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A Numerical Study of the Hydrodynamic Stable Concentration Boundary Layers in a Membrane System Under Microgravitational Conditions

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Abstract

On the basis of the classic formula of the concentration Rayleigh number and the Kedem–Katchalsky equation for diffusive membrane transport, we derived the equations of sixteenth order which show the dependence of the thicknesses of the concentration boundary layers on the difference of the solution concentrations, the concentration Rayleigh number, the solute permeability coefficient of the membrane and the diffusion coefficients in the solution, the kinematic viscosity of the solution, the density of solutions, the temperature and gravitational acceleration. The obtained equation has numerical solutions in the first, third and fourth quadrant of a co-ordinate system. However, only two solutions from the first quadrant of the co-ordinate system have physical meaning. Confining ourselves to the set of solutions with physical meaning only, the thicknesses of concentration boundary layers for different parameters occurring in the obtained equation were calculated numerically.

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Authors and Affiliations

  1. Department of Biophysics, Częstochowa University of Technology, 19b Armia Krajowa Al., 42200, Częstochowa, Poland

    Andrzej Ślęzak & Arkadiusz Bryll

  2. Department of Biophysics, Silesia Medical University, 18 H. Jordan Str., 41808, Zabrze, Poland

    Sławomir Grzegorczyn

Authors
  1. Andrzej Ślęzak
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  2. Arkadiusz Bryll
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  3. Sławomir Grzegorczyn
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Correspondence to Arkadiusz Bryll.

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Ślęzak, A., Bryll, A. & Grzegorczyn, S. A Numerical Study of the Hydrodynamic Stable Concentration Boundary Layers in a Membrane System Under Microgravitational Conditions. J Biol Phys 32, 553–562 (2006). https://doi.org/10.1007/s10867-007-9037-0

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  • DOI: https://doi.org/10.1007/s10867-007-9037-0

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