Nutrient Uptake by a Self-Propelled Steady Squirmer

Active suspensions in thin films: nutrient uptake and swimmer motion

“…The retention of the time variation in fluid and particle motion permits a general solution that collapses to the steady solution and resolves time-dependent phenomena that might occur at the same time scale as the viscous diffusion. For swimming microorganisms ranging in diameter from d = 1 to 100 µm the Reynolds number can range between Re = 10 −5 and 10 −1 (Magar et al 2003). In this low-Reynolds-number flow regime, convection in the fluid is negligible and the unsteady Stokes' equations for fluid flow apply.…”

“…Koch & Subramanian 2011). However, only a few of the numerical studies of individual swimming particles, including biofilms, that provide insight into the behaviour of active suspensions include mass transfer and nutrient uptake (Magar, Goto & Pedley 2003;Magar & Pedley 2005;Michelin & Lauga 2011;Taherzadeh, Picioreanu & Horn 2012). In these studies, the concentration of nutrients in the fluid medium are typically treated as a passive scalar.…”

“…In these studies, the concentration of nutrients in the fluid medium are typically treated as a passive scalar. In the case of individual swimming particles, Magar et al (2003), Magar & Pedley (2005) and Michelin & Lauga (2011) use a widely adopted unsteady and steady swimming cell model first introduced by Lighthill (1952) and Blake (1971). In this model, referred to as the squirmer model, the swimming cell is assumed to be spherical in shape with an applied tangential surface velocity that represents the surface distortion of beating cilia.…”

“…In a study of a single swimming particle, Magar et al (2003) and Magar & Pedley (2005) show that the swimming motion of a single cell increases the mass flux at the surface of the particle in comparison with an inert translating sphere. The mass flux is quantified in terms of the Sherwood number, a dimensionless nutrient concentration gradient at the particle surface.…”

“…All of these results are obtained assuming constant nutrient concentration at the particle surface. In Magar et al (2003) and Magar & Pedley (2005) a first-order nutrient uptake model is also included in an appendix. These authors perform asymptotic analysis in the limit of very small and very large Péclet numbers and show that the uptake decreases in this case.…”