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Keywords:
leaky semipermeable membrane; osmotic pressure; transmission conditions; finite element method
leaky semipermeable membrane; osmotic pressure; transmission conditions; finite element method
Summary:
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.
References:
[1] Cheng, T.: Flux analysis by modified osmotic-pressure model for laminar ultrafiltration of macromolecular solutions. Separation and Purification Technology 13 (1998), 1-8. DOI 10.1016/S1383-5866(97)00051-8
[2] Coleman, P. J., Scott, D., Mason, R. M., Levick, J. R.: Characterization of the effect of high molecular weight hyaluronan on trans-synovial flow in rabbit kness. The Journal of Physiology 514 (1999), 265-282. DOI 10.1111/j.1469-7793.1999.265af.x
[3] Hron, J., Leroux, C., Málek, J., Rajagopal, K.: Flows of incompressible fluids subject to Naviers slip on the boundary. Comput. Math. Appl. 56 (2008), 2128-2143. DOI 10.1016/j.camwa.2008.03.058 | MR 2466718
[4] Kedem, O., Katchalsky, A.: Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochimica et Biophysica Acta 27 (1958), 229-246. DOI 10.1016/0006-3002(58)90330-5
[5] Kocherginsky, N.: Mass transport and membrane separations: Universal description in terms of physicochemical potential and Einstein's mobility. Chemical Engineering Science 65 (2010), 1474-1489. DOI 10.1016/j.ces.2009.10.024
[6] Neuss-Radu, M., Jäger, W.: Effective transmission conditions for reaction-diffusion processes in domains separated by an interface. SIAM J. Math. Anal. 39 (2007), 687-720. DOI 10.1137/060665452 | MR 2349863 | Zbl 1145.35017
[7] Patlak, C., Goldstein, D., Hoffman, J.: The flow of solute and solvent across a two-membrane system. J. Theoretical Biology 5 (1963), 426-442. DOI 10.1016/0022-5193(63)90088-2
[8] Rajagopal, K., Wineman, A.: The diffusion of a fluid through a highly elastic spherical membrane. Int. J. Eng. Sci. 21 (1983), 1171-1183. DOI 10.1016/0020-7225(83)90081-2 | Zbl 0538.76091
[9] Scott, D., Coleman, P., Mason, R., Levick, J.: Concentration dependence of interstitial flow buffering by hyaluronan in sinovial joints. Microvasc. Research 59 (2000), 345-353. DOI 10.1006/mvre.1999.2231
[10] Tao, L., Humphrey, J., Rajagopal, K.: A mixture theory for heat-induced alterations in hydration and mechanical properties in soft tissues. Int. J. Eng. Sci. 39 (2001), 1535-1556. DOI 10.1016/S0020-7225(01)00019-2
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