A one-dimensional model has been developed for diffusion transport in a binary liquid solution with a moving semipermeable boundary. The governing equations are basically Fick’s First and Second Laws in which the solute concentrations are replaced by the logarithms of the solute volume fractions. In the limit of negligible solute volume fraction, the analysis reduces to the classical one-dimensional diffusion equation. The complete form has been employed to describe the concentration polarization of solutes within human erythrocytes during freezing. The results show that the water transport process across the cell membrane is significantly affected by both the water permeation characteristics of the membrane and the diffusion of water within the intracellular medium. These results are consistent with experimental observations of red cell survival during freezing.
Diffusion Transport in a Liquid Solution With a Moving, Semipermeable Boundary
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Levin, R. L., Cravalho, E. G., and Huggins, C. E. (May 1, 1977). "Diffusion Transport in a Liquid Solution With a Moving, Semipermeable Boundary." ASME. J. Heat Transfer. May 1977; 99(2): 322–329. https://doi.org/10.1115/1.3450688
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