Hydrodynamic interactions of active motors in curved membranes

We construct a model to explore the hydrodynamic interactions of active machines in curved membranes. The membrane is modelled as a monolayer of highly viscous fluid, surrounded by external solvents of different viscosities. The active machines are modelled as point defects, such as vortices and force dipoles. We will explore the effects of membrane curvature and topology on the flows sourced by these active machines. We will also understand the hydrodynamic interactions between the active machines and discover interesting regimes where coordinated motion arises. The work can be viewed as a first step to understand collective motion of biological motor proteins in curved membranes and other microfluidic environments arising in nature, thus paving the way for an improved understanding of cellular transport.