A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall

A two-phase model for the flow of blood in narrow tubes is described. The model consists of a central core of suspended erythrocytes and a cell-free layer surrounding the core. It is assumed that the viscosity in the cell-free layer differs from that of plasma as a result of additional dissipation of energy near the wall caused by the red blood cell motion near the cell-free layer. A consistent system of nonlinear equations is solved numerically to estimate: (i) the effective dimensionless viscosity in the cell-free layer (β), (ii) thickness of the cell-free layer (1 - λ) and (iii) core hematocrit (H_c). We have taken the variation of apparent viscosity (μ_app) and tube hematocrit with the tube diameter (D) and the discharge hematocrit (H_D) from in vitro experimental studies [16]. The thickness of the cell-free layer computed from the model is found to be in agreement with the observations [3,21]. Sensitivity analysis has been carried out to study the behavior of the parameters 1 - λ, β, H_c, B (bluntness of the velocity profile) and μ_app with the variation of D and H_D.