Studying the blood plasma flow past a red blood cell, with the mathematical method of Kelvin´s transformation

A mathematical tool, namely the Kelvin transformation, has been employed in order to derive analytical expressions for important hydrodynamic quantities, aiming to the understanding and the study of the blood plasma flow past a Red Blood Cell (RBC). These quantities are the fluid velocity, the drag force exerted on the cell and the drag coefficient. They are obtained by employing the stream function ψ which describes the Stokes flow past a fixed cell. The RBC, being a biconcave disk, has been modelled as an inverted prolate spheroid. The stream function is given as a series expansion in terms of Gegenbauer functions, which converge fast. Therefore the first term of the series suffices for the derivation of simple and ready to use expressions.