Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T14:03:23.105Z Has data issue: false hasContentIssue false

2 - Droplets and Dispersions

Published online by Cambridge University Press:  12 May 2020

Laurence R. Weatherley
Affiliation:
University of Kansas
Get access

Summary

The fundamentals of droplet formation and motion are discussed, highlighting the importance to intensification of contactor hydraulic performance and mass transfer kinetics. A detailed review of the relationships dictating drop formation, drop size, and velocity in liquid–liquid systems is included. Dynamic behavior during drop formation and the mode of drop detachment from a nozzle are described. The behavior of single discrete drops in unhindered motion is considered, and then developed into the analysis of swarms of drops in hindered motion and in sprays. Key literature discussing droplet behavior is reviewed, with presentation of correlations for prediction of drop size and velocity in these cases. An overview of drop size correlations for liquid–liquid mixtures in stirred vessels is presented. This is followed by a review of correlations developed for drop size in continuous column contactors of various types. These include the Kühni column, the pulsed Karr column, packed columns, spray columns, and rotating disk columns. Quantitative modeling of dispersion and coalescence in stirred vessels based on a population balance approach is also described.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abidin, M., Raman, A., and Nor, M (2014). Experimental investigations in liquid−liquid dispersion system: effects of dispersed phase viscosity and impeller speed. Industrial Engineering Chemistry Research, 53, 65546561.Google Scholar
Alopaeus, V., Koskinen, J., and 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. Chemical Engineering Science, 54, 58875899.Google Scholar
Alopaeus, V., Koskinena, J., Keskinena, K. I., and Majander, J. (2002). Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank, Part 2: Parameter fitting and the use of the multiblock model for dense dispersions. Chemical Engineering Science, 57, 18151825.Google Scholar
Al-Rahawi, A. M. I. (2007). New predictive correlations for the drop size in a rotating disc contactor liquid–liquid extraction column. Chemical Engineering & Technology, 30(2), 184192.Google Scholar
Baird, M. H. I. and Lane, S. J. (1973) Drop size and holdup in a reciprocating plate extraction column. Chemical Engineering Science, 28(3), 947957.CrossRefGoogle Scholar
Baumler, K., Wegener, M., Paschedag, A. R., and Bansch, E. (2011). Drop rise velocities and fluid dynamic behavior in standard test systems for liquid/liquid extraction – experimental and numerical investigations. Chemical Engineering Science, 66, 426439.Google Scholar
Bensalem, A., Steiner, L., and Hartland, S. (1986), Effect of mass transfer on drop size in a Karr column. Chemical Engineering and Processing, 20(3), 129135.Google Scholar
Bond, W. N. and Newton, D. A. (1928). Bubbles, drops and Stokes law. Philosophical Magazine, 5(30), 794800.Google Scholar
Calabrese, R. V., Chang, T. P. K., and Dang, P. T. (1986a). Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersed-phase viscosity. American Institute of Chemical Engineers Journal, 32, 657666.Google Scholar
Calabrese, R. V., Wang, C. Y., and Bryner, N. P. (1986b) Drop breakup in turbulent stirred tank contactors. Part III: Correlation for mean size and drop size distributions. American Institute of Chemical Engineers Journal, 32, 677681.Google Scholar
Chatzi, E. (1983). Analysis of Interactions in Fluid–Fluid Dispersion Systems in Agitated Vessels. Cleveland, OH: Cleveland State University Press.Google Scholar
Chatzi, E. G. and Lee, J. M. (1987). Analysis of interactions for liquid–liquid dispersions in agitated vessels. Industrial Engineering Chemistry Research, 26, 22632267.Google Scholar
Chatzi, E. G., Gavrielides, A. D., and Kiparissides, C. (1989). Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels. Industrial Engineering Chemistry Research, 28, 17041711.Google Scholar
