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Rozpad i koalelescencja kropel w intermitentnym polu burzliwym

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Przedmiotem badań, których wyniki przedstawiono w pracy, są zjawiska rozpadu i koalescencji wpływające na rozkład wielkości kropel. Rozważono dyspersje wytwarzane w mieszalnikach w warunkach przepływu burzliwego. W pierwszych rozdziałach pracy zaprezentowano sposób analizy układów rozproszonych w przestrzeni fazowej oraz przedstawiono opis mikrostruktury burzliwości. Przedyskutowano różnicę pomiędzy klasyczną teorią burzliwości Kołmogorowa opartą na uśrednionych statystycznie własnościach burzliwości i podejściem multifraktalnym uwzględniającym intermitentną naturę turbulencji. Zasadniczą część pracy stanowią rozdziały 4 i 5 poświęcone odpowiednio rozpadowi i koalescencji kropel. Każdy z nich zawiera krótki przegląd i dyskusję koncepcji modelowania rozważanego procesu oraz przedstawienie modeli własnych. Zaproponowane modele rozpadu i koalescencji kropel sformułowano przy użyciu formalizmu multifraktalnego. Zastosowane podejście pozwoliło uwzględnić różną aktywność wirów burzliwych o tej samej skali, a także w sposób naturalny wprowadzić do zależności na szybkość rozpadu, częstość zderzeń kropel i szybkość wypływu filmu fazy ciągłej spomiędzy kropel, wpływ dużych wirów energetycznych, a więc i wpływ skali układu. Prócz niehomogeniczności małej skali związanej z intermi-tencją wewnętrzną uwzględniono nierównomierny rozkład uśrednionych lokalnie parametrów burzliwości w mieszalniku. Zaproponowane modele rozpadu i koalescencji zweryfikowano doświadczalnie wykorzystując zarówno wyniki badań własnych, jak i zaczerpnięte z literatury. Przedstawiono zastosowania praktyczne sformułowanych modeli do przewidywania ewolucji rozkładów wielkości kropel w czasie i efektów powiększania skali układu. Zdefiniowano również indeksy dla inwersji faz.
EN
The phenomena of breakup and coalescence, which affect the drop size distribution, are the core subject of investigations presented in this work. Liquid-liquid dispersion, created in stirred tanks, operating in a turbulent regime, are also considered. Initially, an analysis of dispersed systems in the phase space and a description of micro-structure of turbulence are presented. The differences between classical Kolmogorov theory, based on statistically averaged properties of turbulence, and the multifractal approach, taking into account the intermittent character of turbulence are discussed. Chapters 4 and 5 focus on droplet breakup and coalescence, respectively, which constitutes the main part of the work. A brief review and discussion of the modeling concepts of the process being considered, as well as a presentation of the author's own models, are contained in each of these chapters. The proposed models of drop breakup and coalescence were formulated with the use of multifractal formalism. Such an approach enables us to take into account different activity of turbulent eddies of the same scale, and to introduce the influence of large energetic eddies (and therefore influence of the system scale) on drop breakup rate, drop collision frequency and the rate of film drainage. Apart from small scale irregularity relating to the internal intermittency, the non-uniform distribution of locally averaged properties of turbulence in the tank were taken into account. The proposed models of drop breakup and coalescence were verified using both primary and secondary data. Practical applications of the formulated models to predict the time evolution of drop size distribution and the effects of scaling-up were presented. Phase inversion indices were also defined and these can be used in the analysis of the phase inversion process.
Rocznik
Strony
3--264
Opis fizyczny
Bibliogr. 354 poz., tab., rys., wykr.
Twórcy
  • Zakład Mechaniki Technicznej i Dynamiki Stosowanej, Wydział Inżynierii Chemicznej i Procesowej Politechniki Warszawskiej tel: 234 65 94, podgorsw@ichip.pw.edu.pl
Bibliografia
  • Abid S., Chesters A.K., 1994. The drainage and rupture of partially-mobile films between colliding drops at constant approach velocity. Int. J. Multiphase Flow 20, 613-629.
  • Abrahamson J., 1975. Collision rates of small particles in a vigorously turbulent fluid. Chem. Eng. Sci. 30, 1371-1379.
  • Acrivos A., Lo T.S., 1978. Deformation and breakup of a single slender drop in an extensional flow. J. Fluid Mech. 86, 641-672.
  • Alexander S., 1977. Polymer adsorption on small spheres: a scaling approach. J. Physique 38, 977-983.
  • Alopaeus V., Koskinen J., Keskinen K.I., 1999. Simulation model of population balance for liquid-liquid systems in a nonideal stirred tank. Part 1. Description and qualitative validation of the model. Chem. Eng. Sci. 54, 5887-5899.
  • Anselmet F., Antonia R.A., Danaila L., 2001. Turbulent flows and intermittency in laboratory experiments. Planetary and Space Science 49, 1177-1191.
  • Anselmet F., Gagne Y., Hopfinger E.J., Antonia R.A., 1984. High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63-89.
  • Arai K., Konno M., Matunaga Y., Saito S., 1977. Effect of dispersed-phase viscosity on the maximum stable drop size for breakup in turbulent flow. J. Chem. Eng. Japan 10, 325-330.
  • Arashmid M., Jeffreys G.V., 1980. Analysis of the phase inversion characteristics of liquid-liquid dispersions. A.I.Ch.E. Journal 26, 51-55.
  • Aris R., 1962. Vectors, tensors, and the basic equations of fluid mechanics. Prentice-Hall, Englewood Cliffs, N.J.
  • Arneodo A., Baudet C., Belin F., Benzi R. et al., 1996. Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhysics Lett. 34, 411-416.
  • Aveyard R., Binks B.P., Clint J.H., 2003. Emulsions stabilised solely by colloid particles. Adv. Colloid Interface Sci. 100-102, 503-546.
  • Baldi S., Yianneskis M., 2004. On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements. Chem. Eng. Sci. 59, 2659-2671.
  • Bałdyga J., Bourne J.R., 1993. Drop breakup and intermittent turbulence. J. Chem. Eng. Japan 26, 738-741.
  • Bałdyga J., Bourne J.R., 1995. Interpretation of turbulent mixing using fractals and multifractals. Chem. Eng. Sci. 50, 381-400.
  • Bałdyga J., Bourne J.R., 1999. Turbulent mixing and chemical reactions. Wiley & Sons, Chichester, New York, Weinheim, Brisbane, Singapore, Toronto.
  • Bałdyga J., Podgórska W., 1997a. Maximum stable and transient sizes of drops for breakup in turbulent flow. Proceedings of the First European Congress on Chemical Engineering. Florencja, 4-7 May, Vol. 2, pp. 1567-1570.
  • Bałdyga J., Podgórska W., 1998a. Drop break-up in intermittent turbulence: Maximum stable and transient sizes of drops. Canad. J. Chem. Eng. 76, 456-470.
  • Bałdyga J., Podgórska W., 1998b. Model koalescencji kropel w intermitentnym polu burzliwym. XVI Ogólnopolska Konferencja Inżynierii Chemicznej i Procesowej. Muszyna. Materiały Konferencji, tom II, str. 34-39.
  • Bałdyga J., Podgórska W., 2000. Problemy powiększania skali dla układów dyspersyjnych. Zeszyty Naukowe Politechniki Łódzkiej. Inżynieria Chemiczna i Procesowa 27, 17-24.
  • Bałdyga J., Podgórska W., Pohorecki R., 1995. Mixing-precipitation model with application to double feed semibatch precipitation. Chem. Eng. Sci. 50, 1281-1300.
