Solute mass exchange between water phase and biofilm for a single pore

Currently, there are no tractable approaches available for modeling non-equilibrium mass exchange of a solute between water phase and biofilm in porous media. The present work contributes to a quantitative description of the mass exchange of a solute over a single pore domain under a wide range of prevailing conditions. First, we developed a semiempirical model for the rate of solute mass exchange between water phase and biofilm. Then, extensive microscale simulations in a single pore were conducted. Results were averaged over a single pore domain, in order to determine a tube-scale kinetic rate coefficient as a function of various transport and biofilm properties. We illustrated the dependencies of the coefficient on a number of variables like Péclet number, Damköhler number, and biofilm volume fraction. Based on those results, we developed empirical formulae for the tube-scale mass exchange coefficient as a function of Damköhler number and biofilm volume fraction. Finally, we verified the proposed mass exchange rate against microscale simulations of solute transport in a long capillary tube. Good match was obtained over a wide range of conditions.