20.06.2023

# Mathematical model of biological fluid flow through a cylindrical layer taking into account barodiffusion

Employees of the Laboratory of Nonlinear Mechanics of Metamaterials and Multilevel Systems and the Laboratory of Physics of Nanostructured Biocomposites of the Institute of Physics of Applied Mathematics SB RAS proposed a model of the flow of biological fluid in a steady state through a cylindrical layer, taking into account convection and diffusion.

This paper describes a model of fluid flow in a cylindrical porous layer taking into account finite compressibility and concentration expansion associated with both barodiffusion and an additional mechanism of pressure change in the pore volume due to the concentration gradient. An analysis of the features of convective and diffusion flow regimes was carried out. For a related problem, an iterative algorithm for numerical solution of the problem has been developed. The work shows that taking into account the mutual influence of various processes has a significant impact on the distribution of the speed and concentration of the transferred impurity over the thickness of the layer. The influence of model parameters on the distributions of velocity and concentration for a small thickness of a cylindrical layer is qualitatively similar to that considered in the case of a flat layer. Barodiffusion has the greatest effect in the convective mode and for a thin cylinder wall. In the diffusion mode, barodiffusion has virtually no effect on the filtration process.

This work is of interest when describing mass transfer processes in a porous body.

Distribution of velocity (a) and concentration (b) in a cylindrical layer as a result of liquid filtration taking into account diffusion and at different concentration expansion coefficients and different thicknesses of the porous layer; Solid lines - connected model; Symbols - disconnected model

The work was carried out within the framework of the state assignment of the Institute of Physical Problems and Problems of the Siberian Branch of the Russian Academy of Sciences (project FWRW-2021-0007). The results of the work were published in the journal Communications on Applied Mathematics and Computation (Q2 in the categories “Applied Mathematics”, “Computational Mathematics”, SJR).

Nazarenko, N.N., Knyazeva, A.G. **Mathematical Modeling of Biological Fluid Flow Through a Cylindrical Layer with Due Account for Barodiffusion**. Communications on Applied Mathematics and Computation. (2022).

https://doi.org/10.1007/s42967-022-00203-3< /a>