Blood plasma flow past a red blood cell: Mathematical modelling and analytical treatment

摘要

A detailed mathematical analysis of Stokes flow past a rigid biconcave disc shape, motivated by the flow of blood plasma past a fixed red blood cell (RBC) is developed in the present manuscript. The main objective is to provide a new insight in the theoretical investigation of the flow behaviour of RBCs in pathological situations for which the rheological characteristics of the RBCs change or in medical tests like the erythrocyte sedimentation rate. Here, the RBC is described mathematically by an inverted prolate spheroid having its axis of symmetry along the direction of a uniform flow. The method of Kelvin transformation for Stokes flows and the concept of semiseparable spectral decomposition of Stokes flows in spheroidal geometry are employed to obtain an analytical solution. More specifically, by employing Kelvin's inversion, the exterior boundary value problem in the inverse prolate spheroidal system is mapped to a related problem in the interior of the corresponding prolate spheroid. The obtained interior solution is then mapped back to the original domain, under the Kelvin inversion. This procedure leads to a series solution in terms of Gegenbauer functions, which converge fast. Sample streamlines for various values of the geometrical parameters are depicted allowing a better understanding of the flow close to the RBC.