Abstract
The transfer of mass between a slender drop and a liquid in an axisymmetric extensional flow, at zero Peclet numbers, is theoretically studied. We allow the external flow to have a small (but not zero) amount of inertia. The problem is governed by three dimensionless parameters: the capillary number (Ca>>1), the viscosity ratio (λ<<1) and the external Reynolds number (Re<<1). It is shown that the shape of the drop is, at first approximation, a slender spindle suggesting the usage of the bispherical coordinate system. Applying the method presented by Szegö and Pyne, for the electrostatic capacity of a spindle, an analytical solution containing conal functions is obtained. The results show that, as the capillary number or the Reynolds number increase, the drop becomes thinner and longer, the surface area increases, resulting in larger mass transfer rates, with the capillary number being the most influential parameter.
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