  We study the mobility of extended objects (rods) on a spherical liquid-liquid
interface to show how this quantity is modified in a striking manner by both
the curvature and the topology of the interface. We present theoretical
calculations and experimental measurements of the interfacial fluid velocity
field around a moving rod bound to the crowded interface of a water-in-oil
droplet. By using different droplet sizes, membrane viscosities, and rod
lengths, we show that the viscosity mismatch between the interior and exterior
fluids leads to a suppression of the fluid flow on small droplets that cannot
be captured by the flat interface predictions.
