A semi-permeable membrane separates Regions A and B of a microchannel. At time t=0, a dilute mixture of water and a solute flows into the bottom channel and thereafter maintains the concentration in Region B constant with a value of Co . The membrane allows the dissolved species to diffuse into Region A but the fluid remains at rest. The solute has a diffusivity of D. Derive an expression for time as a function of distance from the membrane for the concentration of the solute in Region A to reach a value of 5% of Co . Hint: You can treat the problem as a semi-infinite with a similarity solution.