Mass Transfer in the Dissolution of a Multicomponent Liquid Droplet in an Immiscible Liquid Environment

Abstract

The Epstein Plesset equation has recently been shown to accurately predict 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 upon a reduced surface area approximation and the assumption of ideal homogenous mixing: Mass0.16667emfluxdmidt=AfraciDifalse(ci-csfalse){1R+1πDit}, 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; 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 measured the dissolution of single individual microdroplets of mutually-miscible liquid mixtures (ethyl acetate/butyl acetate, and butyl acetate/amyl acetate) into water. We additionally measured the diffusion coefficient of the pure materials: ethyl acetate, butyl acetate, and amyl acetate, in water at 22 deg C. 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. 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 multi-component droplet closely follows the modified Epstein Plesset model presented here.

From Single Microparticles to Microfluidic Emulsification: Fundamental Properties (Solubility, Density, Phase Separation) from Micropipette Manipulation of Solvent, Drug and Polymer Microspheres

“…First used in a non-mechanical way in 1998 to simply position micro-hydrogel beads with and without a loaded-drug (doxorubicin) in a controlled flow field of different pH [23,24], the micropipette technique was then developed by Needham et al [1][2][3][4][25][26][27][28][29][30][31][32][33][34][35][36][37], Tony Yeung et al [38], and others, in a series of papers on adsorption at interfaces and two-phase oil-aqueous systems. It has now become a highly versatile experimental setup that allows a wide variety of studies at microscopic interfaces and with single-and pairs-of microparticles.…”

“…It has now become a highly versatile experimental setup that allows a wide variety of studies at microscopic interfaces and with single-and pairs-of microparticles. Among other applications, the technique has been established for studying solvent dissolution, measuring fundamental properties such as diffusion coefficients and solubilities of the dissolving liquids [4,27,30], and for evaluating the phase separation, precipitation of droplets containing different solutes upon solvent loss, such as the micro-glassification of proteins by fast removal of water into water-imbibing solvents like octanol [3,31], and drug-containing polymer microspheres by removal of the organic solvent into water [28,29]. It is this last application that has motivated and guided the current studies with poly(lactic-co-glycolic acid) (PLGA) microparticles containing Ibuprofen [34].…”

Towards controlled liquid–liquid microextraction

“…However, the truth lies in the middle: solubility is a matter of time scales, and even heavy oil dissolves in clean water, provided one waits long enough. The dissolution dynamics of an isolated spherical droplet in a bulk liquid at rest was analytically calculated in a classical paper by Epstein & Plesset (1950), originally formulated for bubbles and later extended to droplets (Duncan & Needham 2006;Su & Needham 2013). The result of this exact calculation is that a droplet shrinks with a square-root behaviour in time on a time scale governed by τ EP = R 2 0 ρ d /(Dc s ).…”

“…While the Epstein-Plesset theory can relatively straightforwardly be extended to bubbles consisting of gas mixtures, this does not hold for multicomponent droplets, not even when they are constituted of miscible liquids. Up to now various approximations have been used: Su & Needham (2013) assumed that the instantaneous droplet-bulk interface composition of spherical droplets can be related to the droplet volumetric composition, i.e. for a two-component droplet with liquids i = a, b, they assume V a /V b = A a /A b , where V i /V and A i /A are the volume and area fractions of the total droplet volume V and the total droplet interface A.…”

“…for a two-component droplet with liquids i = a, b, they assume V a /V b = A a /A b , where V i /V and A i /A are the volume and area fractions of the total droplet volume V and the total droplet interface A. Su & Needham (2013) then calculated the dissolution rate of the individual components based on the total droplet radius, and multiplied this by the surface area fraction A i /A occupied by the respective component. This approach is equivalent to the use of Raoult's law to determine the partial gas pressures at the bulk side of the interface, in the sense that both approaches assume negligible interaction between the two components a and b, and a homogeneous mixture inside the droplet.…”