Mathematical Modeling of Biological Fluid Flow Through a Cylindrical Layer with Due Account for Barodiffusion

Abstract

The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion. The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient. Thus, the model is entirely coupled. The paper highlights the complexes composed of scales of physical quantities of different natures. The iteration algorithm for the numerical solution of the problem was developed for the coupled problem. The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive, depending on the relation between the dimensionless complexes. It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different. It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.

Funding

Siberian Branch, Russian Academy of Sciences(FWRW-2021-0007)