Dissolution and growth of a multicomponent drop in an immiscible liquid

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.

History effects on the gas exchange between a bubble and a liquid

“…The phenomena studied in the present work are similar to those considered in a previous recent paper [10] devoted to the dissolution or growth of a multicomponent drop. In that case, the time dependence of the surface concentration of the diffusing species is a consequence of their mutual interaction as the composition of the drop varies in time.…”

Towards controlled liquid–liquid microextraction

“…As predicted by Chu & Prosperetti (2016), we indeed find cases in which a segregation of the (miscible!) droplet components at the droplet interface can take place.…”

“…The pioneering calculations by Chu & Prosperetti (2016) stimulated us to perform detailed experiments on dissolving sessile two-component droplets (Dietrich et al 2016). As predicted by Chu & Prosperetti (2016), we indeed find cases in which a segregation of the (miscible!)…”

“…In a recent paper, Chu & Prosperetti (2016) have now provided a calculation of the dissolution (or growth) problem of a multicomponent droplet, revealing the limitation of the hitherto used approximations. They solve the diffusion equation with concentration boundary conditions at the (moving) droplet interface following from the requirement that the chemical potentials of each of the components have the same value in both phases (Landau & Lifshitz 1986), assuming thermodynamic equilibrium.…”

“…How serious are the deviations from the hitherto used approximations depends strongly on the solubilities and diffusivities of the components. For similar solubilities and diffusivities of the two droplet components, they can be serious, and Chu & Prosperetti (2016) construct a case in which the two-component droplet grows, even though in the solution both constituents of the droplet have a concentration below their saturation concentration, i.e. ζ i < 0 for both i = a, b.…”