Mass transfer around a double emulsion droplet in a uniform flow

Abstract

The transfer of mass around a spherical double emulsion droplet in a uniform creeping flow and at large Peclet numbers is the subject of this theoretical communication. The double emulsion droplet, submerged in an external fluid (fluid 1), is made from an internal spherical drop (fluid 3) covered by a spherical fluid shell (fluid 2). Four dimensionless numbers describe this situation: two viscosity ratios, shell over external (λ21) and internal over shell (λ32); the radii ratio, inner over outer (κ); and the Peclet number (Pe). The external mass transfer rate of a double emulsion having a fast external mobile surface is proportional to Pe1∕2, it increases as λ21 or κ decrease, and for a very small internal drop or a very thick shell (κ→ 0), it behaves like a single drop. On the other hand, the external rate of mass transfer of a double emulsion with a very slow external mobile surface is proportional to Pe1∕3, it increases as λ21 or κ increase, and for a very large internal drop or a very thin shell (κ→ 1), it mimics a single solid particle. The influence of the other viscosity ratio (λ32) on the external mass transfer can be ignored.