On slip of a viscous fluid through proximal renal tubule with linear reabsorption

Abdul M. Siddiqui; Getinet A. Gawo; Khadija Maqbool; Abdul M. Siddiqui; Getinet A. Gawo; Khadija Maqbool

doi:10.3934/biophy.2021006

AIMS Biophysics

2021, Volume 8, Issue 1: 80-102. doi: 10.3934/biophy.2021006

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On slip of a viscous fluid through proximal renal tubule with linear reabsorption

1.
Pennsylvania State University, 1031 Edgecomb Ave, York, PA 17403, USA
2.
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

Received: 05 November 2020 Accepted: 20 December 2020 Published: 05 January 2021

The hydrodynamical problem of flow in proximal renal tubule is investigated. Axisymmetric flow of viscous, incompressible fluid through the proximal renal tubule that undergoes linear reabsorption with slip at the wall is considered. The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions for velocity components, pressure distribution, fractional reabsorption and the shear stress are found. The effect of slip parameter and reabsorption rate on the flow have been investigated. The points of extreme values for the axial and radial velocity components are identified. The solution is applied to physiological data from human and rat kidney, and the results are presented in tables and graphs.
- proximal tubule,
- linear reabsorption,
- slip boundary,
- fractional reabsorption,
- flow rate
Citation: Abdul M. Siddiqui, Getinet A. Gawo, Khadija Maqbool. On slip of a viscous fluid through proximal renal tubule with linear reabsorption[J]. AIMS Biophysics, 2021, 8(1): 80-102. doi: 10.3934/biophy.2021006

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Abstract

The hydrodynamical problem of flow in proximal renal tubule is investigated. Axisymmetric flow of viscous, incompressible fluid through the proximal renal tubule that undergoes linear reabsorption with slip at the wall is considered. The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions for velocity components, pressure distribution, fractional reabsorption and the shear stress are found. The effect of slip parameter and reabsorption rate on the flow have been investigated. The points of extreme values for the axial and radial velocity components are identified. The solution is applied to physiological data from human and rat kidney, and the results are presented in tables and graphs.

Acknowledgments

Getinet Gawo would like to thank Pennsylvania State University, York Campus for the financial support provided for this work through York Campus Advisory Board Scholarly Activity Grant.

Conflict of interest

All authors have no conflict of interest.

Authors contribution

A.M Siddiqui provided the formulation of the problem, defining governing equations and boundary conditions and supervised whole paper. G. Gawo solved the governing equations and results are compared with previous works, and results are also implemented on rat kidney data. K.Maqbool revised the literature review, implemented the result on human kidney and draft the result and handled the paper submission process.

References

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