Bulletin of Mathematical Biology

, Volume 36, Issue 4, pp 365–377 | Cite as

Passive transfer of low-molecular nonelectrolytes across deformable semipermeable membranes—I: Equations of convective-diffusion transfer of nonelectrolytes across deformable membranes of large curvature

  • L. I. Rubinstein


The passive transfer of a low-molecular nonelectrolytes mixture across a semipermeable deformable membrane of large curvature is considered. The equations obtained here make it possible to describe the concentration of species redistribution and the change of the membrane shape.


Rheological Model Middle Surface Passive Transfer Large Curvature Pure Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Fields, W. R. 1970. “Mechanical Properties of the FrogSarcolemma.”Biophys. J.,4, 303–316.Google Scholar
  2. Gage, P. W. and R. S. Eisenberg. 1969. “Capacitance of the Surface and Transverse Tubular Membrane of FrogSartorious Muscle Fibers.”J. Gen. Physiol.,53, 265–278.CrossRefGoogle Scholar
  3. Geiman, H. M. and L. I. Rubinstein. 1974. “Passive Transfer of Low-Molecular Non-electrolytes across Deformable Semipermeable Membranes. II: Dynamics of a Single Muscle Fiber Swelling and Shrinking and Related Changes of theT-System Tubule Form.”Bull. Math. Biology,36, 379–401.MATHCrossRefGoogle Scholar
  4. Grantham, J. L. 1970. “Vasopressin: Effect on Deformability of Urinary Surface of Collecting Duct Cells.”Science,29, 1093–1095.Google Scholar
  5. Haase, R. 1963.Thermodynamic der Irreversiblen Prozesse. Darmstadt.Google Scholar
  6. Hiramoto, Y. 1963. “Mechanical Properties of Sea Urchin Eggs. I: Surface Force and Elastic Modulus of the Cell Membrane.”Exp. Cell Res.,32, 59–75.CrossRefGoogle Scholar
  7. Huxley, R., S. Page and D. Wilkie. 1963. “An Electron Microscopic Study of Muscle Fibre in Hypertonic Solutions.”J. Physiol.,169 (2), 325–329.Google Scholar
  8. Katchalsky, A. and Peter F. Curran. 1967.Nonequilibrium Thermodynamics in Biophysics. Cambridge, Massachusetts: Harvard University Press.Google Scholar
  9. —, O. Kedem, C. Klebansky and A. de Vries. 1960.Rheological Considerations of the Haemolizing Red Blood Cells in Flow Properties of Blood and Other Biological Systems, Copley, A. L. and C. Stainsby, eds. New York: Pergamon Press.Google Scholar
  10. Kotchin, H. E., I. A. Kibel and N. B. Rose. 1948.Theoretical Hydrodynamics, Moscow-Leningrad: CTTI, Vol. II.Google Scholar
  11. Krolenko, S. A., S. Ja. Adamjan and N. E. Shwinka. 1967. “Vacuolization of Skeletal Muscle Fibers. I: Vacuolization after Efflux of Low-molecular Nonelectrolytes.”Tsitologia IX,11, 1346–1353.Google Scholar
  12. — 1969. “Changes in theT-System of Muscle Fibers Under the Influence of Influx and Efflux of Glycerol.”Nature,221, 969.CrossRefGoogle Scholar
  13. Mela, M. J. 1967. “Elastic-Mathematical Theory of Cells and Mitochondria in Swelling Process. I: The Membranous Stresses and Modulus of Elasticity of the Egg Cell of Sea Urchin,Strongylocentrotus purpuratus.”Biophys. J.,7 (1), 95–110.Google Scholar
  14. Prigogine, I. and R. Defay. 1954.Chemical Thermodynamics, London: Longman.Google Scholar
  15. Rand, R. P. 1964. “Mechanical Properties of the Red Cell Membrane. II: Viscoblastic Breakdown of the Membrane.”Biophys. J.,4, 303–316.CrossRefGoogle Scholar
  16. Rapoport, S., L. Peachey and D. Goldstein. 1969. “Swelling of the Transverse Tubular System in Frog Sartorious.“J. Gen. Physiol.,54, 166–177.CrossRefGoogle Scholar
  17. Rubinstein, L. I. and T. S. Friedman. 1971. “Diffusive Transfer of Nonelectrolytes Through Extendible Semipermeable Membranes.”Izvestia A.N. Latv. SSR; Ser. Phys. and Techn.,1971 (3), 87–94.Google Scholar

Copyright information

© Society for Mathematical Biology 1974

Authors and Affiliations

  • L. I. Rubinstein
    • 1
  1. 1.Computing CentreP. Stuchka Latvian State UniversityRigaUSSR

Personalised recommendations