Consider the drug treatment system shown below. A hemisphere cluster of unhealthy cells is surrounded by a larger hemisphere of stagnant dead dead tissue (species B), which is in turn surrounded by a flowing fluid. The bulk, wellmixed fluid contains a drug compound (species A) of constant but dilute concentration cAo. Drug A is also soluble in the unhealthy tissue but does not preferentially partition into it relative to the fluid. The drug (species A) enters the dead tissue and homes in on the unhealthy cells. At the unhealthy cell boundary (r ¼ R1) the flux of A to the unhealthy cells is diffusion limited. All metabolites of drug A produced by the unhealthy cells stay within the unhealthy cells. However, drug A can also degrade to inert metabolite D by the first-order reaction on cA, i.e., A→D, that occurs only within the stagnant dead tissue.
Simplify the general differential equation in terms for mass transfer for drug A. Specify the final differential equation in terms of NA and again in terms of cA. State all assumptions as necessary.
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