  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.

Fluid Dynamics