A critical parameter in the design of bioreactors is the maximum shear

stress experienced by cells while in the reactor. If the shear stress is too high, the cells

will be torn apart or lysed. An example of a common biomedical device in which the

shear stress must be controlled is a blood oxygenator used clinically for heart$/$lung bypass

operations. Hemolysis can occur if red blood cells adhere to the wall of the device and

are subjected to high shear stresses.

Consider a blood oxygenator in which steady laminar flow of blood is directed through a

parallel membrane separated by a distance of $d.$ What is the shear stress at the membrane

surface in terms of the average flow velocity, V$.$ Assume that the blood is a Newtonian

fluid with viscosity $$ and that the semi$-$permeable membranes can be modeled as infinite

planes. The geometry is depicted below: