H2-mediated Electrosynthesis

The maximum concentration of H2 is set by the partial pressure of H2 in the gas and the solubility coefficient of H2 in water through Henry's law.  The thicker the film (for a given density), the more carbon fixing potential a square meter of reactor surface area will have, simplifying reactor construction, but the lower the H2 concentration gradient, slowing H2 transfer, and starving the carbon fixing enzymes in the microbes of electrons needed for carbon fixation. What is the optimal film thickness that  maximizes the electron transfer rate but contains the most carbon fixing cells?  The total carbon fixation ability and electron demand (and hence H2 demand) of an electrosynthetic microbe can be estimated by estimating the number of carbon fixing enzymes (RuBisCOs) that it can express, the catalytic rate of these enzymes, and the number of electrons needed to fix each carbon.  The electron demand rate for fuel synthesis per cell can be calculated as,