Applications of Mathematics

, Volume 56, Issue 1, pp 51–68

# Mathematical modeling and simulation of flow in domains separated by leaky semipermeable membrane including osmotic effect

• Jaroslav Hron
• Petra Pustějovská
Article

## 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.

## Keywords

leaky semipermeable membrane osmotic pressure transmission conditions finite element method

## MSC 2010

74K15 82C70 34C60 76D05

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© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

## Authors and Affiliations

• Jaroslav Hron
• 1
Email author