Abstract
The interaction between osmotic inflow through the wall of a narrow tubule and bulk flow in the tubule is described. Solution are found by a finite difference method, and two approximate analytic solutions are given. Results given here enable more accurate estimates of osmotic permeability to be obtained for the tubule wall. The theory predicts the behaviour of unstirred layers as experimental parameters are varied and enables tubule experiments to be designed so as to reduce unwanted unstirred layer effects.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Aldis, G. K. 1982. “The Unstirred Layer in a Circular Tube.”Proc. Third Int. Conference on Mechanics in Medicine and Biology, Compiegne.
Aldis, G. K. 1983.Concentration Fields Near Transporting Epithelia. PhD thesis. University of Cambridge.
— 1988. “The Osmotic Permeability of a Tubule Wall.”Bull. math. Biol.,50, 547–558.
Andreoli, T. E., J. A. Schafer and S. L. Troutman. 1971. “Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes.”J. gen. Physiol.,57, 479–493.
Barry, P. H. 1981. “Unstirred Layers and Volume Flows Across Biological Membranes.” InWater Transport Across Epithelia, Alfred Benzon Symposium 15, Ussing, Bindslev, Lassen and Sten-Knudsen (Eds) Copenhangen: Munksgaard.
— and J. M. Diamond. 1984. “Effects of Unstirred Layers on Membrane Phenomena.”Physiol. Rev.,64, 763–872.
Batchelor, G. K. 1967.An Introduction to Fluid Mechanics. Cambridge: Cambridge University Press.
Dainty, J. 1963. “Water Relations in Plant Cells,”Adv. Bot. Res.,1, 279–326.
Diamond, J. M. 1979. “Osmotic Water Flow in Leaky Epithelia.”J. Membrane Biol.,51, 195–216.
Du Bois R., A. Verniory and M. Abramov. 1976. “Computation of the Osmotic Water Permeability of Perfused Tubule Segments.”Kidney Int.,10, 478–479.
Friedlander, S. K. and M. Walser. 1965. “Some Aspects of Flow and Diffusion in the Proximal Tubule of the Kidney.”J. theor. Biol. 8, 87–96.
House, C. R. 1974Water Transport in Cells and Tissues. London: Edward Arnold.
Lévêque, M. A. 1928. “Transmission de Chaleur par Convection.”Ann. des Mines 13, 201–362.
O'Donnell, M. J., G. K. Aldis and S. H. P. Maddrell. 1982. “Measurements of Osmotic Permeability in the Malpighian Tubules of an Insect,Rhodnius prolixus Stal.”Proc. R. Soc. B216, 267–277.
Pedley, T. J. 1980. “The Interaction Between Stirring and Osmosis. Part 1.”J. Fluid Mech.,101, 843–861.
— 1981. “The Interaction between Stirring and Osmosis. Part 2.”J. Fluid Mech.,107, 281–296.
— 1982. “Nature Convection Driven by Osmosis.”SIAM J. appl. Math.,42, 1202–1216.
— 1983. “Calculation of Unstirred Layer Thickness in Membrane Transport Experiments: a Survey.”Q. Rev. Biophysics,16, 115–150.
— and J. Fischbarg. 1978. “The Development of Osmotic Flow Through an Unstirred Layer.”J. theor. Biol.,70, 427–447.
— and —. 1980. “Unstirred Layer Effects in Osmotic Water Flow Across Gallbladder Epithelium.”J. memb. Biol.,54, 89–102.
Schafer, J. A., C. S. Patlak and T. E. Andreoli. 1974. “Osmosis in Cortical Collecting Tubules. A Theoretical and Experimental Analysis of the Osmotic Transient Phenomenon.”J. gen. Physiol.,64, 201–227.
Schultz, S. G. 1980.Basic Principles of Membrane Transport. Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aldis, G.K. The unstirred layer during osmotic flow into a tubule. Bltn Mathcal Biology 50, 531–545 (1988). https://doi.org/10.1007/BF02458851
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02458851