Mass transfer around a compound drop in an extensional flow

Abstract

AbstractMass transfer around a spherical compound drop in an extensional creeping flow and at large Peclet numbers is theoretically studied. The compound drop, embedded in an external fluid (fluid 1), is composed from a spherical inner drop (fluid 3), which is engulfed by a spherical fluid shell (fluid 2). The study is governed by four dimensionless parameters: two viscosity ratios, shell over external fluid (λ21) and internal drop over shell (λ32); the radii ratio, inner over outer (κ); and the large Peclet number (Pe). For very fast mobile interfaces, the rate of mass transfer is proportional to Pe1/2, it increases as λ21 or κ decrease, and in the limit of a very small internal drop (κ → 0) it reduces to the case of a single drop. For very slow mobile interfaces or immobile interfaces, the rate of mass transfer is proportional to Pe1/3, it increases as λ21 or κ increase, and in the limit of a very thin shell (κ → 1) it behaves like a single solid particle. For both interface speed cases, the effect of the other viscosity ratio (λ32) on the external mass transfer is practically negligible.