On the diffusion around a slender drop in a simple shear flow

Abstract

AbstractMass transfer around a slender drop in a simple shear and creeping flow, at zero Peclet numbers (Pe = 0), is the subject of this theoretical report. The problem is governed by two dimensionless parameters: the capillary number (Ca >> 1) and the viscosity ratio (λ << 1). The fluid mechanics model of Hinch and Acrivos predicts an S‐shaped drop with pointed ends that is almost parallel with the direction of the flow. Making use of the analogy between electrostatics and diffusion (Pe = 0), both governed by the Laplace equation, together with the work of Szegö on the capacity of a condenser, a simple model is suggested by assuming the drop to be a slender prolate spheroid with rounded ends. The results suggest the following: (a) as the capillary number increases, the drop becomes thinner and longer and its surface area increases, leading to larger mass transfer rates; and (b) for the same capillary number, extensional flow is much more effective than simple shear flow in mass transfer operations.