Criteria to assess when biodegradation is kinetically limited by intraparticle diffusion and sorption

To determine when intraparticle diffusion and sorption can influence the rate of biodegradation, we consider the biodegradation of a pollutant diffusing into or out of porous aggregates suspended in a liquid medium, where the reactant is metabolized by bacteria. The pollutant that diffuses into the aggregates obeys a sorption-desorption equilibrium isotherm at sites on inner pore surfaces. The governing partial differential equations for the transient process describe (a) the local equilibrium sorption-desorption and the diffusion of the pollutant in the porous aggregate, (b) the mass transfer of the pollutant from the external surface of the spherical aggregates to the reaction medium, and (c) the biodegradation of the pollutant in the external medium. Illustrative calculations are presented for a linear sorption calculations are presented for a linear sorption isotherm and first-order biodegradation kinetics. A dimensionless group, comprised of the diffusion coefficient, biodegradation rate coefficient, aggregate characteristics length (radius), and adsorption capacity, serves as a criterion for determining when intraparticle diffusion can be ignored. The model provides a realistic description of experimental data for biodegradation of a pollutant subject to intraparticle diffusion and sorption.