Chen, C. T., Maa, J., Yang, Y., and Chang, C. (2001). Drop formation from flat tip nozzles in a liquid–liquid system. International Communications in Heat Mass Transfer, 28(5), 681692.Google Scholar
Cherlo, S. K. R., Kariveti, S., and Pushpavanam, S. (2010). Experimental and numerical investigations of two-phase (liquid–liquid) flow behavior in rectangular microchannels. Industrial Engineering Chemistry Research, 49, 893899.Google Scholar
Clift, R,. Grace, J. R., and Weber, M. E. (1978). Bubbles, Drops and Particles. New York: Academic Press.Google Scholar
Coulaloglou, C. A. and Tavlarides, L. L. (1977). Description of interaction processes in agitated liquid–liquid dispersions. Chemical Engineering Science, 32, 12891297.Google Scholar
Deshpande, K. B. and Zimmerman, W. B. (2006). Simulation of interfacial mass transfer by droplet dynamics using the level set method. Chemical Engineering Science, 61, 64866498.Google Scholar
Garner, F. H. and Skelland, A. H. P. (1955). Some factors affecting droplet behaviour in liquid–liquid systems. Chemical Engineering Science, 4(4), 149158.CrossRefGoogle Scholar
Grace, J. R., Wairegi, T., and Nguyen, T. H. (1976). Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. Transactions of the Institution of Chemical Engineers, 54, 167.Google Scholar
Hadamard, J. S. (1911). Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. (in French), 152, 17351738.Google Scholar
Hamielec, A. E., Storey, S. H., and Whitehead, J. M. (1963). Viscous flow around fluid spheres at intermediate Reynolds-numbers. Canadian Journal of Chemical Engineering, 12, 246251.Google Scholar
Harkins, W. D. and Brown, F. E. (1919). The determination of surface tension (free surface energy) and the weight of falling drops: the surface tension of water and benzene by the capillary height method. Journal of the American Chemical Society, 41(4), 499524.Google Scholar
Harper, J. F. and Moore, D. W. (1968). Motion of a spherical liquid drop at high Reynolds number. Journal of Fluid Mechanics, 32, 367391.Google Scholar
Hayworth, C. B. and Treybal, R. E. (1950). Drop formation in two-liquid phase systems. Industrial and Engineering Chemistry Research, June, 1174–1181.Google Scholar
Hesketh, R. P., Etchells, A. W., and Russell, T. W. F. (1991). Experimental observations of bubble breakage in turbulent flow. Industrial and Engineering Chemistry Research, 30, 835841.CrossRefGoogle Scholar
Hinze, J. O. (1955). Fundamentals of the hydrodynamic mechanism of splitting dispersion process. American Institute of Chemical Engineers Journal, 1, 289295.Google Scholar
Hu, S. and Kintner, R. C. (1955). The fall of single drops through water. American Institute of Chemical Engineers Journal, 1(1), 4248.Google Scholar
Hughmark, G. A. (1971). Drop breakup in turbulent pipe flow. American Institute of Chemical Engineers Journal, 17(4), 1000.Google Scholar
Kalyanasundaram, C. V., Kumar, R., and Kuloor, N. R. (1968). Direct contact heat transfer between two immiscible phases during drop formation. International Journal of Heat and Mass Transfer, 11(12), 18261830.Google Scholar
Klee, A. J. and Treybal, R. E. (1956). Rate of rise or fall of liquid drops. American Institute of Chemical Engineers Journal, 2(4), 444447.Google Scholar
Krishna, P. M., Venkateswarlu, D., and Narasimhamurty, G. S. R. (1959). Fall of liquid drops in water. Drag coefficients, peak velocities, and maximum drop sizes. Journal of Chemical Engineering Data, 4, 340343.Google Scholar
Kumar, A. and Hartland, S. (1986). Prediction of drop size in rotating-disk extractors. Canadian Journal of Chemical Engineers, 64(6), 915924.Google Scholar
Kumar, A., and Hartland, S. (1988). Prediction of dispersed-phase holdup and flooding velocities in Karr reciprocating-plate extraction columns. Industrial and Engineering Chemistry Research, 27(1), 131138.Google Scholar
Kumar, A. and Hartland, S. (1996). Unified correlations for the prediction of drop size in liquid–liquid extraction columns. Industrial and Engineering Chemistry Research, 35, 26822695.CrossRefGoogle Scholar
Laso, M., Steiner, L., and Hartland, S. (1987). Dynamic simulation of agitated liquid–liquid dispersions: II. Experimental determination of breakage and coalescence rates in a stirred tank. Chemical Engineering Science, 42(10), 24372445.Google Scholar