  • Bałdyga J., Podgórska W., Smit L., 1997b. Turbulent dispersion of drops in intermittent turbulence. Recents Progres en Genie des Procedes 11, No 52, 247-254.
  • Bałdyga J., Podgórska W., Zawada D., Żuławnik D., 1998. Badania eksperymentalne w układach dwufazowych ciecz-ciecz. XVI Ogólnopolska Konferencja Inżynierii Chemicznej i Procesowej. Muszyna. Materiały Konferencji, tom IV, str. 8-11.
  • Baranaev M.K., Teverovskij J.N., Tregubova E.L., 1949. O razmiere minimalnych pulsacij v turbulentnom potokie. Dokl. Akad. Nauk SSSR 49, 821-824.
  • Barnea E., Mizrahi J., 1976. On the "effective" viscosity of liquid-liquid dispersions. Ind. Eng. Chem. Fundam. 15, 120-125.
  • Barthes-Biesel D., Acrivos A., 1973. Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1-21.
  • Batchelor G.K., 1953. The theory of homogeneous turbulence. Cambridge University Press, Cambridge, New York, Melbourne.
  • Batchelor G.K., Townsend A.A., 1949. The nature of turbulent motion at large wave-numbers. Proc. R. Soc. London A 199, 238-255.
  • Bazhlekov I.B., Chesters A.K., van de Vosse F.N., 2000. The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops. Int. J. Multiphase Flow 26, 445-466.
  • Bentley B.J., Leal L.G., 1986. An experimental investigation of drop deformation and break-up in steady, two-dimensional linear flows. J. Fluid Mech. 167, 241-283.
  • Benzi R., Biferale L., Paladin G., Vulpiani A., Vergasola M., 1991. Multifractals in the statistics of the velocity gradients in turbulence. Phys. Rev. Lett. 67, 2299-2302.
  • Benzi R., Biferale L., Parisi G., 1993a. On intermittency in a cascade model for turbulence. Physica D 65, 163-171.
  • Benzi R., Ciliberto S., Baudet C., Ruiz Chavarria G., Tripiccione R., 1993b. Extended self-similarity in the dissipation range of fully developed turbulence. Europhys. Lett. 24, 275-279.
  • Benzi R., Ciliberto S., Tripiccione R., Baudet C., Masaioli F., Succi S., 1993c. Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29-R32.
  • Benzi R., Ciliberto S., Baudet C., Ruiz Chavarria G., 1995. On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80, 385-398.
  • Benzi R., Biferale L., Ciliberto S., Struglia M.V., Tripiccione R., 1996. Generalized scaling in fully developed turbulence. Physica D 96, 162-181.
  • Benzi R., Paladin G., Parisi G., Vulpiani A., 1984. On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A17, 3521-3531.
  • Berkman P.D., Calabrese R.V., 1988. Dispersion of viscous liquids by turbulent flow in a static mixer. A.I.Ch.E. Journal 34, 602-609.
  • Binks B.P., 2002. Particles as surfactants - similarities and differences. Curr. Opin. Colloid Interface Sci. 7, 21-41.
  • Binks B.P., Cho W-G., Fletcher P.D.I., Petsev D.N., 2000. Stability of oil-in-water emulsions in a low interfacial tension system. Langmuir 16, 1025-1034.
  • Bławzdziewicz J., Cristini V., Loewenberg M., Collins L.R., 1998. Direct numerical simulation of three-dimensional drop breakup in isotropic turbulence. Forth Microgravity Fluid Physics and Transport Phenomena Conference, Cleveland, Ohio, August 12-14, pp. 461-466.
  • Boger D.V., 1980. Separation of shear-thinning and elastic effects in experimental rheology. Rheology 1, 195-218.
  • Bourne J.R., Yu S., 1994. Investigation of micromixing in stirred tank reactors using parallel reactions. Ind. Eng. Chem. Res. 33, 41-55.
  • Boye A.M., Lo M-Y.A., Shamlou P.A., 1996. The effect of two-liquid phase rheology on drop breakage in mechanically stirred vessels. Chem. Eng. Comm. 96, 149-167.
  • Bradshaw P., 1975. Introduction to turbulence and its measurement. Pergamon Press, Oxford.
  • Brooks B.W., Richmond H.N., 1994a. Phase inversion in non-ionic surfactant-oil-water systems - I. The effect of transitional inversion on emulsion drop sizes. Chem. Eng. Sci. 49, 1053-1064.
  • Brooks B.W., Richmond H.N., 1994b. Phase inversion in non-ionic surfactant-oil-water systems - II. Drop size studies in catastrophic inversion with turbulent mixing. Chem. Eng. Sci. 49, 1065-1075.
  • Bujalski W., Nienow A.W., Chatwin S., Cooke M., 1987. The dependences on scale of power number of Rushton disc turbines. Chem. Eng. Sci. 42, 317-326.
  • Butt H-J., Graf K., Kappl M., 2003. Physics and chemistry of interfaces. Wiley-VCH, Weinheim.
  • Calabrese R.V., Yung B., Ruszkowski S., 1993. Analysis of dilute liquid-liguid dispersions: Mechanisms for drop breakup. Paper presented at Mixing XIV, Engineering Foundation Mixing Conference, Santa Barbara CA, June 20-25, 1993.
  • Calabrese R.V., Chang T.P.K., Dang P.T., 1986. Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersed-phase viscosity. A.I.Ch.E. Journal 32, 657-666.
  • Cengel J.A., Faruqui A.A., Finnigan J.W., Wright C.H., Knudsen J.G., 1962. Laminar and turbulent flow of unstable liquid-liquid emulsions. A.I.Ch.E. Journal 8, 335-339.
  • Charles G.E., Mason S.G., 1960. The coalescence of liquid drops with flat liquid/liquid interfaces. J. Colloid Sci. 15, 236-267.
  • Chen J-D., 1985. A model of coalescence between two equal-sized spherical drops or bubbles. J. Colloid Interface Sci. 107, 209-220.
  • Chen S., Cao N., 1995. Inertial range scaling in turbulence. Phys. Rev. E 52, R5757-R5759.
  • Chen C-T., Maa J-R., Yabg Y-M., Chang C-H., 1998. Effects of electrolytes and polarity of organic liquids on the coalescence of droplets at aqueous-organic interfaces. Surface Sci. 406, 167-177.
  • Chen J-D., Slattery J.C., 1982. Effect of London-van der Waals forces on the thinning of a dimpled liquid film as a small drop or bubble approaches a horizontal solid plane. A.I.Ch.E. Journal 28, 955-963.
  • Chesters A.K., 1988. A first-order model for drainage of partially mobile films between colliding drops. Euromech 234, Tolouse.
  • Chesters A.K., 1991. The modeling of coalescence processes in fluid-liquid dispersions: A review of current understanding. Trans. IChemE. 69, Part A, 259-270.
  • Chesters A.K., Bazhlekov I.B., 2000. Effect of insoluble surfactants on drainage and rupture of a film between drops interacting under a constant force. J. Colloid Interface Sci. 230, 229-243.
  • Chesters A.K., Hoffman G., 1982. Bubble coalescence in pure liquids. Appl. Sci. Research 38, 353-361.
  • Chhabra A.B., Meneveau C., Jensen R.V., Sreenivasan K.R., 1989. Direct determination of the f(α) singularity spectrum and its application to fully developed turbulence. Phys. Rev. A 40, 5284-5294.
  • Chhabra A.B., Sreenivasan K.R., 1992. Scale-invariant multiplier distributions in turbulence. Phys. Rev. Lett. 68, 2762-2765.
