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Dissolution and growth of a multicomponent drop in an immiscible liquid

  • Shigan Chu (a1) and Andrea Prosperetti (a1) (a2)
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.

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Email address for correspondence: prosperetti@jhu.edu
References
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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.
Ahuja S.(Ed.) 2000 Handbook of Bioseparations. Academic.
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.
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.
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.
California Department of Toxic Substances Control 2014 HERO_Soil-Gas_Screening_Model_March2014.xlsm. https://dtsc.ca.gov.
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.
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.
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.
Epstein P. S. & Plesset M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18, 15051509.
Fukumoto K., Yoshizawa M. & Ohno H. 2005 Room temperature ionic liquids from 20 natural amino acids. J. Am. Chem. Soc. 127, 23982399.
Haynes W. M. 2014 CRC Handbook of Chemistry and Physics, 96th edn. CRC.
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.
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.
Kaisers U., Kelly K. P. & Busch T. 2003 Liquid ventilation. Brit. J. Anaesthesia 91, 143151.
Landau L. & Lifshitz E. M. 1980 Statistical Physics, 3rd edn. Elsevier.
Magnussen T., Rasmussen P. & Fredenslund A. 1981 UNIFAC parameter table for prediction of liquid–liquid equilibria. Ind. Engng Chem. Proc. Des. Dev. 20, 331339.
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.
Poling B. E., Prausnitz J. M. & O’Connell J. P. 2000 The Properties of Gases and Liquids, 5th edn. McGraw-Hill.
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.
Reed T. M. & Taylor T. E. 1959 Viscosities of liquid mixtures. J. Phys. Chem. 63, 5867.
Riddick J. A., Bunger W. B. & Sakano T. K. 1986 Organic Solvents: Physical Properties and Methods of Purification. Wiley.
Rydberg J., Cox M., Musikas C. & Choppin G. R. 2004 Solvent Extraction Principles and Practice, 2nd edn. Marcel Dekker.
Sørensen J. M. & Arlt W. 1980 Liquid–Liquid Equilibrium Data Collection, vol. V. DECHEMA.
Su J. T. & Needham D. 2013 Mass transfer in the dissolution of a multicomponent liquid droplet in an immiscible liquid environment. Langmuir 29, 1333913345.
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.
Taylor R.(Ed.) 2015 Reprocessing and Recycling of Spent Nuclear Fuel. Elsevier.
Taylor R. & Krishna R. 1993 Multicomponent Mass Transfer. Wiley.
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.
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.
Wesselingh J. A. & Krishna R. 2000 Mass Transfer in Multicomponent Mixtures. Delft University Press.
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.
Yalkowsky S. H., He Y. & Jain P. 2010 Handbook of Aqueous Solubility Data, 2nd edn. CRC.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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