / Colloids and Surfaces A: Physicochem. Eng. Aspects 317 (2008) 262–269 [23] N. Blakebrough, The application of flotation to clarification of biological suspensions, downstream processing in biotechnology, in: Proceeding Int. Seminar, McGraw-Hill Pub., 1992, pp. 1–11. [24] R.H. Yoon, G.H. Lutterll, Miner. Pros. Extractive Metall. 5 (1989) 101–122. [25] G.J. Jameson, S. Nam, M. Yong, Miner. Sci. Eng. 9 (1977) 103–118. [26] D. Reay, G.A. Ratcliff, Separation of plastics by aphron flotation, experimental testing of the hydrodynamic collision model of fine particle flotation, Can. J. Chem. Eng. 53 (1975) 481–486. [27] S.J. Read, G.C. Lees, S.J. Hurst, Separation of plastics by aphron flotation, Polym. Recycl. 2 (1996) 49–56. [28] G. Johansson, R.J. Pugh, The influence of particle size and hydrophobicity on the stability of mineralized froths, Int. J. Miner. Process 34 (1) (1992) 1–21. [29] D.A. Wallis, D.L. Michelson, F. Sebba, J.K. Carpenter, D. Houle, Application of aphron technology to biological separation, Biotechnol. Bioeng. Symp. Ser. 15 (1985) 399–408. [30] M.B. Subramaniam, N. Blakebrough, H.A. Hashim, Clarification of suspension by colloidal gas aphrons, J. Chem. Technol. Biotechnol. 48 (1990) 41–50. [31] S.V. Save, V.G. Pangarkar, Harvesting of Saccharomyces cerevisiae using colloidal gas aphrons, J. Chem. Technol. Biotechnol. 62 (1995) 192–199. [32] S.V. Save, V.G. Pangarkar, A model for harvesting of microorganisms using colloidal gas aphrons, J. Chem. Technol. Biotechnol. 61 (1994) 367–373. [33] D. Roy, R.R. Kommalapati, K.T. Valsaraj, W.D. Constant, Soil flushing of residual transmission fluid: application of colloidal gas aphron suspensions and conventional surfactant solutions, Water Res. 29 (1995) 589–595. [34] D. Roy, S. Kongara, K.T. Valsaraj, Application of surfactant solutions and colloidal gas aphron suspensions in flushing naphthalene from a contaminated soil matrix, J. Hazard. Mater. 42 (1995) 247–263. [35] S.V. Save, V.G. Pangarkar, S. Vasanthkumar, Intensification of mass transfer in aqueous two phase extraction, Biotechnol. Bioeng. 41 (1) (1993) 72–78. [36] D.L. Michelson, J.A. Kaster, W.H. Velander, Increased oxygen transfer in a yeast fermentation using a micro bubble dispersion, in: 11th Symposium on Biotechnology for fuels and Chemicals, Oak Ridge National Laboratory, 1989. [37] N. Bjordalen, E. Kuru, Stability of micro bubble based drilling fluids under downhole conditions, in: 7th Canadian International Petroleum Conference, 2006.

[38] [39] [40] [41] [42] [43] [44]

[45] [46]

[47] [48]

[49]

[50] [51]

[52]

[53] [54] [55] [56]

269

T. Brookey, US patent 5881826 (1999). T. Brookey, US patent 6390208 B1 (2002). T. Brookey, US patent 6422326 (2002). T. Brookey, US patent 6739414 B2 (2004). T. Brookey, US patent 6770601 B1 (2004). T. Brookey, US patent 7033977 B2 (2006). C.C. White, A.P. Chesters, C.D. Ivan, Aphron based drilling fluid: novel technology for drilling depleted formations in the North Sea, in: SPE 79840, SPE/IADC drilling Conference, Amsterdam, 2003, pp. 19–21. F. Growicock, Enhanced Wellbore Stabilization and Reservoir Productivity with Aphron Drilling Fluid Technology, MASI Technologies LLC, 2005. E. Donaldson, J. Cuy, Poly vinyl alcohol amine acid hydro gel fabricated into tissue engineering scaffolds by colloidal gas aphron technology, Macromol. Symp. 227 (2005) 115–122. M.C. Amiri, E.T. Woodburn, A method for the characterization of colloidal gas aphrons, Trans. Inst. Chem. Eng. A68 (1990) 159–160. Y.L. Yan, C.T. Qu, N.S. Zhang, Z.G. Yang, L. Liu, A study on the kinetics of liquid drainage from colloidal gas aphrons (CGAs), Colloids Surfact. A: Physicochem. Eng. Aspects 29 (2005) 167–172. D. Bahtia, G. Goel, S.K. Bhimania, A.N. Bhaskarwar, Characterization and drainage kinetics of colloidal gas aphrons, AIChE J. 51 (11) (2005) 3048–3058. R. Leonard, R. Lemlich, Laminar longitudinal flow between close-packed cylinders, AIChE J. 11 (1965) 18–25. S.A. Koehler, S. hilgenfeldt, H.A. Stone, Liquid flow through aqueous foams: the node-dominated foam drainage equation, Phys. Rev. Lett. 82 (1999) 4232–4235. P.G. Chaphalkar, K.T. Valsaraj, D. Roy, Study of the size distribution and stability of colloidal gas aphrons using a particle size analyzer, Sep. Sci. Technol. 28 (1993) 1287–1302. S.V. Save, V.G. Pangarkar, Characterization of colloidal gas aphron, Chem. Eng. Commun. 127 (1994) 35. P. Jauregi, J. Varley, Colloidal gas aphrons (CGA): dispersion and structural features, Biotechnol. Bioeng. 59 (1998) 471–481. P. Jauregi, G.R. Mitchel, J. Varley, Colloidal gas aphrons (CGA): dispersion and structural features, AIChE J. 46 (1) (2000) 24–36. M.C. Amiri, Micro- and macroscopic observations on the structure of colloidal gas aphron, 17th Int. Congress of Chemical and Process Eng. (2006), B.2.3. Praha, Czech Republic.