  • Chhabra R.P., 1986. Steady non-Newtonian flow about a rigid sphere. Chap. 30 in: Encyclopedia of Fluid Mechanics. Vol. 1. Flow phenomena and measurement. N.P. Cheremisinoff (Ed.). Gulf Publishing Company, Houston, Texas, pp. 983-1033.
  • Chhabra R.P., Uhler P.H.T., Boger D.V., 1980. The influence of fluid elasticity on the drag coefficient for creeping flow around a sphere. J. Non-Newtonian Fluid Mech. 6, 187-199.
  • Church J.M., Shinnar, R., 1961. Stabilizing liquid-liquid dispersions by agitation. Ind. Eng. Chem. 53, 479-484.
  • Ciliberto S., Leveque E., Ruiz Chavarria G., 2001. Non-homogeneous scalings in boundary layer turbulence. In: Intermittency in turbulent flows. Ed. J.C. Vassilicos. Cambridge University Press, Cambridge, pp. 118-135.
  • Collins S.B., Knudsen J.G., 1970. Drop-size distributions produced by turbulent pipe flow of immiscible liquids. A.I.Ch.E. Journal 16, 1072-1080.
  • Coulaloglou C.A., Tavlarides L.L., 1977. Description of interaction processes in agitated liquid-liquid dispersions. Chem. Eng. Sci. 32, 1289-1297.
  • Danov K.D., Petsev D.N., Denkov N.D., 1993. Pair interaction energy between deformable drops and bubbles. J. Chem. Phys. 99, 7179-7189.
  • Das P., Kumar R., Ramkrishna D., 1987. Coalescence of drops in stirred dispersions. A white noise model for coalescence. Chem. Eng. Sci. 42, 213-220.
  • Davies J.T., 1985. Drop size of emulsions related to turbulent energy dissipation rates. Chem. Eng. Sci. 40, 839-842.
  • 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.
  • Davis R.H., Schonberg J.A., Rallison J.M., 1989. The lubrication force between two viscous drops. Phys. Fluids A 1, 77-81.
  • Davis H.T., Scriven L.E., 1981. Gradient theory of fluid microstructures. J. Stat. Phys. 24, 243-268.
  • Davis H.T., Scriven L.E., 1982. Stress and structure in fluid interfaces. Adv. Chem. Phys. 49, 357-454.
  • de Gennes P.G., 1987. Polymers at an interface; a simplified view. Adv. Colloid Interface Sci. 27, 189-209.
  • Delichatsios M.A., Probstein R.F., 1975. Coagulation in turbulent flow: theory and experiment. J. Colloid Interface Sci. 51, 394-405.
  • Denkov N.D., Petsev D.N., Danov K.D., 1993. Interaction between deformable Brownian droplets. Phys. Rev. Lett. 71, 3226-3229.
  • Deshikan S.R., Papadopoulos K.D., 1995. London-van der Waals and EDL effects in the coalescence of oil drops. II. Ionic strength and pH effects. J. Colloid Interface Sci. 174, 313-318.
  • Desnoyer C., Masbernat O., Gourdon C., 2003. Experimental study of drop size distributions at high phase ratio in liquid-liquid dispersions. Chem. Eng. Sci. 58, 1353-1363.
  • Desphande K.B., Kumar S., 2003. A new characteristic of liquid-liquid systems - inversion holdup of intensly agitated dispersions. Chem. Eng. Sci. 58, 3829-3835.
  • Diemer R.B., Olson J.H., 2002. A moment methodology for coagulation and breakage problems: Part 3 - generalized daughter distribution functions. Chem. Eng. Sci. 57, 4187-4198.
  • Dolan A.K., Edwards S.F., 1974. Theory of the stabilization of colloids by adsorbed polymer. Proc. R. Soc. London A 337, 509-516.
  • Dubruelle B., 1994. Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance. Phys. Rev. Lett. 73, 959-962.
  • Eastwood C., Cartellier A., Lasheras J.C., 2000. The break-up time of a droplet in a fully-developed turbulent flow. Advances in turbulence VIII. Proceedings of the Eighth Turbulence Conference. C. Dapaza et al. (Eds.), 573-576.
  • Einstein A., 1906. Eine neue Bestimmung der Molekul-dimensionen. Ann. Phys. 19, 289-306.
  • Einstein A., 1911. Eine neue Bestimmung der Molekul-dimensionen. Ann. Phys. 34, 591-592.
  • Elsner J.W., 1987. Turbulencja przepływów. PWN, Warszawa.
  • Feller W., 1981. Wstęp do rachunku prawdopodobieństwa. Tom 2. PWN, Warszawa.
  • Fredrickson A.G., Mantzaris N.V., 2002. A new set of population balance equations for microbial and cell cultures. Chem. Eng. Sci. 57, 2265-2278.
  • Friedlander S.K., 2000. Smoke, dust, and haze. Fundamentals of aerosol dynamics. Oxford University Press. New York, Oxford.
  • Frisch U., 1991. From global scaling, a la Kolmogorov, to local multifractal scaling in fully developed turbulence. Proc. R. Soc. London A 434, 89-99.
  • Frisch U., 1995. Turbulence. The legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge.
  • Frisch U., Sulem P-L., Nelkin M., 1978. A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719-736.
  • Gardiner C.W., 1990. Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer-Verlag, Berlin.
  • Gilchrist A., Dyster K.N., Moore I.P.T., Nienow A.W., 1989. Delayed phase inversion in stirred liquid-liquid dispersions. Chem. Eng. Sci. 44, 2381-2384.
  • Gledzer E.B., 1973. System of hydrodynamic type admitting two quadratic integrals of motion. Sov. Phys. Dokl. 18, 216-217.
  • Grace H.P., 1982. Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem. Eng. Comm. 14, 225-277.
  • Gregory J., 1969. The calculation of Hamaker constants. Adv. Colloid Interface Sci. 2, 396-417.
  • Groeneweg F., Agterof W.G.M., Jaeger P., Janssen J.J.M., Wieringa J.A., Klahn J.K., 1998. On the mechanism of the inversion of emulsions. Trans IChemE 76, Part A, 55-63.
  • Grosso J.L., Briceno M.I., Paterno J., Layrisse I., 1986. Influence of crude oil and surfactants concentration on the rheology and flowing properties of heavy crude oil-in-water emulsions. In: Surfactants in Solutions (Edited by K.L. Mittal), pp. 1653-1673.
  • Guido S., Simeone M., Greco F., 2003. Deformation of a Newtonian drop in a viscoelastic matrix under steady shear flow. Experimental validation of slow flow theory. J. Non-Newtonian Fluid Mech. 114, 65-82.
  • Guilinger T.R., Grislingas A.K., Erga O., 1988. Phase inversion behavior of water-kerosene dispersions. Ind. Eng. Chem. Res. 27, 978-982.
  • Gummeran R.J., Homsy G.M., 1975. The stability of radially bounded thin films. Chem. Eng. Comm. 2, 27-36.
  • Gurvich A.S., Yaglom A.M., 1967. Breakdown of eddies and probability distributions for small-scale turbulence, boundary layers and turbulence. Phys. Fluids Suppl. 10, S 59-65.
  • Halsey T.S., Jensen M.H., Kadanoff L.P., Procaccia I., Shraiman B.I., 1986. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A 33, 1141-1151.
  • Hagesaether L., Jakobsen H.A., Svendsen H.F., 2002. A model for turbulent binary breakup of dispersed fluid particles. Chem. Eng. Sci. 57, 3251-3267.
