Assume blood flow down a long tube may be thought of as the flow of two immiscible fluids, one in the core of the tube (modeled as normal whole blood) and the other as a cell-free layer near the wall (modeled as plasma). Assume the cell-free layer has a thickness x, the tube has a radius R, the blood viscosity is u_b and the plasma viscosity is u_p. For the steady uniform flow of a Newtonian fluid in a long straight tube, what do the Navier-Stokes equations in cylindrical coordinates reduce to? Derive expressions for the velocity in the plasma layer and the core region. These expressions should be functions of deltaP/deltax (assume this to be a constant), R, x, u_b, u_p and r.
In this problem, both fluids behave like Newtonian fluids. Therefore, it can be state that:
d(Vb)/dr = -1/Mb *r ( considering the origin the longitudinal
Full solution where both fluids behave like Newtonian fluids, and it is stated that d(Vb)/dr = -1/Mb *r (considering the origin the longitudinal axe of the conduction). 100 words.