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Calculation of unstirred layer thickness in membrane transport experiments: a survey

Published online by Cambridge University Press:  17 March 2009

T. J. Pedley
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Extract

It has long been recognized that measurements of the permeability characteristics of membranes (and of epithelia) may be strongly influenced by the presence of unstirred, or diffusion, layers adjacent to the membranes: see Dainty (1963) for the first systematic discussion of the subject in a biological context and Barry & Diamond (1983) for an important recent review. Consider a homogeneous, plane, uncharged membrane separating two solutions of the same solute at different bulk concentrations Cb+ and Cb- (Fig. 1), but at the same hydrostatic pressure and electrostatic potential (note that in this paper subscripts + and − refer to the two sides of the membrane, not to cation and anion parameters; electroneutrality is assumed throughout).

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 16 , Issue 2 , May 1983 , pp. 115 - 150
Copyright
Copyright © Cambridge University Press 1983

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References

REFERENCES

Barry, P. H. (1981). Unstirred layers and volume flows across biological membranes. In Water Transport across Epithelia (ed. by Ussing, H. H., Bindslev, N., Lassen, N. A. and Sten-Knudsen, O.), Alfred Benzon Symposium no. 15, pp. 132–153. Copenhagen: Munksgaard.Google Scholar
Barry, P. H. & Diamond, J. M. (1983). Effects of unstirred layers on membrane phenomena: everything that you resisted believing but now need to know. Submitted to Physiological Reviews.Google Scholar
Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.Google Scholar
Crank, J. (1956). The Mathematics of Diffusion. Oxford: Clarendon Press.Google Scholar
Dainty, J. (1963). Water relations in plant cells. Adv. bot. Res. 1, 279–326.CrossRefGoogle Scholar
Dainty, J. & House, C. R. (1966). ‘Unstirred layers’ in frog skin. J. Physiol., Land. 182, 66–78.CrossRefGoogle ScholarPubMed
Diamond, J. M. (1979). Osmotic water flow in leaky epithelia. J. Membrane Biol. 51, 195–216.CrossRefGoogle ScholarPubMed
Everitt, C. T. & Haydon, D. A. (1969). Influence of diffusion layers during osmotic flow across bimolecular lipid membranes. J. theor. Biol. 22, 9–19.CrossRefGoogle ScholarPubMed
Everitt, C. T., Redwood, W. R. & Haydon, D. A. (1969). Problem of boundary layers in the exchange diffusion of water across bimolecular lipid membranes. J. theor. Biol. 22, 20–32.CrossRefGoogle ScholarPubMed
Fischbarg, J. & Montoreano, R. (1982). Osmotic permeabilities across corneal endothelium and ADH-stimulated toad urinary bladder structures. Biochim. biophys. Acta 690, 207–214.CrossRefGoogle Scholar
Foster, T. D. (1965). Stability of a homogeneous fluid cooled from above. Physics Fluids 8, 1249–1257.CrossRefGoogle Scholar
Gill, W. N., Tien, C. & Zeh, D. W. (1966). Analysis of continuous reverse osmosis systems for desalination. Int. J. Heat Mass Transfer 9, 907–923.CrossRefGoogle Scholar
Green, K. & Otori, T. (1970). Direct measurements of membrane unstirred layers. J. Physiol, Land. 207, 93–102.CrossRefGoogle ScholarPubMed
Hendricks, T. J., Macquin, J. F. & Williams, F. A. (1972). Observations on buoyant convection in reverse osmosis. Ind. Engng Chem. Fund. 11, 276–279.CrossRefGoogle Scholar
House, C. R. (1974). Water Transport in Cells and Tissues. London: Arnold.Google Scholar
Johnson, A. R. & Acrivos, A. (1969). Concentration polarization in reverse osmosis under natural convection. Ind. Engng Chem. Fund. 8, 359–361.CrossRefGoogle Scholar
