A three-dimensional analysis of plasma skimming at microvascular bifurcations

This paper analyzes an important underlying mechanism for the discharge hematocrit reduction observed in microvessels, which refers to the plasma skimming from the cell-free layer near the parent tube wall in the presence of a side branch. The three-dimensional theory recently developed by the authors (Yan et al., 1991, J. Fluid Mech., in press) for treating the simple shear flow past a side branch tube in a plane wall with suction is first summarized and then extended to treat T bifurcations from parent vessels with an upstream Poiseuille flow. For unequal vessel bifurcations, a fundamental new dimensionless group, Q = 1/8(qb/qp)(Rp/Rb)3, is derived whose value determines the shape of the upstream capture tube of the plasma phase, when the partitioning qb/qp of the flow into the side branch and the ratio Rp/Rb of the radii of the parent and side branch vessels are varied. Closed form expressions are then presented for the three-dimensional fluid capture tube shape upstream of the bifurcation which are valid when Q greater than 1 or Q less than 0.2. Based on this theory and its modification for an upstream Poiseuille velocity profile, the separating surface shape, the critical minimum fractional flux for incipient cell capture, and the discharge hematocrit defect and its dependence on the flow rate are predicted. It is shown, furthermore, that for flows typical of the microcirculation, a single dimensionless number, P = 3 pi Q(Rb/gamma 2), with gamma being the cell-free layer thickness, can be defined whose value determines the discharge hematocrit defect that arises from plasma skimming. The minimum critical flow rate for any red cells to enter the side branch is then given by the criterion P = 1. Although this theory does not account for the cell screening effect arising from the hydrodynamic interaction between the cells and the tube walls, it leads to predictions which exhibit the same trends as the experimental observations and is able to explain the results of several seemingly contradictory microvascular experiments that have puzzled investigators in recent years.