Skip to main content
SpringerLink
Log in

Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Creeping flow of a Newtonian fluid through a rigid permeable tube is considered and the transmural seepage is assumed to obey Darcy's law. Closed-form solutions for the pressure and velocity fields are presented and equations describing the axial variation of the mean cross-sectional pressure, the axial volumetric flow and the transmural fluid flux are derived. Approximate solutions for small seepage rates are given and are applied to the flow in the proximal renal tubule. Probable values for the epithelium permeability and the intraluminal hydrostatic pressure drop are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Allison, M. E. M., E. M. Lipham and C. W. Gottschalk. 1972. “Hydrostatic Pressure in the Rat Kidney.”Am. J. Physiol. 223, 975–983.

    Google Scholar 

  • Darcy, H. 1856.Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmint.

    Google Scholar 

  • Deen, W. M., C. R. Robertson and B. M. Brenner. 1972. “A Model of Glomerular Ultrafiltration in the Rat”.Am. J. Physiol. 223, 1178–1183.

    Google Scholar 

  • —— and. 1973. “A Model of Peritubular Capillary Control of Isotonic Fluid Reabsorption by the Renal Proximal Tubule”.Biophysical J. 13, 340–356.

    Article  Google Scholar 

  • Friedlander, S. K. and MacKenzie Walser. 1965. “Some Aspects of Flow and Diffusion in the Proximal Tubule of the Kidney”.J. Theor. Biology,8, 87–96.

    Article  Google Scholar 

  • Giebisch, G., R. M. Klose, G. Malnic, W. T. Sullivan and E. E. Windhager. 1964. “Sodium Movement across Single Perfused Tubules of Rat Kidneys”.J. gen. Physiol.,47, 1175–1194.

    Article  Google Scholar 

  • Gottschalk, C. W. and M. Mylle. 1956. “Micropuncture Study of Pressure in the Proximal Tubule and Peritubular Capillaries of the Rat Kidney and their Relation to Ureteral and Renal Venous Pressures”Am. J. Physiol. 185, 430–439.

    Google Scholar 

  • — 1961. “Micropuncture Studies of Tubular Function in the Mammalian Kidney”.Physiologist, Wash.,4, 35–55.

    Google Scholar 

  • —. 1962. “Renal Tubular Function: Lessons from Micropuncture”.Harvey Lect.,58, 99–124.

    Google Scholar 

  • Happel, J. and H. Brenner. 1965.Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media. New Jersey: Prentice-Hall.

    MATH  Google Scholar 

  • Kelman, R. B. 1962. “A Theoretical Note on Exponential Flow in the Proximal Part of the Mammalian Nephron.”.Bull. Math. Biophysics,24, 303–317.

    Google Scholar 

  • Kozinski, A. A., F. P. Schmidt and E.W. Lightfoot. 1970. “Velocity Profiles in Porouswalled Ducts”.Ind. Eng. Chem. Fundam. 9, 502–505.

    Article  Google Scholar 

  • Landis, E. M. and J. R. Pappenheimer. 1963. “Exchange of Substances through Capillary Walls”. InHandbook of Physiology—Circulation. Washington: American Physiological Society, Vol. II, pp. 961–1034.

    Google Scholar 

  • Lassiter, W. E., C. W. Gottschalk and M. Mylle. 1961. “Micropuncture Study of Net Transtubular Movement of Water and Urea in Non-Diuretic Mammalian Kidney”.Am. J. Physiol.,200, 1139–1147.

    Google Scholar 

  • Ludwig, C. F. W.. 1858–1861.Lehrbuch der Physiologie des Menschen. Leipzig: Winter, Vol. 2, p. 562.

    Google Scholar 

  • Macey, R. I. 1963. “Pressure Flow Patterns in a Cylinder with Reabsorbing Walls”.Bull. Math. Biophysics,25, 1–9.

    Google Scholar 

  • — 1965. “Hydrodynamics in the Renal Tubule”.,2, 117–124

    Google Scholar 

  • Makiya, K. K., W. L. Conger and C. E. Hamrin, Jr. 1972. “Capillary Mass Transfer”.A.I.Ch.E. Journal,18, 861–864.

    Google Scholar 

  • Malnic, G., R. M. Klose and G. Giebisch. 1966. “Micropuncture Study of Distal Tubular Potassium and Sodium Transport in Rat Nephron.Am. J. Physiol.,211, 529–547.

    Google Scholar 

  • Marshall, E. A. and E. A. Trowbridge. 1974. “A Model for the Ultra-Filtration Process in a Single Glomerular Capillary”.J. Theor. Biology, in press.

  • Pitts, R. F. 1963.Physiology of the Kidney and Body Fluids. Chicago: Year Book Medical Publishers.

    Google Scholar 

  • Streeter, V. L. (ed.). 1961.Handbook of Fluid Dynamics. New York: McGraw-Hill.

    Google Scholar 

  • Ullrich, K. J., B. Schmidt-Nielson, R. O'Dell, G. Pehling, C. W. Gottschalk, W. E. Lassiter and M. Mylle. 1963. “Micropuncture Study of Composition of Proximal and Distal Tubular Fluid in Rat Kidney”Am. J. Physiol.,204, 527–531.

    Google Scholar 

  • Windhager, E. E. 1968.Micropuncture Techniques and Nephron Function. New York: Appleton-Century-Crofts.

    Google Scholar 

  • Yuan, S. W. and A. B. Finkelstein. 1956. “Laminar Pipe Flow with Injection and Suction through a Porous Wall”.Trans. Amer. Soc. Mech. Engrs. 78, 719.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computing Science, University of Sheffield, England

    E. A. Marshall & E. A. Trowbridge

Authors
  1. E. A. Marshall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Trowbridge
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marshall, E.A., Trowbridge, E.A. Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule. Bltn Mathcal Biology 36, 457–476 (1974). https://doi.org/10.1007/BF02463260

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02463260

Keywords

Search

Navigation