Mass Transfer in the Dissolution of a Multi-Component Liquid Droplet in an Immiscible Liquid Environment.

Langmuir : the ACS journal of surfaces and colloids

PubMedID: 24050124

Su JT, Needham D. Mass Transfer in the Dissolution of a Multi-Component Liquid Droplet in an Immiscible Liquid Environment. Langmuir. 2013;.
The Epstein Plesset equation, (originally developed for gas bubbles in water) has recently been shown to accurately predict the dissolution of a (single component) pure liquid microdroplet into a second immiscible solvent, such as oil into water. Here, we present a series of new experiments and a modification to this equation to model the dissolution of a two-component oil-mixture microdroplet into a second immiscible solvent (water), in which the two materials of the droplet have different solubilities in water. The model is based upon a reduced surface area approximation and the assumption of ideal homogenous mixing: Mass flux (dm_i)/dt=?Afrac?_i D_i (c_i-c_s){1/R+1/v(pD_i t)}, where Afraci is the area fraction of component i; ci and cs are the initial and saturation concentrations of the droplet material in the surrounding medium, respectively; R is the radius of the droplet; t is time; and Di is the coefficient of diffusion of component i in the surrounding medium. This new model has been tested by use of a two-chamber micropipette-based method, which measures the dissolution of single individual microdroplets of mutually-miscible liquid mixtures (ethyl acetate/butyl acetate, and butyl acetate/amyl acetate) into water. We have also measured the diffusion coefficient of the pure materials: ethyl acetate, butyl acetate, and amyl acetate, in water at 22 deg C using the same micropipette-based technique. Diffusion coefficients for the pure acetates in water were: 8.65 x 10-6, 7.61 x 10-6, and 9.14 x 10-6 cm2/s respectively. Using solubility data from the literature, this model accurately predicts the dissolution of microdroplets for the ethyl acetate/butyl acetate and butyl acetate/amyl acetate systems given the solubility and diffusion coefficients of each of the individual components in water as well as the initial droplet radius. The average mean squared error was 8.96%, which is a good experimental fit. Dissolution time is a function of the composition of the droplet, i.e., for a given droplet size, the droplet mixtures have a dissolution time between the dissolution time of the pure fastest dissolving droplet and the pure slowest dissolving droplet. Dissolution of mixed-component microdroplets follows a process in which both components leave the droplet at the same time, though at different rates and depend on the fraction of microdroplet surface area that they can occupy. The dissolution of a spherical ideally mixed multi-component droplet closely follows the modified Epstein Plesset model also presented here.