Optimal feeding of ciliated microorganisms in concentration gradients.

The flow field generated by ciliated microorganisms in a viscous fluid can influence the microorganisms' nutrient environment, and the stirred concentration field can correspondingly influence the microorganisms' nutrients uptake. We consider a classic model of ciliated organisms consisting of a spherical body with continuous wave-like surface deformations. This model, known as Blake's spherical envelope model or a squirmer model, emulates the action of tightly-packed distribution of cilia on the organism's surface. Using the ideal solution for the flow field around this spherical body in Stokes flow and solving the advection-diffusion equation numerically using the Legendre polynomial spectral method, we compute the concentration field and nutrient uptake of the microorganism. We analyze the nutrient uptake in a uniform background concentration and in a background concentration with constant gradient. In each case, we discuss the optimal ciliary strokes that maximize nutrient uptake.