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Dissolution and growth of a multicomponent drop in an immiscible liquid

Published online by Cambridge University Press:  10 June 2016

Shigan Chu
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Andrea Prosperetti*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Department of Science & Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands
*
Email address for correspondence: prosperetti@jhu.edu

Abstract

The mass flux at the surface of a drop in an immiscible host liquid is dictated by the composition of the drop surface. In a binary system, this composition is essentially constant in time and equals the solubility of the drop constituent in the host liquid. This situation has been treated in a classic study by Epstein and Plesset (J. Chem. Phys., vol. 18, 1950, pp. 1505–1509). The situation is very different for ternary and higher-order systems in which, due to the mutual interaction of the drop constituents, their concentration at the drop surface markedly differs from the respective solubilities and depends on time. This paper presents a thermodynamically consistent analysis of this situation, for both growing and dissolving drops, with and without an initial concentration of the drop constituents in the host liquid. In some cases the results, which have important implications e.g. for solvent extraction processes in the chemical and environmental remediation industries, show major deviations from the predictions of approximations in current use, including simple extensions of the Epstein–Plesset theory.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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References

Abrams, D. S. & Prausnitz, J. M. 1975 Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 21, 116128.Google Scholar
Ahuja, S.(Ed.) 2000 Handbook of Bioseparations. Academic.Google Scholar
Anderson, T. F. & Prausnitz, J. M. 1978a Application of the UNIQUAC equation to calculation of multicomponent phase equilibria: 1. Vapor–liquid equilibria. Ind. Engng Chem. Process Des. Dev. 17, 552561.Google Scholar
Anderson, T. F. & Prausnitz, J. M. 1978b Application of the UNIQUAC equation to calculation of multicomponent phase equilibria: 2. Liquid–liquid equilibria. Ind. Engng Chem. Process Des. Dev. 17, 561567.Google Scholar
Arce, A., Alonso, L. & Vidal, I. 1999 Liquid–liquid equilibria of the systems ethyl acetate+ ethanol+ water, butyl acetate+ ethanol+ water, and ethyl acetate+ butyl acetate+ water. J. Chem. Engng Japan 32, 440444.Google Scholar
California Department of Toxic Substances Control 2014 HERO_Soil-Gas_Screening_Model_March2014.xlsm. https://dtsc.ca.gov.Google Scholar
Carroll, K. C. & Brusseau, M. L. 2009 Dissolution, cyclodextrin-enhanced solubilization, and mass removal of an ideal multicomponent organic liquid. J. Contam. Hydrol. 106, 6272.CrossRefGoogle ScholarPubMed
Chasanis, P., Brass, M. & Kenig, E. Y. 2010 Investigation of multicomponent mass transfer in liquid–liquid extraction systems at microscale. Intl J. Heat Mass Transfer 53, 37583763.Google Scholar
Chen, Y., Wen, C., Zhou, X. & Zeng, J. 2014 Phase equilibria of ternary and quaternary systems containing diethyl carbonate with water. J. Solution Chem. 43, 13741387.Google Scholar
Epstein, P. S. & Plesset, M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18, 15051509.CrossRefGoogle Scholar
Fukumoto, K., Yoshizawa, M. & Ohno, H. 2005 Room temperature ionic liquids from 20 natural amino acids. J. Am. Chem. Soc. 127, 23982399.Google Scholar
