Hydrodynamic behaviour of an ensemble of encapsulated liquid drops in creeping motion: a fluid-mechanic based model for liquid membranes

Abstract

The free surface cell model is used with the Stokes approximation, to characterize the Newtonian flow of an ensemble of concentric two-phase liquid drops (i.e. globules) in steady, creeping motion through an immiscible continuous liquid phase. The drag on each globule is determined analytically, and its dependence on globule concentration in the ensemble is investigated. Closed form expressions are derived for the stream functions both in the continuous phase and within each globule phase. The effect of globule concentration on streamline patterns and flow velocity is also investigated. The drag and internal circulation patterns are analysed in the limiting situations of a single globule, a rigid sphere ensemble and a fluid sphere ensemble, and their dependence on globule concentration and the other flow parameters is determined.