Abstract
In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect.
The model is solved numerically for the situation of a domain in two dimensions, consisting of two subdomains separated by a rigid fixed membrane.
The numerical results for different values of the material parameters and different computational settings are compared.
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References
T. Cheng: Flux analysis by modified osmotic-pressure model for laminar ultrafiltration of macromolecular solutions. Separation and Purification Technology 13 (1998), 1–8.
P. J. Coleman, D. Scott, R.M. Mason, J.R. Levick: Characterization of the effect of high molecular weight hyaluronan on trans-synovial flow in rabbit kness. The Journal of Physiology 514 (1999), 265–282.
J. Hron, C. Leroux, J. Malek, K. Rajagopal: Flows of incompressible fluids subject to Naviers slip on the boundary. Comput. Math. Appl. 56 (2008), 2128–2143.
O. Kedem, A. Katchalsky: Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochimica et Biophysica Acta 27 (1958), 229–246.
N. Kocherginsky: Mass transport and membrane separations: Universal description in terms of physicochemical potential and Einstein’s mobility. Chemical Engineering Science 65 (2010), 1474–1489.
M. Neuss-Radu, W. Jager: Effective transmission conditions for reaction-diffusion processes in domains separated by an interface. SIAM J. Math. Anal. 39 (2007), 687–720.
C. Patlak, D. Goldstein, J. Hoffman: The flow of solute and solvent across a two-membrane system. J. Theoretical Biology 5 (1963), 426–442.
K. Rajagopal, A. Wineman: The diffusion of a fluid through a highly elastic spherical membrane. Int. J. Eng. Sci. 21 (1983), 1171–1183.
D. Scott, P. Coleman, R. Mason, J. Levick: Concentration dependence of interstitial flow buffering by hyaluronan in sinovial joints. Microvasc. Research 59 (2000), 345–353.
L. Tao, J. Humphrey, K. Rajagopal: A mixture theory for heat-induced alterations in hydration and mechanical properties in soft tissues. Int. J. Eng. Sci. 39 (2001), 1535–1556.
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Dedicated to Professor K. R. Rajagopal on the occasion of his 60th birthday
This work was partly done during the visit of P. Pustějovska at the Interdisciplinary Center for Scientific Computing (IWR) in July 2010, in the frame of the PhD exchange program of the Heidelberg Graduate School MathComp. P. Pustějovska was also supported by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling) financed by MŠMT, by GAČR grant no. 201/09/0917 and grant SVV-2010-261316. J. Hron was supported by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling) financed by MŠMT.
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Hron, J., Neuss-Radu, M. & Pustějovská, P. Mathematical modeling and simulation of flow in domains separated by leaky semipermeable membrane including osmotic effect. Appl Math 56, 51–68 (2011). https://doi.org/10.1007/s10492-011-0009-0
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DOI: https://doi.org/10.1007/s10492-011-0009-0