The effect of osmotic pressure on the flow of solutions through semi-permeable hollow fibers

We study the laminar flow of binary liquid mixture, whose components are a Newtonian fluid (solvent) and a solute, in a hollow fiber. The fiber walls are porous, but the pores size is small enough preventing the solute molecules to be transported across the membrane. This produces an osmotic pressure that offers resistance (in many cases non negligible) to the fluid cross flow.