Axisymmetric Squirmers in Stokes Fluid with Nonuniform Viscosity

Abstract

The ciliary locomotion and feeding of an axisymmetric micro-swimmer in a complex fluid whose viscosity depends on nutrient concentration are investigated numerically. The micro-swimmer is modeled as having spheroidal geometry, and ciliary beating is modeled by a slip velocity; i.e. a squirmer is adapted. Looking at the coupling between swimming and feeding of spheroidal squirmers, it is found that swimming speed and feeding are most affected by a non-uniform viscosity environment when the ratio of advection-forces to diffusion-transport, characterized by the nondimensional Pecl\'et number, is moderate ($\text{Pe}\approx 10$). These changes are correlated to significant increases in the pressure force on the surface of the squirmer. The swimming and feeding changes are found to be more significant in oblate spheroids than prolate spheroids. Most interestingly, nontrivial symmetric slip boundary conditions on the surface of the squirmer, which results in zero net motion in a constant viscosity fluid, can yield non-zero propulsion when paired with asymmetric nutrient boundary conditions. The fact that symmetric fluid boundary conditions can result in asymmetric propulsion has implications for the design of artificial micro-swimmers and other low-$\text{Re}$ squirmers in complex fluids.