A modeling study of the effect of pH on carbon limited algal biofilms

A model was developed that describes concentration profiles and flux of carbon into inorganic carbon-limited algal biofilms. The model considers carbon dioxide utilization and production from photosynthesis and respiration, diffusion of the inorganic carbon species, and pH changes due to CO 2 utilization. The overall material balance gave a nonlinear ordinary differential equation coupled with an integral differential equation. This system was solved using a Runge-Kutta-Verner fifth and sixth order method. The bulk (interfacial) total carbon and pH were assumed fixed. The boundary value problem was solved with a shooting technique, where the interfacial slope was initially guessed and subsequently adjusted using the secant method. The results showed that bulk carbon concentration and bulk pH were both important aspects of inorganic carbon limitation. Parameter sensitivity was also addressed; model parameters that were found to be important to the results include diffusion coefficients, maximum utilization rate, half-saturation coefficient, and biofilm density. Results were found to be insensitive to the respiration coefficient.