  • He Y., Howes T., Lister J.D., Ko G.H., 2002. Experimental study of drop-interface coalescence in the presence of polymer stabilisers. Colloids and Surfaces A: Physicochemical and Engineering Aspects 207, 89-104.
  • Hentschel H.G.E., Procaccia I., 1983. The infinite number of generalized dimensions of fractals and strange attractors. Physica 8D, 435-444.
  • Hesketh R.P., Etchells A.W., Russell T.W.F., 1991a. Experimental observations of bubble breakage in turbulent flow. Ind. Eng. Chem. Res. 30, 835-841.
  • Hesketh R.P., Etchells A.W., Russell T.W.F., 1991b. Bubble breakage in pipeline flow. Chem. Eng. Sci. 46, 1-9.
  • Hesketh R.P., Russel T.W.F., Etchels A.W., 1987. Bubble size in horizontal pipelines. A.I.Ch.E. Journal 33, 663-667.
  • Hill P.J., Ng K.M., 1996. Statistics of multiple particle breakage. A.I.Ch.E. Journal 42, 1600-1611.
  • Hinze O., 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. A.I.Ch.E. Journal 1, 289-295.
  • Holmberg K., Jönsson B., Kronberg B., Lindman B., 2004. Surfactants and polymers in aqueous solution. Wiley & Sons, Chichester.
  • Howarth W.J., 1967. Measurement of coalescence frequency in an agitated tank. A.I.Ch.E. Journal 13, 1007-1013.
  • Hsia M.A., Tavlarides L.L., 1983. Simulation analysis of drop breakage, coalescence and micromixing in liquid-liquid stirred tanks. Chem. Eng. J. 26, 189-199.
  • Hu B., Angeli P., Matar O.K., Hewitt G.F., 2005. Prediction of phase inversion in agitated vessels using a two-region model. Chem. Eng. Sci. 60, 3487-3495.
  • Hu Y.T., Pine D.J., Gary Leal L., 2000. Drop deformation, breakup, and coalescence with compatibilizer. Phys. Fluids 12, 484-488.
  • Hulburt H.M., Akiyama T., 1969. Liouville equations for agglomeration and dispersion processes. I & E C Fundamentals 8, 319-324.
  • Hulburt H.M., Katz S., 1964. Some problems in particle technology. A statistical mechanical formulation. Chem. Eng. Sci. 19, 555-574.
  • Israelachvili J., 1992. Intermolecular & surface forces. Academic Press, Amsterdam, Boston, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore.
  • Ivanov I.B., Kralchevsky P.A., 1997. Stability of emulsions under equilibrium and dynamic conditions. Colloids Surf. A: Physicochemical and Engineering Aspects 128, 155-175.
  • Jeffreys G.V., Davies G.A., 1971. Coalescence of liquid droplets and liquid dispersion. In: Recent advances in liquid-liquid extraction (Ed. by C. Hanson). Pergamon Press, Oxford, New York, Toronto, Sydney, Braunschweig, pp. 495-584.
  • Jeelani S.A.K., Hartland S., 1991a. Collision of oscillating liquid drops. Chem. Eng. Sci. 46, 1807-1814.
  • Jeeleni S.A.K., Hartland S., 1991b. Effect of approach velocity on binary and interfacial coalescence. Trans IChemE 69, Part A, 271-281.
  • Jeeleni S.A.K., Hartland S., 1998. Effect of surface mobility on collision of spherical drops. J. Colloid Interface Sci. 206, 83-93.
  • Jimenez J., 1998. Small scale intermittency in turbulence. Eur. J. Mech. B/Fluids 17, 405-419.
  • Kamieński J., 2004. Mieszanie układów wielofazowych. WNT, Warszawa.
  • Karam H.J., Belinger J.C., 1968. Deformation and breakup of liquid droplets in a simple shear field. I&EC Fundamentals 7, 576-781.
  • Kholmyansky M., Tsinober A., 2001. On the origins of intermittency in real turbulent flows. In: Intermittency in turbulent flows (Ed. by J.C. Vassilicos). Cambridge University Press, Cambridge, pp. 183-192.
  • Klasebor E., Chevaillier J.Ph., Gourdon C., Masbernat O., 2000. Film drainage between colliding drops at constant approach velocity: Experiments and modelling. J. Colloid Interface Sci. 229, 274-285.
  • Kolmogorov A.N., 1941a. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299-303 (reprinted in Proc. R. Soc. London A 434, 9-13 (1991)).
  • Kolmogorov A.N., 1941b. On decay of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk SSSR 31, 538-540.
  • Kolmogorov A.N., 1941c. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16-18 (reprinted in Proc. R. Soc. London A 434, 15-17 (1991).
  • Kolmogorov A.N., 1949. Disintegration of drops in turbulent flows. Dokl. Akad. Nauk SSSR 66, 825-828.
  • Kolmogorov A.N., 1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82-85.
  • Konno M., Aoki M., Saito S., 1983. Scale effect on breakup process in liquid-liquid agitated tanks. J. Chem. Eng. Japan 16, 312-319.
  • Konno M., Kosaka N., Saito S., 1993. Correlation of transient drop sizes in breakup process in liquid-liquid agitation. J. Chem. Eng. Japan 26, 37-40.
  • Konno M., Matsunaga Y., Arai K., 1980. Simulation model for breakup process in an agitated tank. J. Chem. Eng. Japan 13, 67-73.
  • Konno M., Muto T., Saito S., 1988. Coalescence of dispersed drops in an agitated tank. J. Chem. Eng. Japan 21, 335-338.
  • Konno M., Saito S., 1987. Correlation of drop sizes in liquid-liquid agitation at low dispersed phase volume fractions. J. Chem. Eng. Japan 20, 533-535.
  • Koshy A., Das T.R., Kumar R., 1988a. Effect of surfactant on drop breakage in turbulent liquid dispersions. Chem. Eng. Sci. 43, 649-654.
  • Koshy A., Das T.R., Kumar R., Gandhi K.S., 1988b. Breakage of viscoelastic drops in turbulent stirred dispersions. Chem. Eng. Sci. 43, 2625-2631.
  • Koshy A., Kumar R., Gandhi K.S., 1989. Effect of drag-reducing agents on drop breakage in stirred dispersions. Chem. Eng. Sci. 44, 2113-2120.
  • Kostoglou M., Dovas S., Karabelas A.J., 1997. On the steady-state size distribution of dispersions in breakage processes. Chem. Eng. Sci. 52, 1285-1299.
  • Kraichnan R.H., 1974. On Kolmogorov’s inertial-range theories. J. Fluid Mech. 62, 305-330.
  • Kraichnan R.H., 1991. Turbulent cascade and intermittency growth. Proc. R. Soc. London A 434, 65-78.
  • Kralchevsky P.A., Danov K.D., Denkov N.D., 2002. Chemical physics of colloid systems and interfaces. Chapter 5 in: Handbook of surface and colloid chemistry. Second expanded and updated edition (Ed. by K.S. Birdi). CRC Press, New York.
  • Kralchevski P.A., Denkov N.D., 1995. Analytical expression for the oscillatory structural surface force. Chem. Phys. Letters 240, 385-392.
  • Kraume M., Gäbler A., Schulze K., 2003. Influence of physical properties and agitation conditions on drop size distributions of stirred liquid/liquid dispersions. Proceedings of 11th European Conference on Mixing, Bamberg, Germany. FUCK-DRUCK, pp 229-236.
  • Kruis F.E., Kusters K.A., 1997. The collision rate of particles in turbulent flow. Chem. Eng. Comm. 158, 201-230.
