Active suspensions in thin films: nutrient uptake and swimmer motion

Abstract

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.

Emergent behavior in active colloids

“…The time correlation function of these density fluctuations shows oscillatory behavior with a well defined frequency. Recently, the dynamics of many squirmers confined between two hard walls has also been studied [161,254,[342][343][344]. For a separation distance much larger than the swimmer size, a huge dynamically evolving cluster again emerges.…”

Nutrient uptake in a suspension of squirmers

“…This finding was predicted by Magar et al (2003) imposing a boundary condition for nutrient uptake that takes into account both the absorption of nutrients and the nutrient diffusion inside of the cell. Lambert et al (2013) also found that, as the volume fraction of squirmers increased, the squirmers consumed less nutrients and required more power for the same swimming motion. These findings are important in understanding nutrient uptake in a confined environment.…”

“…In the non-dilute regime, nutrient uptake by a swimming micro-organism has received little attention, except for Lambert et al (2013). However, mixing of chemicals and tracers in non-dilute suspensions of cells has been reported by many researchers (Pedley & Kessler 1992;Hill & Pedley 2005;Ishikawa 2009;Ishikawa, Locsei & Pedley 2010;Koch & Subramanian 2011;Kurtuldu et al 2011;Molina & Yamamoto 2014;Wagner, Young & Lauga 2014;Goldstein 2015).…”

“…Recently, Lambert et al (2013) investigated nutrient uptake by steady squirmers in a dense suspension in a thin film. At the cell surface, they imposed a nutrient flux proportional to the local concentration with a coefficient that indicated the ratio of the uptake rate to the viscous time scale.…”

“…These findings are important in understanding nutrient uptake in a confined environment. The results of Lambert et al (2013), however, were restricted to a film flow, and the vertical motion of squirmers was limited. To construct a more general understanding of 483 nutrient uptake in the non-dilute regime, a three-dimensional (3D) suspension must be investigated.…”