Lee, C. H., Erickson, L. E., and Glasgow, L. A. (1987a). Bubble breakup and coalescence in turbulent gas–liquid dispersions. Chemical Engineering Communications, 59, 6584.Google Scholar
Lee, C. H., Erickson, L. E., and Glasgow, L. A. (1987b). Dynamics of bubble size distribution in turbulent gas–liquid dispersions. Chemical Engineering Communications, 61, 181195.CrossRefGoogle Scholar
Lehr, F., Millies, M., and Mewes, D. (2001). Coupled calculation of bubble size distribution and flow fields in bubble columns. Chemie Ingenieur Technik, 73, 12451259.Google Scholar
Lehr, F., Millies, M., and Mewes, D. (2002). Bubble-size distributions and flow fields in bubble columns. AIChE Journal, 48, 24262443.Google Scholar
Letan, R. and Kehat, E. (1967). The mechanics of a spray column. American Institute of Chemical Engineers Journal, 13(3), 443449.Google Scholar
Liao, Y. and Lucas, D. A. (2009). Literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chemical Engineering Science, 64, 33893406.Google Scholar
Loth, E. (2008). Quasi-steady shape and drag of deformable bubbles and drops. International Journal of Multiphase Flow, 34(6), 523546.Google Scholar
Luo, H. and Svendsen, H. F.(1996). Theoretical model for drop and bubble breakup in turbulent dispersions. American Institute of Chemical Engineers Journal, 42, 12251233.Google Scholar
Martinez-Bazan, C., Montanes, J. L., and Lasheras, J. C. (1999a). On the breakup of an air bubble injected into fully developed turbulent flow. Part 1. Breakup frequency. Journal of Fluid Mechanics, 401, 157182.Google Scholar
Martinez-Bazan, C., Montanes, J. L., and Lasheras, J. C. (1999b). On the breakup of an air bubble injected into fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics, 401, 183207.Google Scholar
Moore, D. W. (1959).The rise of a gas bubble in a viscous liquid. Journal of Fluid Mechanics, 6(1), 113130.CrossRefGoogle Scholar
Moore, D. W. (1963). The boundary layer on a spherical gas bubble. Journal of Fluid Mechanics, 16(2), 161176.Google Scholar
Narsimhan, G. and Gupta, J. P. (1979). A model for transitional breakage probability of droplets in agitated lean liquid–liquid dispersions. Chemical Engineering Science, 34, 257265.Google Scholar
Null, H. R. and Johnson, H. F. (1958). Drop formation in liquid–liquid systems from single nozzles. American Institute of Chemical Engineers Journal, 4(3), 273281.Google Scholar
Pacek, A. W. Man, C. C., and Nienow, A. W. (1998). On the Sauter mean diameter and size distributions in turbulent liquid−liquid dispersions in a stirred vessel. Chemical Engineering Science, 53(11), 20052011.Google Scholar
Parlange, J. Y. (1970). Motion of spherical drops at large Reynolds numbers. Acta Mechanica, 9, (3–4), 323328.Google Scholar
Petera, J. and Weatherley, L.R. (2001). Modelling of mass transfer from falling droplets. Chemical Engineering Science, 56, 49294947.Google Scholar
Prince, M. J. and Blanch, H. W. (1990). Bubble coalescence and break-up in air-sparged bubble columns. American Institute of Chemical Engineers Journal, 36,14851499.Google Scholar
Rodger, W. A., Trice, V. G., and Rushton, J. H. (1956). Effect of fluid motion on interfacial area of dispersions. Chemical Engineering Progress, 52(12), 515520.Google Scholar
Rybczynski, W. (1911). Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Acad. Sci. Cracovie, A. (in German), 40–46.Google Scholar
Samani, M. G., Asl, A. H., Safdari, J. M., and Torag-Moestaedi, M. (2012). Drop size distribution and mean drop size in a pulsed packed extraction column. Chemical Engineering Research and Design, 90, 21482154.Google Scholar
Scheele, G. F. and Meister, B. J. (1968). Drop formation at low velocities in liquid–liquid systems: prediction of drop volume. American Institute of Chemical Engineers Journal, 1968, 14(1), 915.Google Scholar
Shinnar, R. (1961). On the behaviour of liquid dispersions in mixing vessels. Journal of Fluid Mechanics, 10, 259275.Google Scholar
Singh, K. K., Mahajani, S. M., Shenoy, K. T., and Ghosh, S. K. (2008). Representative drop sizes and drop size distributions in A/O dispersions in continuous flow stirred tank. Hydrometallurgy, 90, 121136.Google Scholar
