# American Institute of Mathematical Sciences

September  2016, 11(3): 471-499. doi: 10.3934/nhm.2016005

## Osmosis for non-electrolyte solvents in permeable periodic porous media

 1 Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Göteborg, Sweden 2 Narvik University College, Postbox 385, 8505 Narvik, Norway and P.N. Lebedev Physical Institute RAS, Leninski ave., 53, Moscow 119991, Russian Federation

Received  April 2015 Revised  September 2015 Published  August 2016

The paper gives a rigorous description, based on mathematical homogenization theory, for flows of solvents with not charged solute particles under osmotic pressure for periodic porous media permeable for solute particles. The effective Darcy type equations for the flow under osmotic pressure distributed within the porous media are derived. The effective Darcy law contains an additional flux term representing the osmotic pressure. Coefficients in the effective homogenized equations are related to the values of the phenomenological coefficients in the Kedem-Katchalsky formulae (2).
Citation: Alexei Heintz, Andrey Piatnitski. Osmosis for non-electrolyte solvents in permeable periodic porous media. Networks & Heterogeneous Media, 2016, 11 (3) : 471-499. doi: 10.3934/nhm.2016005
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