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# A fermentation broth consists of a dilute aqueous solution of nutrients and cells. As the cells grow, they cluster into spherical pellets of radius...

A fermentation broth consists of a dilute aqueous solution ofnutrients 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 pelletvolume. The dissolved oxygen concentration in the broth is 5 μg/cm3 and can beassumed to be very dilute. The cells utilize oxygen at a rate of 1.2 mmol of oxygen perhour per gram of cell mass via a zero-order reaction (i.e., the reaction is independent ofthe 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 centerof the pellet? Assume that the broth external to the pellets is well mixed and that both thecells and the broth have bulk densities close to that of water. The diagram below showsthe simplified system of interest. Be sure to state all your assumptions when solving theproblem.