A fermentation broth consists of a dilute aqueous solution of nutrients and cells. As the cells grow, they cluster into spherical pellets of radius R(t). On average, the cell density inside a pellet is 0.02 mg of cell mass per mm3 of pellet volume. The dissolved oxygen concentration in the broth is 5 μg/cm3 and can be assumed to be very dilute. The cells utilize oxygen at a rate of 1.2 mmol of oxygen per hour per gram of cell mass via a zero-order reaction (i.e., the reaction is independent of
the oxygen concentration).

Assumes that the diffusion coefficient DAB of oxygen within the pellet is 1.8 x 10-5 cm2/s. How large can R(t) become before the oxygen concentration becomes zero at the center of the pellet? Assume that the broth external to the pellets is well mixed and that both the cells and the broth have bulk densities close to that of water. The diagram below shows the simplified system of interest. Be sure to state all your assumptions when solving the problem.