Fig. 4: Optimal shapes of active surface-driven droplets.
From: Minimum entropy production by microswimmers with internal dissipation
a The optimal shapes of active droplets with three different ratios of the internal to external viscosity μi/μ and their flow fields. b The dissipation \({\hat{P}}_{{{{{{{{\rm{A}}}}}}}}}={P}_{{{{{{{{\rm{A}}}}}}}}}/(6\pi (2\mu+3{\mu }_{{{\mbox{i}}}})a{V}_{{{{{{{{\rm{A}}}}}}}}}^{2})\) of the optimal active surface-driven droplet, relative to the equivalent droplet of a spherical shape (13), as a function of the viscosity ratio. The red dot indicates a topological bifurcation above which a toroidal shape (solid line) has a dissipation lower than the optimal swimmer with spherical topology (dashed line). The insets show the optimal shapes at viscosity ratios marked with squares.