Skartlien, R., Sollum, E. and Schumann, H. (2013) Droplet size distributions in turbulent emulsions: breakup criteria and surfactant effects from direct numerical simulations. Journal of Chemical Physics, 139, 174901.Google Scholar
Skelland, A. H. P. and Wellek, R. M. (1964). Resistance to mass transfer inside droplets. American Institute of Chemical Engineers Journal, 10, 491496.Google Scholar
Skelland, A. H. P., Woo, S., and Ramsay, G. G. (1987). Effects of surface-active agents on drop size, terminal velocity, and droplet oscillation in liquid–liquid systems. Industrial & Engineering Chemistry Research, 26, 907911.CrossRefGoogle Scholar
Srilatha, C., Morab, V. V., Mundada, T. P., and Patwardhan, A. W. (2010). Relation between hydrodynamics and drop size distributions in pump–mix mixer. Chemical Engineering Science, 65, 34093426.Google Scholar
Syll, O. S., Mabille, I., Moscosa-Santillan, M., Traore, M., and Amouroux, J. (2011). Study of mass transfer and determination of drop size distribution in a pulsed extraction column. Chemical Engineering Research and Design, 89, 6068.Google Scholar
Takamatsu, T., Hashimoto, Y., Yamaguchi, M., and Katayma, T. (1981). Theoretical and experimental studies of charged drop formation in a uniform electric field. Journal of Chemical Engineering of Japan, 14(3), 178182.Google Scholar
Takamatsu, T., Yamaguchi, M., and Katayma, T. (1982). Formation of single charged drops in liquid media under a uniform electric field. Journal of Chemical Engineering of Japan, 15(5), 349355.Google Scholar
Taylor, T. D. and Acrivos, A. (1964). On the deformation and drag of a falling viscous drop at low Reynolds number. Journal of Fluid Mechanics, 18 , 466476.Google Scholar
Thorsen, G., Stordalen, R. M., and Terjesen, S. G. (1968). On the terminal velocity of circulating and oscillating liquid drops. Chemical Engineering Science, 1968, 23, 413426.Google Scholar
Torab-Mostaedi, M., Ghaemi, A., and Asadollahzadeh, M. (2011). Flooding and drop size in a pulsed disc and doughnut extraction column. Chemical Engineering Research and Design, 89, 27422751.Google Scholar
Tsouris, C. and Tavlarides, L. L. (1994). Breakage and coalescence models for drops in turbulent dispersions. American Institute of Chemical Engineers Journal, 40, 395406.Google Scholar
Usman, M. R., Sattar, H., Hussain, S. N., et al. (2009). Drop size in a liquid pulsed sieve-plate extraction column. Brazilian Journal of Chemical Engineering, 26 (4), 677683.Google Scholar
Vermeulen, T., Williams, G. M., and Langlois, G. E. (1955). Interfacial area in liquid–liquid and gas–liquid agitation. Chemical Engineering Progress, 51(2), 8594.Google Scholar
Waheed, M. A., Henschke, M., and Pfennig, A. (2004). Simulating sedimentation of liquid drops. International Journal for Numerical Methods in Engineering, 59,18211837.Google Scholar
Wang, C. Y. and Calabrese, R. V. (1986). Drop breakup in stirred-tank contactors, Part II: Relative influence of viscosity and interfacial tension. American Institute of Chemical Engineers Journal, 32(4), 667676.Google Scholar
Watanabe, T. and Ebihara, K. (2003). Numerical simulation of coalescence and breakup of rising droplets. Computers & Fluids, 32, 823834.Google Scholar
Weatherley, L. R. and Wilkinson, D. T. (1988). Droplet size studies in a whole broth liquid/liquid extraction system. Process Biochemistry, 23(5), 149156.Google Scholar
Weinstein, B. and Treybal, R. E. (1973). Liquid–liquid contacting in unbaffled agitated vessels. American Institute of Chemical Engineers Journal, 19, 304312.Google Scholar
Wellek, R. M., Agrawal, A. K., and Skelland, A. H. P. (1966). Shape of liquid drops moving in liquid media. American Institute of Chemical Engineers Journal, 12(5), 854862.Google Scholar
Winnikow, S. and Chao, B. T. (1966). Droplet motion in purified systems. Physics of Fluids, 9, 5061.Google Scholar
Yuan, S., Shi, Y., Yin, H., Chen, Z., and Zhou, J. (2012). Correlation of the drop size in a modified Scheibel extraction column. Chemical Engineering and Technology, 35, 18101816.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×