1. Under suitable circumstances the rate of oxygen metabolism by bacterial cells is very nearly zero order with respect to oxygen concentration. We examine such a case here and focus our attention on a spherical aggregate of cells, which has a radius R. We wish to determine the total rate of oxygen uptake by the aggregate as a function of aggregate size, oxygen mass concentration 0 at the aggregate surface, the metabolic activity of the cells, and the diffusional behavior of the oxygen. For simplicity we consider the aggregate to be homogeneous. We then approximate the metabolic rate by an effective volumetric reaction rate rO2=k0 and the diffusional behavior by Fick's law, with an effective pseudo-binary diffusivity DO2M. Because the solubility of oxygen is very low in this system, both convective oxygen transport and transient effects may be neglected. (a) Show by means of a shell mass balance that the quasi-steady-state oxygen concentration profile is described by the differential equation. 21dd(2dd)=N where =0O2,=r/R, and N=k0R2/0DO2M (b) There may be an oxygen-free core in the aggregate, if N is sufficiently large, such that =0 for