A continuum theory of blood cells filtration at low flow rates

Blood cells filtration with decreasing pressure under gravity was studied for evaluation of the cell fluidity or deformability at a low shear state. A continuum approach was made to the flow and pressure in the filter at the low flow state to relate macro- and micro-scopic quantities. The mass conservation law of each species provided a set of differential equations with respect to the pore fraction and filter resistance. The numerical calculation was made for various values of hematocrit and leukocrit. It was shown that the filter resistance might be increased with decreasing pressure, resulting from both red and white cells. The leukocrit, more than 0.05% white cells, may influence the filtration, depending upon the cell deformation. Even in the absence of the white cell, a decrease in pressure increased the filter resistance markedly. The present result indicates that single red cell shows a nonlinear behavior of flow in pores at the low pressure level.