The effect of porosity on the catalytic performance of constant-mass, spherical beads containing immobilized enzyme

The mass balances to a spherical bead with increasing porosity, ε (obtained by plain expansion of an otherwise compact bead), containing an immobilized enzyme and surrounded by a stagnant film are developed in dimensionless form for the case of Michaelis-Menten kinetics by considering three alternative situations in terms of pore structure (either setting the pore number, the pore radius or the pore length as a constant). The pore pattern of the porous bead does not play a major role in the variation of the lowest concentration of substrate ever reached in the bulk of the bead, which increases as e increases and eventually levels off when ε approaches unity. The ratio between the rate of reaction brought about by the immobilized enzyme within the porous bead and that obtained for a compact bead is greater when ε is higher, and a vertical asymptote is apparently reached when the porosity approaches unity, a trend that is similarly observed for all pore patterns considered.