  • Kuboi R., Komasawa I., Otake T., 1972. Collision and coalescence of dispersed drops in turbulent liquid flow. J. Chem. Eng. Japan 5, 423-424.
  • Kumar S., 1996. On phase inversion characteristics of stirred dispersion. Chem. Eng. Sci. 51, 831-834.
  • Kumar S., Kumar R., Gandhi K.S., 1991a. Influence of the wetting characteristics of the impeller on phase inversion. Chem. Eng. Sci. 46, 2365-2367.
  • Kumar S., Kumar R., Gandhi K.S., 1991b. Alternative mechanisms of drop breakage in stirred vessels. Chem. Eng. Sci. 46, 2483-2489.
  • Kumar S., Kumar R., Gandhi K.S., 1992. A multi-stage model for drop breakage in stirred vessels. Chem. Eng. Sci. 47, 971-980.
  • Kumar S., Kumar R., Gandhi K.S., 1993. A simplified procedure for predicting dmax in stirred vessels. Chem. Eng. Sci. 48, 3092-3096.
  • Kumar S., Ramkrishna D., 1996. On the solution of population balance equations by discretization - I. A fixed pivot technique. Chem. Eng. Sci. 51, 1311-1332.
  • Kumar S., Ganvir V., Satyanand C., Kumar R., Gandhi K.S., 1998. Alternative mechanism of drop breakup in stirred vessels. Chem. Eng. Sci. 53, 3269-3280.
  • Kuriyama M., Ono M., Tokanai H., Konno H., 1996. Correlation of transient sizes of highly viscous drops in dispersion process in liquid-liquid agitation. Trans. I. Chem. E. 74, Part A, 431-437.
  • Kusters K.A., 1991. The influence of turbulence aggregation of small particles in agitated vessels. PhD Thesis, Technische Universiteit Eindhoven.
  • Lagisetty J.S., Das P.K., Kumar R., Gandhi K.S., 1986. Breakage of viscous and non-Newtonian drops in stirred dispersions. Chem. Eng. Sci. 41, 65-72.
  • Lam A., Sathyagal A.N., Kumar S., Ramkrishna D., 1996. Maximum stable drop diameter in stirred dispersions. A.I.Ch.E. Journal 42, 1547-1552.
  • Lamb H., 1932. Hydrodynamics. Cambridge University Press, Cambridge.
  • Landau L., Lifszic E., 1958. Mechanika ośrodków ciągłych. PWN, Warszawa.
  • Lane G.L., Schwartz M.P., Evans G.M., 2000. Comparison of CFD methods for modelling of stirred tanks. In: H.E.K. van der Akker and J.J. Derksen (Eds.). Proceedings of the 10th European Conference on Mixing, Delft, The Netherlands, July 2-5, pp. 273-280.
  • Lankveld J.M.G., Lyklema J., 1972a. Adsorption of polyvinyl alcohol on the paraffin-water interface. I. Interfacial tension as a function of time and concentration. J. Colloid Interface Sci. 41, 454-465.
  • Lankveld J.M.G., Lyklema J., 1972b. Adsorption of polyvinyl alcohol on the paraffin-water interface. II. Spread and adsorbed monolayers. J. Colloid Interface Sci. 41, 466-474.
  • Lankveld J.M.G., Lyklema J., 1972c. Adsorption of polyvinyl alcohol on the paraffin-water interface. III. Emulsification of paraffin in aqueous solutions of polyvinyl alcohol and the properties of paraffin-in-water emulsions stabilized by polyvinyl alcohol. J. Colloid Interface Sci. 41, 475-483.
  • Lasheras J.C., Eastwood C., Martinez-Bazan C., Montaňes J.L., 2002. A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow. Int. J. Multiphase Flow 28, 247-278.
  • Lee C-H., Erickson L.E., Glasgow L.A., 1987. Dynamics of bubble size distribution in turbulent gas-liquid dispersions. Chem. Eng. Comm. 61, 181-195.
  • Lee K.C., Yianneskis M., 1998. Turbulence properties of the impeller stream of a Rushton turbine. A.I.Ch.E. Journal 44, 13-24.
  • Lehr F., Mewes D., 2001. A transport equation for the interfacial area density applied to bubble columns. Chem. Eng. Sci. 56, 1159-1166.
  • Lehr F., Millies M., Mewes D., 2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2442.
  • Lesieur M., 1997. Turbulence in fluids. Kluwer Academic Publishers. Dordrecht, Boston, London.
  • Levich V.G., 1962. Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, N.J.
  • Li D., Liu S., 1996. Coalescence between small bubbles or drops in pure liquids. Langmuir 12, 5216-5220.
  • Lin C-Y., Slattery J.C., 1982a. Thinning of a liquid film as a small drop or bubble approaches a solid plane. A.I.Ch.E. Journal 28, 147-156.
  • Lin C-Y., Slattery J.C., 1982b. Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface. A.I.Ch.E. Journal 28, 786-792.
  • Liu S., Li D., 1999. Drop coalescence in turbulent dispersions. Chem. Eng. Sci. 54, 5667-5675.
  • Liu L., Matar O.K., Perez de Ortiz E.S., Hewitt G.F., 2005. Experimental investigation of phase inversion in a stirred vessel using LIF. Chem. Eng. Sci. 60, 85-94.
  • Lobo L., Svereika A., 2003. Coalescence during emulsification. 2. Role of small molecule surfactants. J. Colloid Interface Sci. 261, 498-507.
  • Luo H., Svendsen H.F., 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225-1233.
  • Lyklema J., 1991. Fundamentals of interface and colloid science. Vol. 1. Fundamentals. Academic Press, London.
  • MacKay G.D.M., Mason S.G., 1963. A gravity approach and coalescence of fluid drops at liquid interfaces. Can. J. Chem. Eng. 41, 203-212.
  • Mandelbrot B.B., 1974. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331-358.
  • Martinez-Bazan C., Montaňes J.L., Lasheras J.C., 1999a. On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency. J. Fluid Mech. 401, 157-182.
  • Martinez-Bazan C., Montaňes J.L., Lasheras J.C., 1999b. On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles. J. Fluid Mech. 401, 183-207.
  • May K., Jeelani S.A.K., Hartland S., 1998. Influence of ionic surfactants on separation of liquid-liquid dispersions. Colloids and Surfaces A: Physicochemical and Engineering Aspects 139, 41-47.
  • McAvoy R.M., Kintner R.C., 1965. Approach of two identical rigid spheres in a liquid field. J. Colloid Sci. 20, 188-190.
  • McComb W.D., 1991. The physics of fluid turbulence. Oxford University Press, Oxford.
  • Meneveau C., Sreenivasan K.R., 1987a. The multifractal spectrum of the dissipation field in turbulent flow. Nuclear Physics B (Proc. Suppl.) 2, 49-76.
  • Meneveau C., Sreenivasan K.R., 1987b. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1424-1427.
  • Meneveau C., Sreenivasan K.R., 1989. Measurement of F(α) from scaling of histograms and applications to dynamical systems and fully developed turbulence. Phys. Let. A 137, 103-112.
  • Meneveau C., Sreenivasan K.R., 1990. Interface dimension in intermittent turbulence. Phys. Rev. A 41, 2246-2248.
  • Meneveau C., Sreenivasan K.R., 1991. The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429-484.
  • Miller R.S., Ralph J.L., Curl R.L., Towell G.D., 1963. Dispersed phase mixing: II. Measurements in organic dispersed systems. A.I.Ch.E. Journal 9, 196-202.
