Mass transfer in the dissolution of a multicomponent liquid droplet in an immiscible liquid environment

The Epstein-Plesset equation has recently been shown to predict accurately the dissolution of a 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 in which the two materials of the droplet have different solubilities. The model is based on a reduced surface area approximation and the assumption of ideal homogeneous mixing [mass flux d(m(i))/dt = A(frac(i))D(i)(c(i) - c(s)){(1/R) + (1/(πD(i)t)(1/2)}] where A(frac(i)) is the area fraction of component i, c(i) and c(s) are the initial and saturation concentrations of the droplet material in the surrounding medium, R is the radius of the droplet, t is time, and D(i) is the coefficient of diffusion of component i in the surrounding medium. This new model has been tested by the use of a two-chamber micropipet-based method, which measured the dissolution of single individual microdroplets of mutually miscible liquid mixtures (ethyl acetate/butyl acetate and butyl acetate/amyl acetate) in water. We additionally measured the diffusion coefficient of the pure materials-ethyl acetate, butyl acetate, and amyl acetate-in water at 22 °C. Diffusion coefficients for the pure acetates in water were 8.65 × 10(-6), 7.61 × 10(-6), and 9.14 × 10(-6) cm(2)/s, respectively. 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%. The dissolution of a spherical ideally mixed multicomponent droplet closely follows the modified Epstein-Plesset model presented here.