Mass transfer around a slender drop in a nonlinear extensional flow

Abstract

Abstract Mass transfer around a slender drop in a nonlinear extensional and creeping flow is theoretically studied. The fluid mechanics problem is governed by three dimensionless parameters: The capillary number (Ca ≫ 1), the viscosity ratio (λ ≪ 1), and the nonlinear intensity of the flow (|E| ≪ 1). The transfer of mass around such a drop is studied for the two asymptotic cases of large and zero Peclet numbers (Pe). The results show that as the capillary number increases, the drop becomes longer, thinner, its surface area increases, leading to larger mass transfer rates, especially at large Peclet numbers, since then convection contributes to the overall mass transfer as well. Taking a slender inviscid drop (λ = 0) in a linear extensional flow (E = 0) as our reference case, we find that the addition of nonlinear effects to the flow sometimes increases (Eλ−1Ca−2 < 64/9) and sometimes decreases (Eλ−1Ca−2 > 64/9) the rate of mass transfer.