(Solved): Consider a tissue of thickness and mass diffusivity surrounded on both sides by fluids 1 an ...

Consider a tissue of thickness ? and mass diffusivity ???? surrounded on both sides by fluids 1 and 2. A species S is diffusing across this tissue and has concentrations ????1 ???? and ????2 ???? in the fluids on the two sides of the tissue. The solubility of species S inside the tissue is different from its solubility in the fluids. We therefore define partition coefficients: ?1F = ????1 ???? /????1 ???? and ?2???? = ????2 ???? /????2 ???? , where ????1 ???? and ????2 ???? are the concentrations of species S in the tissue at the interfaces 1 and 2, respectively.

Hence ?iF < 1 means that S is less soluble in the tissue than in fluid ????, and vice versa.

a) Solve the diffusion equation with appropriate boundary conditions to find the concentration of species S across the tissue at steady state

b) Write down an expression for the mass-transfer coefficient across the tissue in terms of ????1 ???? , ????2 ???? ,????, ?, and the partition coefficients.