Molecular transport in the vicinity of a biofilm subjected to variable fluid flow

The molecular distribution around a bacterial biofilm can be affected by fluid flows in the environment, as occurs on the surfaces of river rocks, water pipes, and intestinal tissues. Inspired by experimental studies of shared-resource dynamics between producing and non-producing cells of V. cholerae, we use numerical simulations to quantify the concentration of molecules around a biofilm subjected to fluid flows of varying strength. We solve the three-dimensional Stokes flow and a coupled advection-diffusion equation with a constant production of molecules at the biofilm surface. In the absence of fluid flow, we find a near-uniform axisymmetric concentration gradient around the biofilm. However, we find that any nonzero, transverse fluid velocity breaks the axisymmetry, creating a tail-like structure. We compare the depth-averaged concentration profile at different flow speeds and quantify the protection range around the biofilm where non-producing cells can exploit the molecules. By making qualitative comparisons with experiments, we find that the protection range decreases with increasing fluid velocity. Our numerical approach is very general and in the future can offer insights into both quorum sensing and the public goods dilemma in biofilms.