A singularly altered streamline topology allows faster transport from deformed drops

We analyse the effect of drop-deformation-induced change in streamline topology on the scalar transport rate (the Nusselt number $Nu$) in an ambient planar linear flow. The drop-phase resistance is assumed dominant, and the drop deformation is characterised by the capillary number ($Ca$). For a spherical drop ($Ca = 0$) in an ambient planar extension, closed streamlines lead to $Nu$ increasing with the Péclet number ($Pe$), from $Nu_0$, corresponding to purely diffusive transport, to $4.1Nu_0$, corresponding to a large-$Pe$ diffusion-limited plateau. For non-zero $Ca$, we show that the flow field consists of spiralling streamlines densely wound around nested tori foliating the deformed drop interior. Now $Nu$ increases beyond the aforementioned primary plateau, saturating in a secondary one that approaches $22.3Nu_0$ for $Ca \rightarrow 0$, $Pe\,Ca \rightarrow \infty$. The enhancement appears independent of the drop-to-medium viscosity ratio. We further show that this singular dependence, of the transport rate on drop deformation, is generic across planar linear flows; chaotically wandering streamlines in some of these cases may even lead to a tertiary enhancement regime.