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

TL;DR

This paper investigates how drop deformation affects scalar transport in planar extensional flow, revealing that streamline topology changes significantly enhance the transport rate beyond classical limits, especially at higher Capillary and Peclet numbers.

Contribution

It introduces a detailed analysis of the impact of drop deformation-induced streamline topology changes on scalar transport, highlighting the emergence of secondary and tertiary enhancement regimes.

Findings

Deformation leads to spiralling streamlines that increase transport rate.

Transport rate saturates at a secondary plateau for finite Capillary numbers.

Streamline topology changes significantly enhance scalar transport beyond classical diffusion limits.

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 $Nu$). The importance of drop deformation is characterized by the Capillary number ($Ca$). For a spherical drop ($Ca = 0$), closed streamlines lead to the ratio $Nu/Nu_0$ increasing with the Peclet number($Pe$), from unity to a diffusion-limited plateau value ($\approx 4.1$); $Nu_0$ 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. $Nu$ now increases beyond the aforementioned primary plateau, saturating in a secondary plateau that approaches $23.3$ for $Ca \rightarrow 0$, $Pe Ca \rightarrow \infty$, and appears independent of the drop-to-medium viscosity ratio. $Nu/Nu_0$ 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.