Kozinski, A. A. & Lightfoot, E. N. (1971). Ultrafiltration of proteins in stagnation flow. A. I. Ch. E. J. 17, 81–85.CrossRefGoogle Scholar
Krishnamurti, R. (1970). On the transition to turbulent convection. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.CrossRefGoogle Scholar
Lerche, D. (1976). Temporal and local concentration changes in diffusion layers at cellulose membranes due to concentration differences between the solutions on both sides of the membrane, J. Membrane Biol. 27, 193–205.CrossRefGoogle ScholarPubMed
Lévêque, M. A. (1928). Transmission de chaleur par convection. Annls Mines 13, 201–362.Google Scholar
Levich, V. G. (1944). The theory of concentration polarization [in Russian]. Zhur. fiz. Khim. 18, 335–355.Google Scholar
Levich, V. G. (1962). Physicochemical Hydrodynamics. Englewood Cliffs, N. J.: Prentice Hall.Google Scholar
O'Donnell, M. F., Alois, G. K. & Maddrell, S. H. P. (1982). Measurements of osmotic permeability in the Malpighian tubule of an insect, Rhodnius prolixus Stal. Proc. R. Soc. Land. B 216, 267–277.Google Scholar
Pedley, T. J. (1980). The interaction between stirring and osmosis: Part 1. J. Fluid Mech. 101, 843–861.CrossRefGoogle Scholar
Pedley, T. J. (1981). The interaction between stirring and osmosis: Part 2. J. Fluid Mech. 107, 281–296.CrossRefGoogle Scholar
Pedley, T. J. (1982). Natural convection driven by osmosis. SIAM J. appl. Math. 42, 1202–1216.CrossRefGoogle Scholar
Pedley, T. J. (1983). The decay of osmosis in an unstirred chamber. (MS in preparation.)Google Scholar
Pedley, T. J. & Fischbarg, J. (1978). The development of osmotic flow through an unstirred layer. J. theor. Biol. 70, 426–446.CrossRefGoogle ScholarPubMed
Pedley, T. J. & Fischbarg, J. (1980). Unstirred layer effects in osmotic water flow across gallbladder epithelium. J. Membrane Biol. 54, 89–102.CrossRefGoogle ScholarPubMed
Rich, G. T., Sha'afi, R. I., Barton, T. C. & Solomon, A. K. (1967). Permeability studies on red cell membranes of dog, cat and beef. J. gen. Physiol. 50, 2391–2405.CrossRefGoogle Scholar
Rogers, M. H. & Lance, G. N. (1960). The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disc. J. Fluid Mech. 7, 617–631.CrossRefGoogle Scholar
Schafer, J. A., Patlak, C. S. & Andreoli, T. E. (1974). Osmosis in cortical collecting tubules. J. gen. Physiol. 64, 201–227.CrossRefGoogle ScholarPubMed
Schlichting, H. (1968). Boundary-layer Theory, 6th ed.New York: McGraw-Hill.Google Scholar
Smith, K. A. & Colton, C. K. (1972). Mass transfer to a rotating fluid. I. Transport from a stationary disk to a fluid in Bodewadt flow. A. I. Ch. E. J. 18, 949–966.CrossRefGoogle Scholar
Smulders, A. P. & Wright, E. M. (1971). The magnitude of non-electrolyte selectivity in the gall-bladder epithelium. J. Membrane Biol. 5, 297–318.CrossRefGoogle Scholar
Tomlan, P. F. & Hudson, J. L. (1971). Flow near an enclosed rotating disk: analysis. Chem. Eng. Sci. 26, 1591–1600.CrossRefGoogle Scholar
Ullrich, K. J., Rumrich, G. & Fuchs, G. (1964). Wasser permeabilität und transtubulärer Wasserfluss corticaler Nephronabschnitte bei verschiedenen Diuresezustanden. Pflügers Arch. ges. Physiol. 280, 99–119.CrossRefGoogle Scholar
Van Os, C. H., Wiedner, G. & Wright, E. M. (1979). Volume flows across gallbladder epithelium induced by small hydrostatic and osmotic gradients. J. Membrane Biol. 49, 1–20.CrossRefGoogle ScholarPubMed
Westergaard, H. & Dietschy, J. M. (1974). Delineation of the dimensions and permeability characteristics of the two major diffusion barriers to passive mucosal uptake in the rabbit intestine. J. clin. Invest. 54, 718–732.CrossRefGoogle ScholarPubMed