Active suspensions in thin films: nutrient uptake and swimmer motion

A numerical study of swimming particle motion and nutrient transport is conducted for a semidilute to dense suspension in a thin film. The steady squirmer model is used to represent the motion of living cells in suspension with the nutrient uptake by swimming particles modelled using a first-order kinetic equation representing the absorption process that occurs locally at the particle surface. An analysis of the dynamics of the neutral squirmers inside the film shows that the vertical motion is reduced significantly. The mean nutrient uptake for both isolated and populations of swimmers decreases for increasing swimming speeds when nutrient advection becomes relevant as less time is left for the nutrient to diffuse to the surface. This finding is in contrast to the case where the uptake is modelled by imposing a constant nutrient concentration at the cell surface and the mass flux results to be an increasing monotonic function of the swimming speed. In comparison to non-motile particles, the cell motion has a negligible influence on nutrient uptake at lower particle absorption rates since the process is rate limited. At higher absorption rates, the swimming motion results in a large increase in the nutrient uptake that is attributed to the movement of particles and increased mixing in the fluid. As the volume fraction of swimming particles increases, the squirmers consume slightly less nutrients and require more power for the same swimming motion. Despite this increase in energy consumption, the results clearly demonstrate that the gain in nutrient uptake make swimming a winning strategy for micro-organism survival also in relatively dense suspensions.