# Axisymmetric Squirmers in Stokes Fluid with Nonuniform Viscosity

## TL;DR

This study numerically investigates how nonuniform viscosity in complex fluids influences the swimming and feeding of axisymmetric micro-swimmers modeled as spheroidal squirmers, revealing significant effects at moderate Peclét numbers and conditions for propulsion.

## Contribution

It demonstrates that nonuniform viscosity environments can induce propulsion in symmetric squirmers with symmetric boundary conditions, highlighting new mechanisms for micro-swimmer movement in complex fluids.

## Key findings

- Swimming speed and feeding are most affected at Pe ≈ 10.
- Nonuniform viscosity causes significant pressure force increases.
- Symmetric boundary conditions can produce propulsion with asymmetric nutrient distribution.

## 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.