Qualitative Differences Between the Semi-separable and the "Almansi-Type" Stokes Stream Function Expansions in the Study of Biological Fluids.

The creeping motion of a Newtonian fluid around particles simulating the relative motion of biological fluids such as blood plasma flow past red blood cells can be modeled through Stokes equations in spheroidal coordinates. By employing a stream function ψ, the irrotational and the rotational Stokes flow are described through a second- and a fourth-order elliptic-type partial differential equations: Eψ = 0 and Eψ = 0, respectively. Firstly, the complete set of the solution expansion has been obtained, in terms of particular combinations of Gegenbauer functions, in separable and semiseparable forms. Each of these terms, the so-called eigenflow, represents in a clearly and distinct way either rotational or irrotational type of flow. This information is of great value in the study of biofluids, as it may be correlated to characteristics observed in various diseases. Secondly, the Almansi-type solution is obtained as a kind of perturbation of the irrotational flow solution implying that no clear identification of the kind of flow is available. In the present manuscript, we demonstrate the advantages of the semiseparable form of solution and provide a reduction formula from the "Almansi-type" solution to the semiseparable one, indicating a way of revealing the hidden physical information.