Scalar transport from deformed drops: the singular role of streamline topology

Abstract

We examine scalar transport from a neutrally buoyant drop, in an ambient planar extensional flow, in the limit of a dominant drop phase resistance. For this interior problem, we consider the effect of drop-deformation-induced change in streamline topology on the transport rate (the Nusselt number N u). The importance of drop deformation is characterized by the Capillary number (Ca). For a spherical drop (Ca = 0), closed streamlines lead to the ratio N u/N u0 increasing with the Peclet number (P e), from unity to a diffusion-limited plateau value (≈ 4.1); N u0 here denotes the purely diffusive rate of transport. For any finite Ca, the flow field consists of spiralling streamlines that densely wind around nested tori foliating the deformed drop interior. N u now increases beyond the aforementioned primary plateau, saturating in a secondary plateau that approaches 23.3 for Ca → 0, P e Ca → ∞, and appears independent of the drop-to-medium viscosity ratio. N u/N u0 exhibits an analogous variation for other planar linear flows, although chaotically wandering streamlines in these cases are expected to lead to a tertiary enhancement regime.