A Numerical Study of the Hydrodynamic Stable Concentration Boundary Layers in a Membrane System Under Microgravitational Conditions |
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Authors: | Andrzej Ślęzak Arkadiusz Bryll Sławomir Grzegorczyn |
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Institution: | (1) Department of Biophysics, Częstochowa University of Technology, 19b Armia Krajowa Al., 42200 Częstochowa, Poland;(2) Department of Biophysics, Silesia Medical University, 18 H. Jordan Str., 41808 Zabrze, Poland |
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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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Keywords: | Membrane transport Concentration boundary layers Concentration Rayleigh number |
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