  • Monin A.S., Yaglom A.M., 1975. Statistical fluid mechanics, Vol. 2. MA: MIT Press, Cambridge.
  • Morrison I.D., Ross S., 2002. Colloidal Dispersions. Suspensions, emulsions, and foams. Wiley-Interscience, New York.
  • Muralidhar R., Ramkrishna D., 1986. Analysis of droplet coalescence in turbulent liquid-liquid dispersions. Ind. Eng. Chem. Fundam. 25, 554-560.
  • Muralidhar R., Ramkrishna D., Das P.K., Kumar R., 1988. Coalescence of rigid droplets in a stirred dispersion - II. Band-limited force fluctuations. Chem. Eng. Sci. 43, 1559-1568.
  • Nambiar D.K.R., Kumar R., Das T.R., Gandhi K.S., 1992. A new model for the breakage frequency of drops in turbulent stirred dispersions. Chem. Eng. Sci. 47, 2989-3002.
  • Nambiar D.K.R., Kumar R., Das T.R., Gandhi K.S., 1994. A two-zone model of breakage frequency of drops in stirred dispersions. Chem. Eng. Sci. 49, 2194-2198.
  • Narsimhan G., 2004. Model for drop coalescence in a locally isotropic turbulent flow field. J. Colloid Interface Sci. 272, 197-209.
  • Narsimhan G., Gupta J.P., Ramkrishna D., 1979. A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions. Chem. Eng. Sci. 34, 257-265.
  • Nelkin M., 2000. Resource Letter TF-1: Turbulence in fluids. Am. J. Phys. 68, 310-318.
  • Nelkin M., 1995. Inertial range scaling of intense events in turbulence. Phys. Rev. E 52, R4610-R4611.
  • Nelkin M., Bell T.L., 1978. One-exponent scaling for very high-Reynolds-number turbulence. Phys. Rev. A 17, 363-369.
  • Nienow A.W., Pacek A.W., Franklin R., Nixon A.J., 2000. The impact of fine particles and their wettability on the coalescence of sunflower oil drops in water. Proceedings of the 10th European Conference on Mixing, Delft. H.E.A. van der Akker and J.J. Derksen (Editors). Elsevier Science, Amsterdam, Lusanne, New York, Oxford.
  • Nikolov A.D., Wasan D.T., 1989. Ordered micelle structuring in thin films formed from anionic surfactant solutions. I. Experimental. J. Colloid Interface Sci. 133, 1-12.
  • Nishikawa M., Mori F., Fujieda S., Kayama T., 1987. Scale-up of liquid-liquid phase mixing vessels. J. Chem. Eng. Japan 20, 454-459.
  • Norato M.A., Tsouris C., Tavlarides L.L., 1998. Phase inversion studies in liquid-liquid dispersions. Canad. J. Chem. Eng. 76, 486-494.
  • Novikov E.A., 1992. Probability distribution for three-dimensional vectors of velocity increments in turbulent flow. Phys. Rev. A 46, R6147-R6149.
  • Novikov E.A., 1994. Infinitely divisible distributions in turbulence. Phys. Rev. E 50, R3303-R3305.
  • Novikov E.A., Dommermuth D.G., 1997. Distribution of droplets in a turbulent spray. Phys. Rev. E 56, 5479-5482.
  • Novikov E.A., Stewart R.W., 1964. The intermittency of turbulence and the structure of turbulent flow. Isv. Akad. Nauk USSR, Ser. Geophys 3, 408-413.
  • Obukhov A.M., 1941a. On the distribution of energy in the spectrum of turbulent flow. Dokl. Akad. Nauk SSSR 32 (1), 22-24.
  • Obukhov A.M., 1941b. Spectral energy distribution in a turbulent flow. Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 5(4-5), 453-466.
  • Obukhov A.M., 1962. Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77-81.
  • Okamoto Y., Nishikawa M., Hashimoto K., 1981. Energy dissipation rate distribution in mixing vessels and its effect on liquid-liquid dispersion and solid-liquid mass transfer. Int. Chem. Eng. 21, 88-94.
  • Okhitani K., Yamada M., 1989. Temporal intermittency in the energy cascade process and local Lyapunov analysis in fully developed model turbulence. Prog. Theoret. Phys. 89, 329-341.
  • Pacek A.W., Chamsart S., Nienow A.W., Bakker A., 1999. The influence of impeller type on mean drop size distribution in an agitated vessel. Chem. Eng. Sci. 54, 4211-4222.
  • Pacek A.W., Nienow A.W., 1995. A problem for the description of turbulent dispersed liquid-liquid systems. Int. J. Multiphase Flow 21, 323-328.
  • Pal R., 1996. Effect of droplet size on the rheology of emulsions. A.I.Ch.E. Journal 42, 3181-3190.
  • Pal R., Yan Y., Masliyah J., 1992. Rheology of emulsions. In: Emulsions. Fundamentals and applications in the petroleum industry (Ed. by L.L. Schramm), pp. 131-170.
  • Parisi G., Frisch U., 1985. On the singularity structure of fully developed turbulence. In: Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. Eds. M. Ghil, R. Benzi and G. Parisi. North-Holland, Amsterdam.
  • Pedrizzetti G., Novikov E.A., Praskovsky A.A., 1995. Cytowane wg Nelkin M., 1995. Phys. Rev. E 52, R4610-R4611.
  • Podgórska W., 1993. Wpływ mikromieszania na precypitację. Rozprawa doktorska. Politechnika Warszawska, Warszawa.
  • Podgórska W., 2002a. Charakterystyka przepływu burzliwego w mieszalniku - modelowanie CFD i pomiary LDA. Inż. Ap. Chem. 41(33), 4s, 105-106.
  • Podgórska W., 2002b. Dynamical stabilization of liquid-liquid dispersions. Proceedings of the 29th Conference SSCHE, Tatranske Matliare 2002, Paper MP6, pp. 1-8.
  • Podgórska W., 2003a. Rozpad i koalescencja kropel w intermitentnym polu burzliwym - teoria, modelowanie i eksperyment. Sprawozdanie z realizacji projektu badawczego KBN nr 3 T09C 059 18.
  • Podgórska W., 2003b. Experimental study of coalescing liquid-liquid dispersions. Proceedings of 11th European Conference on Mixing, Bamberg, Germany. FUCK-DRUCK, pp. 511-518.
  • Podgórska W., 2005. Scale-up effects in coalescing dispersions - comparison of liquid-liquid systems differing in interface mobility. Chem. Eng. Sci. 60, 2115-2125.
  • Podgórska W., 2006a. Modelling of high viscosity oil drop breakage process in intermittent turbulence. Chem. Eng. Sci. 61, 2986-2993.
  • Podgórska W., 2006b. Daughter particle distribution for liquid-liquid dispersion in turbulent flow. Inż. Chem. Proc. (przyjęto do druku w Z2).
  • Podgórska W., Bałdyga J., 1995. Modeling of drop breakup and coalescence in turbulent flow. Report 1. Internal DSM Report.
  • Podgórska W., Bałdyga J., 1996. Modeling of drop breakup and coalescence in turbulent flow. Final Report. Internal DSM Report.
  • Podgórska W., Bałdyga J., 1997. Modeling of drop breakup and coalescence in liquid-liquid dispersions. Report 1. Project II. Internal DSM Report.
  • Podgórska W., Bałdyga J., 1998. Modeling of drop breakup and coalescence in liquid-liquid dispersions. Project II. Final Report. Internal DSM Report.
  • Podgórska W., Bałdyga J., 1999. Stabilizacja dynamiczna dyspersji. Prace Wydziału Inżynierii Chemicznej i Procesowej Politechniki Warszawskiej T. XXV, z. 1-3, 195-200.
