Consider a cylindrical fiber membrane dialyzer (B) of length L which transfers solute molecules (A) by diffusion from concentrated solution (CA1) to a dilute solution. This phenomenon is used to remove solutes from liquid mixtures in the biomedical, biotechnology, and chemical industries. These kinds of membranes can be used to manufacture artificial kidneys that can replace the function of human kidneys. a) Assuming the concentration at the exterior side of the membrane (point 2) is equal to CA2, write a shell balance for steady state conditions in the absence of any reaction. Use the boundary conditions to find an expression for the rate of diffusion when A. b) Now, assume a convective mass transfer coefficient outside the membrane for the very dilute solution is kc. Using the result of part (a), find an expression that would allow you to calculate the diffusion coefficient for A in the membrane assuming you knew the numeric values of kc, CA1, Caz, R1, and R2. (You will need to assume a value for CA.bulkfluid, far from the surface). In other words, this is a series resistance problem. (Assume the equilibrium distribution coefficients are equal to one for the entire system) Consider a cylindrical fiber membrane dialyzer (B) of length L which transfers solute molecules (A) by diffusion from concentrated solution (CA1) to a dilute solution. This phenomenon is used to remove solutes from liquid mixtures in the biomedical, biotechnology, and chemical industries. These kinds of membranes can be used to manufacture artificial kidneys that can replace the function of human kidneys. a) Assuming the concentration at the exterior side of the membrane (point 2) is equal to CA2, write a shell balance for steady state conditions in the absence of any reaction. Use the boundary conditions to find an expression for the rate of diffusion when A. b) Now, assume a convective mass transfer coefficient outside the membrane for the very dilute solution is kc. Using the result of part (a), find an expression that would allow you to calculate the diffusion coefficient for A in the membrane assuming you knew the numeric values of kc, CA1, Caz, R1, and R2. (You will need to assume a value for CA.bulkfluid, far from the surface). In other words, this is a series resistance problem. (Assume the equilibrium distribution coefficients are equal to one for the entire system)