Enhanced feeding of model ciliates in non-uniform concentration fields

Aquatic sessile microorganisms often use cilia to generate feeding currents. Existing studies

focus on feeding in uniform background concentrations. Although concentrations that are non-

uniform at length scales comparable to the organism are more common, little is known about

whether and how sessile organisms can generate flows that benefit from this non-uniformity. Here,

we consider a classic squirmer, based on Blake’s spherical envelope model, fixed in a non-uniform

background concentration, and we analyze the effects of the squirming motion on nutrients up-

take. The squirmer model emulates packed cilia as a continuous deformable surface for which an

analytical solution of the cilia-generated flow field exists as a Legendre expansion in terms of the

fundamental squirming modes. Using the analytical solution of the flow field in conjunction with

direct numerical simulation of the advection-diffusion equation, we solve for the steady and un-

steady concentration fields and compute nutrients uptake in uniform and non-uniform background

concentrations. The steady and unsteady results consistently show that the surface cilia motion,

dominantly putting energy into the squirming mode bringing flows from the direction of higher

concentration, enhances the feeding nutrients of the squirmer.