  • Podgórska W., Bałdyga J., 2000a. Drop break-up and coalescence in intermittent turbulent flow. In: van der Akker, H.E.K., Derksen, J.J., (Eds.), Proceedings of the 10th European Conference on Mixing, Delft, July 2-5. Elsevier Science, Amsterdam, Lusanne, New York, Oxford, pp. 141-148.
  • Podgórska W., Bałdyga J., 2000b. Formulation of the phase inversion indices using drop break-up and coalescence modelling for intermittent turbulence. Proceedings of 14th International Congress of Chemical and Process Engineering CHISA 2000, Paper 3.38, pp. 1-18.
  • Podgórska W., Bałdyga J., 2000c. Modele burzliwej koalescencji kropel - klasyfikacja i porównanie. Inż. Ap. Chem. 39, 110-111.
  • Podgórska W., Bałdyga J., 2001. Scale-up effects on the drop size distribution of liquid-liquid dispersion in agitated vessels. Chem. Eng. Sci. 56, 741-746.
  • Podgórska W., Bałdyga J., 2002a. Effect of structure of turbulence on drop breakage. Chem. Pap. 56, 412-417.
  • Podgórska W., Bałdyga J., 2002b. Effects of large- and small-scale inhomogeneity of turbulence in an agitated vessel on drop size distribution. 17th International Symposium on Chemical Reaction Engineering ISCRE 17, Hongkong, 25-28 October. Available from: http://www.ust.hk/iscre17, Paper MS#0398, pp. 1-21.
  • Podgórska W., Bałdyga J., 2003. Drop break-up and coalescence in a stirred tank. Task Quarterly 7, 409-424.
  • Podgórska W., Bałdyga J., Makowski Ł., 2001. Wpływ niehomogeniczności burzliwości na dyspersje ciecz-ciecz. Inż. Chem. Proc. 22, 3D, 1127-1132.
  • Podgórska W., Strybuć A., 2004. Badanie wpływu lepkości fazy rozproszonej na ewolucję rozkładu wielkości kropel w czasie dla rozpadu kropel w polu burzliwym. Inż. Chem. Proc. 25, 1503-1508.
  • Prasad R.R., Sreenivasan K.R., 1990. Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flow. J. Fluid Mech. 216, 1-34.
  • Prince M.J., Blanch H.W., 1990. Transition electrolyte concentrations for bubble coalescence. A.I.Ch.E. Journal 36, 1425-1429.
  • Radoev B.P., Scheludko A.D., Manev E.D., 1983. Critical thickness of thin liquid films: Theory and experiment. J. Colloid Interface Sci. 95, 254-265.
  • Rallison J.M., 1981. A numerical study of the deformation and burst of a viscous drop in general shear flows. J. Fluid Mech. 109, 465-482.
  • Rallison J.M., Acrivos A., 1978. A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191-200.
  • Ramkrishna D., 1985. The status of population balances. Reviews in Chem. Eng. 3, 49-95.
  • Ramkrishna D., 2000. Population balances. Theory and applications to particulate systems in engineering. Academic Press, San Diego.
  • Ramkrishna D., Mahoney A.W., 2002. Population balance modeling. Promise for future. Chem. Eng. Sci. 57, 595-606.
  • Randolph A.D., Larson M.A., 1964. A population balance for countable entities. Can. J. Chem. Eng. 42, 280-281.
  • Randolph A.D., Larson M.A., 1988. Theory of particulate processes. Academic Press, New York, London.
  • Revill B.K., 1982. Pumping capacity of disc turbine agitators - a literature review. In: Proc. 4th European Conference on Mixing. Paper B1. Noordwijkerhout, The Netherlands, April 27-29, pp. 11-24.
  • Reynolds O., 1881. On drops floating on the surface of water. Chem. News 44, 211-212.
  • Reynolds O., 1886. On the theory of lubrication and its application to Mr. Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil. Phil. Trans. Roy. Soc. London A177, 157-235.
  • Ribeiro L.M., Regueiras P.F.R., Guimaraes M.M.L., Madureira C.M.N., Cruz-Pinto J.J.C., 1995. The dynamic behaviour of liquid-liquid agitated dispersions - I. The hydrodynamics. Comput. Chem. Eng. 19, 333-343.
  • Ross S.L., 1971. Measurements and models of the dispersed phase mixing process. Ph.D. Dissertation, University of Michigan, Ann Arbor, Michigan.
  • Ross S.L., Curl R.L., 1973. Measurement and models of the dispersed phase mixing process. Joint Chem. Eng. Conf., Paper 29b, Vancouver, September 1973.
  • Ruelle D., Takens F., 1971. On the nature of turbulence. Commun. Math. Phys. 20, 167-192.
  • Ruiz Chavarria G., Baudet C., Ciliberto S., 1995. Hierarchy of the energy dissipation moments in fully developed turbulence. Phys. Rev. Lett. 74, 1986-1989.
  • Rumscheidt F.D., Mason S.G., 1961. Particle motions in sheared suspensions. XII. Deformation and burst of fluid drops in shear and hyperbolic flows. J. Colloid Interface Sci. 16, 238-261.
  • Saboni A., Gourdon C., Chesters A.K., 1995. Drainage and rupture of partially mobile films during coalescence in liquid-liquid systems under a constant interaction force. J. Colloid Interface Sci. 175, 27-35.
  • Saboni A., Gourdon C., Chesters A.K., 1999. The influence of inter-phase mass transfer on the drainage of partially-mobile liquid films between drops undergoing a constant interaction force. Chem. Eng. Sci. 54, 461-473.
  • Saboni A., Alexandrova S., Gourdon C., Chesters A.K., 2002. Interdrop coalescence with mass transfer: comparison of the approximate drainage models with numerical results. Chem. Eng. J. 88, 127-139.
  • Saffman P.G., Turner J.S., 1956. On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16-30.
  • Salager J., 1988. In: Encyclopedia of emulsion technology, Vol. 3, Ed. P. Becher, p. 79.
  • Sarimseli A., Kelbaliyev G., 2004. Modeling of the break-up of deformable particles in developed turbulent flow. Chem. Eng. Sci. 59, 1233-1240.
  • Sathyagal A., Ramkrishna D., Narsimhan G., 1996. Droplet breakage in stirred dispersions. Breakage functions from experimental drop-size distributions. Chem. Eng. Sci. 51, 1377-1391.
  • Scheele G.F., Leng D.E., 1971. An experimental study of factors which promote coalescence of two colliding drops suspended in water - I. Chem. Eng. Sci. 26, 1867-1879.
  • Schulze K., Ritter J., Kraume M., 2000. Investigation of local drop size distributions and scale-up in stirred liquid-liquid dispersions. In: van der Akker, H.E.K., Derksen, J.J. (Eds.), Proceedings of the 10th European Conference on Mixing, Delft, July 2-5. Elsevier, Amsterdam, pp. 181-188.
  • Schwartzberg H.G., Treybal R.E., 1968a. Fluid and particle motion in turbulent stirred tanks. Fluid motion. Ind. Eng. Chem. Fundam. 7, 1-6.
  • Schwartzberg H.G., Treybal R.E., 1968b. Fluid and particle motion in turbulent stirred tanks. Particle motion. Ind. Eng. Chem. Fundam. 7, 6-12.
  • Selker A.H., Sleicher C.A., 1965. Factors affecting which phase will disperse when immiscible liquids are stirred together. Can. J. Chem. Eng. 43, 298-301.
