Chemotaxis in shear flow: Similarity solutions of the steady-state chemoattractant and bacterial distributions

When chemotactic bacteria are exposed to a concentration gradient of chemoattractant while flowing along a channel, the bacteria accumulate at the interface between the chemoattractant source and bacterial suspension. Assuming that the interface is no-slip, we can apply the shear flow approximation near the no-slip boundary and solve a steady-state convection-diffusion model for both chemoattractant and bacterial concentrations. We suggest similarity solutions for the two-dimensional problem and identify a critical length scale η_c for bacteria chemotaxis in a given concentration gradient. The analysis identifies three dimensionless groups representing, respectively, chemotactic sensitivity, the chemotaxis receptor constant, and the bacteria diffusion coefficient, which typically show coupled effects in experimental systems. We study the effect of the dimensionless groups separately and provide understanding of the system involving shear flow and chemotaxis.