Effect of slip on the rheology of a composite fluid: application to blood

The laminar flow in a rigid tube of a fluid system composed of very thin, coaxial shells of distinct viscous fluids is studied theoretically. The study waives the usual boundary condition of fluid dynamics of zero slip at the boundary. Rather, a finite slip at the wall is allowed and retained in the discussions as a flow parameter, by hypothesis a function of shear stress at the wall, the fluid in contact and the nature of the surface. Slips are also allowed at all fluid interfaces, but assumed negligible as a first approximation after general flow relations are developed. Slip at the wall is assumed small in comparison with flow velocity to simplify computations. As an application to blood, a two phase particular case of the general fluid system, formed by plasma and red cells in alternate shells, is studied for the following properties: velocity distribution, discharge rate, “apparent” viscosity, dependence of the latter on tube radius, pressure rate and hematocrit. These properties are found to be in agreement with known experimental facts about blood flow. The two phase system exhibits a migration of the red cells toward the tube axis for the small slip-to-velocity ratios considered; the system again parallels blood in its generally acknowledged phenomenon of “axial drift”.

Slip appears as a significant element in the interpretation of certain properties of blood flow.