Coupling between swimming and feeding efficiencies of ellipsoidal squirmers in a nutrient-dependent viscous flow

Ciliary locomotion is a wildly used method of transportation employed by bacteria and other single-celled organisms. Due to the Stokes limit that these creatures move in, their thrust is entirely made by viscous stresses. Recently we analytically studied the effect of a weak-dependence of viscosity on the dynamic nutrient field surrounding a mobile spherical squirmer and presented that the optimal stroke modes for the variable-viscosity environment can be different from those in the constant-viscosity environment, where nutrient and viscosity are uncoupled. The current work extends these findings to the case where the fluid viscosity is fully dependent on the nutrient. This dependence creates feedback between the nutrient field and the fluid flow with intriguing consequences. Using the Finite Element method, the effects of nutrient Peclet number, stroke modes, and form of nutrient-viscosity dependence are investigated. The changes in the speed and feeding efficiencies achieved by the model bacteria compared to the constant-viscosity case are shown and we discuss how the shape of the swimmer affects the observed feedback between its swimming and feeding performances.