Haynes, W. M. 2014 CRC Handbook of Chemistry and Physics, 96th edn. CRC.CrossRefGoogle Scholar
Islam, A. W., Javvadi, A. & Kabadi, V. N. 2011 Universal liquid mixture models for vapor–liquid and liquid–liquid equilibria in the hexane-butanol-water system. Ind. Engng Chem. Res. 50, 10341045.Google Scholar
Islam, A. W., Zavvadi, A. & Kabadi, V. N. 2012 Analysis of partition coefficients of ternary liquid–liquid equilibrium systems and finding consistency using UNIQUAC model. Chem. Proc. Engng 33, 243253.Google Scholar
Kaisers, U., Kelly, K. P. & Busch, T. 2003 Liquid ventilation. Brit. J. Anaesthesia 91, 143151.Google Scholar
Landau, L. & Lifshitz, E. M. 1980 Statistical Physics, 3rd edn. Elsevier.Google Scholar
Magnussen, T., Rasmussen, P. & Fredenslund, A. 1981 UNIFAC parameter table for prediction of liquid–liquid equilibria. Ind. Engng Chem. Proc. Des. Dev. 20, 331339.Google Scholar
McCray, J. E. & Dugan, P. J. 2002 Nonideal equilibrium dissolution of trichloroethane from a decane-based nonaqueous phase liquid mixture: experimental and modeling investigation. Water Resour. Res. 38, 1097.Google Scholar
Poling, B. E., Prausnitz, J. M. & O’Connell, J. P. 2000 The Properties of Gases and Liquids, 5th edn. McGraw-Hill.Google Scholar
Prausnitz, J. M., Anderson, T. F., Grens, E. A., Eckert, C. A., Hsieh, R. & O’Connell, J. P. 1980 Computer Calculations for Multicomponent Vapor–Liquid and Liquid–Liquid Equilibria. Prentice-Hall.Google Scholar
Reed, T. M. & Taylor, T. E. 1959 Viscosities of liquid mixtures. J. Phys. Chem. 63, 5867.Google Scholar
Riddick, J. A., Bunger, W. B. & Sakano, T. K. 1986 Organic Solvents: Physical Properties and Methods of Purification. Wiley.Google Scholar
Rydberg, J., Cox, M., Musikas, C. & Choppin, G. R. 2004 Solvent Extraction Principles and Practice, 2nd edn. Marcel Dekker.Google Scholar
Sørensen, J. M. & Arlt, W. 1980 Liquid–Liquid Equilibrium Data Collection, vol. V. DECHEMA.Google Scholar
Su, J. T. & Needham, D. 2013 Mass transfer in the dissolution of a multicomponent liquid droplet in an immiscible liquid environment. Langmuir 29, 1333913345.Google Scholar
Tamura, K., Chen, Y., Tada, K., Yamada, T. & Nagata, I. 2000 Representation of multicomponent liquid liquid equilibria for aqueous and organic solutions using a modified UNIQUAC model. J. Solution Chem. 29, 463488.Google Scholar
Taylor, R.(Ed.) 2015 Reprocessing and Recycling of Spent Nuclear Fuel. Elsevier.Google Scholar
Taylor, R. & Krishna, R. 1993 Multicomponent Mass Transfer. Wiley.Google Scholar
Uribe-Ramirez, A. R. & Korchinsky, W. J. 2000 Fundamental theory for prediction of multicomponent mass transfer in single-liquid drops at intermediate Reynolds numbers (10⩽Re⩽250). Chem. Engng Sci. 55, 33193328.Google Scholar
Waheed, M. Adekojo, Henschke, M. & Pfenning, A. 2002 Mass transfer by free and forced convection from single spherical liquid drops. Intl J. Heat Mass Transfer 45, 45074514.Google Scholar
Wesselingh, J. A. & Krishna, R. 2000 Mass Transfer in Multicomponent Mixtures. Delft University Press.Google Scholar
Wohlfarth, C. 2009 Viscosity of the mixture (1) acetonitrile; (2) propionitrile. In Viscosity of Pure Organic Liquids and Binary Liquid Mixtures, Landolt–Börnstein – Group IV Physical Chemistry (ed. Lechner, M. D.), vol. 25, pp. 12061206. Springer.Google Scholar
Yalkowsky, S. H., He, Y. & Jain, P. 2010 Handbook of Aqueous Solubility Data, 2nd edn. CRC.Google Scholar