  • She Z-S., Leveque E., 1994. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336-339.
  • She Z-S., Waymire E.C., 1995. Quantized energy cascade and Log-Poisson statistics in fully developed turbulence. Phys. Rev. Lett. 74, 262-265.
  • Shinnar R., Church J.M., 1960. Predicting particle size in agitated dispersions. Ind. Eng. Chem. 52, 253-256.
  • Shinnar R., 1961. On the behaviour of liquid dispersions in mixing vessels. J. Fluid Mech. 10, 259-275.
  • Sleicher C.A., 1962. Maximum stable drop size in turbulent flow. A.I.Ch.E. Journal 8, 471-477.
  • Smit L., 1994. An alternative scale procedure for stirred vessels. Proceedings of the Eighth European Conference on Mixing, Cambridge, September 21-23, IChEME Symposium Series No. 136, 309-315.
  • Sommerfeld M., 2001. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int. J. Multiphase Flow 27, 1829-1858.
  • Sovova H., 1981. Breakage and coalescence of drops in a batch stirred vessel - II. Comparison of model and experiments. Chem. Eng. Sci. 36, 1567-1573.
  • Sprow F.B., 1967. Drop size distributions in strongly coalescing agitated liquid-liquid systems. A.I.Ch.E. Journal 13, 995-998.
  • Sreenivasan K.R., Antonia R.A., 1997. The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435-472.
  • Sreenivasan K.R., Kailasnath P., 1993. An update on the intermittency exponent in turbulence. Phys. Fluids A 5, 512-514.
  • Stevens G.W., Pratt H.R.C., 1990. Drop coalescence in aqueous electrolyte solutions. J. Colloid Interface Sci. 136, 470-479.
  • Stokes R.J., Evans D.F., 1997. Fundamentals of interfacial engineering. Wiley-VCH, New York.
  • Stone H.A., Leal L.G., 1989. Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399-427.
  • Stone H.A., Leal L.G., 1990. The effect of surfactants on drop deformation and breakup. J. Fluid Mech. 220, 161-186.
  • Svendsen H.F., Luo H., 1996. Modeling of approach process for equal or unequal sized fluid particles. Can. J. Chem. Eng. 74, 321-330.
  • Tadros Th.F., Vandamme A., Levecke B., Booten K., Stevens C.V., 2004. Stabilization of emulsions using polymeric surfactants based on inulin. Adv. Colloid Interface Sci. 108-109, 207-226.
  • Taylor G.I., 1932. The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. 138A, 41-48.
  • Taylor G.I., 1934. The formation of emulsions in deformable fields of flow. Proc. R. Soc. 29, 501-523.
  • Taylor M.A., Kurien S., Eyink G.L., 2003. Recovering statistics in turbulence simulations: The Kolmogorov 4/5th law. Phys. Rev. E 68, 026310-1-0263108.
  • Tennekes H., Lumley J.L., 1972. A first course in turbulence. MIT Press, Cambridge, Massachusetts, London.
  • Tidhar M., Merchuk J.C., Sembira A.N., Wolf D., 1986. Characteristics of a motionless mixer for dispersion of immiscible fluids - II. Phase inversion of liquid-liquid systems. Chem. Eng. Sci. 41, 457-462.
  • Tobin T., Muralidhar R., Wright H., Ramkrishna D., 1990. Determination of coalescence frequencies in liquid-liquid dispersions: effect of drop size dependence. Chem. Eng. Sci. 45, 3491-3504.
  • Tobin T., Ramkrishna D., 1992. Coalescence of charged droplets in agitated liquid-liquid dispersions. A.I.Ch.E. Journal 38, 1199-1205.
  • Tobin T., Ramkrishna D., 1999. Modeling the effect of drop charge on coalescence in turbulent liquid-liquid dispersions. Can. J. Chem. Eng. 77, 1090-1104.
  • Tomotika S., 1935. On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. Roy. Soc. A 150, 322-337.
  • Tsouris C., Tavlarides L.L., 1994. Breakage and coalescence models for drops in turbulent dispersions. A.I.Ch.E. Journal 40, 395-406.
  • Urbina-Villalba G., Garcia-Sucre M., 2001. Influence of surfactant distribution on the stability of oil/water emulsions towards flocculation and coalescence. Colloids and Surfaces A: Physicochemical and Engineering Aspects 190, 111-116.
  • Valentas K.J., Amundson N.R., 1966. Breakage and coalescence in dispersed phase systems. I & E C Fundamentals 5, 533-542.
  • Valentas K.J., Bilous O., Amundson N.R., 1966. Analysis of breakage in dispersed phase systems. I & E C Fundamentals 5, 271-279.
  • Vihkansky A., Kraft M., 2004. Modelling of a RDC using a combined CFD-population balance approach. Chem. Eng. Sci. 59, 2597-2606.
  • Vincent A., Meneguzzi M., 1991. The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1-25.
  • Visser J., 1972. On Hamaker constants: A comparison between Hamaker constants and Lifshitz-van der Waals constants. Adv. Colloid Interface Sci. 3, 331-363.
  • Wang T., Wang J., Jin J., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem. Eng. Sci. 58, 4629-4637.
  • Wang T., Wang J., Jin J., 2004. An efficient numerical algorithm for "a novel theoretical break-up kernel function of bubble/droplet in a turbulent flow". Chem. Eng. Sci. 59, 2593-2595.
  • Wilczyński K., 2001. Reologia w przetwórstwie tworzyw sztucznych. WNT, Warszawa.
  • Williams M.M.R., Loyalka S.K., 1991. Aerosol science theory and practice with special applications to the nuclear industry. Pergamon Press, Oxford.
  • Wu H., Patterson G.K., 1989. Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer. Chem. Eng. Sci. 44, 2207-2221.
  • Yaglom A.M., 1966. O vlijanii fluktuacij energii na formu charakteristik turbulentnosti v inercjonnom intervale. Dokl. Akad. Nauk. SSSR 166, 49-52.
  • Yeo L.Y., Matar O.K., Perez de Ortiz E.S., Hewitt G.F., 2001. The dynamics of Marangoni driven local film drainage between two drops. J. Colloid Interface Sci. 241, 233-247.
  • Yeo L.Y., Matar O.K., Perez de Ortiz E.S., Hewitt G.F., 2002. A simple predictive tool for modelling phase inversion in liquid-liquid dispersions. Chem. Eng. Sci. 57, 1069-1072.
  • Yeo L.Y., Matar O.K., Perez de Ortiz E.S., Hewitt G.F., 2003. Film drainage between two surfactant-coated drops colliding at constant approach velocity. J. Colloid Interface Sci. 257, 93-107.
  • Yiantsios S.G., Davis R.H., 1991. Close approach and deformation of two viscous drops due to gravity and van der Waals forces. J. Colloid Interface Sci. 144, 412-433.
  • Yuu S., 1984. Collision rate of small particles in a homogeneous and isotropic turbulence. A.I.Ch.E. Journal 30, 802-807.
  • Zakrzewska B., Jaworski Z., 2001. Badania przyściennego przepływu przejściowego i burzliwego w mieszalniku cieczy. II. Modelowanie numeryczne przepływu burzliwego. Inż. Chem. Proc. 22, 3E, 1525-1530.
  • Zerfa M., Brooks B.W., 1998. Experimental investigation of PVA adsorption at the vinyl chloride/water interface in monomer suspensions. Colloids and Surfaces A: Physicochemical and Engineering Aspects 132, 267-273.
  • Zhou G., Kresta S.M., 1998. Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank. Chem. Eng. Sci. 53, 2063-2079.
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