Mathematical Model of Fluid Flow and Solute Transport in ‎Converging-diverging Permeable Tubes

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Varunkumar M.; Muthu P.; Srinivas S.

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Journal Paper

Paper Information

Journal: JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS Year:2023 | Volume:9 | Issue:4 Page(s): 900-914

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Title

Mathematical Model of Fluid Flow and Solute Transport in ‎Converging-diverging Permeable Tubes

Author(s)

Varunkumar M. | Muthu P. | Srinivas S. | Issue Writer Certificate

Keywords

Glomerular capillary

Finite difference method

Ultrafiltration

Converging-diverging tubes

Permeable wall‎

Abstract

This article presents a mathematical model for fluid and solute transport in an ultra-filtered Glomerular capillary. Capillaries ‎are assumed to be Converging-diverging tubes with permeable boundaries. According to Starling's hypothesis, Ultrafiltration is ‎related to the variations in hydrostatic and osmotic pressures in the capillary and Bowman's space and takes place along the ‎length of the capillary. The governing equations of fluid flow for the case of axisymmetric motion of viscous incompressible ‎Newtonian fluid have been considered along with the solute transfer equation. The non-uniform geometry has been mapped ‎into a finite regular computational domain via a coordinate transformation. Correspondingly, the governing equations are ‎transformed to the computational space and solved to get the velocity and pressure values. The solute transfer equation is ‎also solved numerically using a finite difference scheme. The solutions provide the predictions of the axial distribution of ‎hydrostatic pressure and osmotic pressure, velocities, and concentration profiles at various points along the axis and solute ‎clearance quantities along the capillary. The current results are in good agreement with the earlier findings in limiting cases of ‎cylindrical tubes with a constant radius. It is found that there is a significant effect of osmotic pressure on the solute ‎concentration. Using a set of data, the influence of various physiological parameters on the velocity components and solute ‎concentration are presented and discussed through graphs to correlate with physiological situations. The generic structure of ‎the current model also provides an acceptable approach to exploring fluid exchange in organs apart from the glomerular ‎capillary.‎

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