The Effect of Barodiffusion on the Distribution of Biological Fluid Velocity and Concentration During Filtration Through
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THE EFFECT OF BARODIFFUSION ON THE DISTRIBUTION OF BIOLOGICAL FLUID VELOCITY AND CONCENTRATION DURING FILTRATION THROUGH A CYLINDRICAL LAYER N. N. Nazarenko
UDC 532.5,54.03
A model of filtration of a biological fluid for a cylindrical layer in a stationary regime is presented. The model takes into consideration finite compressibility and concentration expansion associated with barodiffusion. Dimensionless complexes relating characteristic physical scales of different phenomena are singled out. The influence of the revealed effects on the flow characteristics are studied numerically. The flow can be either convective or diffusive, depending on the relation between the dimensionless complexes. New qualitative relationships are distinguished in the component concentration and flow velocity distributions. A significant influence of the thickness of the porous cylinder wall is shown. It is found out that barodiffusion has a significant effect on the flow in the convective mode and a small cylinder wall thickness. Keywords: filtration, diffusion, convective and diffusive flow regimes, barodiffusion.
INTRODUCTION In the study of numerous physical phenomena one has to consider the motion of fluids in porous media. There are a large number of natural media and bodies, such as soils, rocks, wood, leather, bones, soft tissues and many artificial materials: constructional materials (concrete, brick), foods (bread), ceramics, metal parts, etc. A characteristic feature of all these materials is their ability to accumulate fluid and provide its motion under the action of external forces. One of the most important aspects of life directly depends on the motion of fluids through porous media. In particular, fluid exchange in cells and tissues and other subtle motions control the transport of nutrients to cells and the removal of metabolism products from the organisms. Porosity is the most important quantitative characteristic of porous bodies, it is determined as the fraction of the body volume corresponding to the pores or the pore volume per unit material volume. The ability of a porous medium to allow passage of a fluid is characterized by its permeability. Its determination is closely related to the principal law of liquid motion referred to as the Darcy law. As an alternative to the Darcy, Forchheimer, etc. relations, the Brinkman equation is used for describing the fluid dynamics in porous media. It contains the permeability coefficient depending on the porous medium properties only and is mainly determined by the pore space geometry. A most complete review of the theoretical and experimental studies on convection in porous media is presented in [1]. In [2] there is a brief review of the equations of momentum, energy and mass conservation during fluid filtration in a porous medium. The expressions for calculating the particle, molecule and ion mobilities in different filtration processes in arbitrary porous media are also proposed. The available literature contains a sufficiently large number of works on the fluid transfer
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