Fig. 5: Optimal shapes of swimmers with surface dissipation.
From: Minimum entropy production by microswimmers with internal dissipation
a Numerically obtained optimal shape that minimizes the dissipation as a function of the internal dissipation density ζs while keeping the total volume of the swimmer fixed (V = 4πa3/3). The shapes are restricted by the minimum curvature radius \({r}_{\min }={\hat{r}}_{\min }a\). b Streamlines in the co-moving frame and propulsion velocity \(\tilde{v}\) (color coded) for three optimal shapes, obtained with aζs/μ = 4. c The dissipation by optimal swimmers as a function of the prescribed minimum curvature radius for a set of internal dissipation densities aζs/μ. The dissipation is normalized by that of a spherical swimmer, \({\hat{P}}_{{{{{{{{\rm{A}}}}}}}}}={P}_{{{{{{{{\rm{A}}}}}}}}}/(6\pi a{V}_{{{{{{{{\rm{A}}}}}}}}}^{2}(2\mu+a{\zeta }_{{{{{{{{\rm{s}}}}}}}}}))\).
