Osmotic flow equations for leaky porous membranes.
A basic set of equations describing the flows of volume (Jv) and solute (Js) across a leaky porous membrane, coupled to the differences of osmotic and hydrostatic pressures d pi and dP has been derived by using general frictional theory. Denoting the mean pore concentration of solute by c*s and the hydraulic and diffusive conductances by Lp and Ps/RT the equations take the form Jv = LpdP + sigma sLp d pi Js = c*s(1 - sigma f)Jv + Ps d pi/RT sigma s = theta (1 - DsVs/DwVw - Ds/Dos) sigma f = 1 - theta DsVs/DwVw - Ds/Dos in which Dw and Ds are the diffusion coefficients for water and solute in the pore and Dos that for free solution. The relation between the reflection coefficients sigma s and sigma f for osmosis and ultrafiltration is then given by sigma s = sigma f - (1- theta)(1 - Ds/Dos), where theta is the diffusive-driven:pressure-driven flow ratio. These equations follow from the fact that in leaky pores osmosis occurs by diffusion alone and that there cannot be any Onsager symmetry leading to sigma s = sigma f. Symmetry holds in the limits where either the pore is small, when sigma s = sigma f = 1, or where the pore is large when sigma s = sigma f = 0.
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Physiological Laboratory, University of Cambridge, U.K.
D001692:Biological Transport; D006874:Hydrostatic Pressure; D008433:Mathematics; D008566:Membranes / Q000502:physiology*; D008962:Models, Theoretical; D009995:Osmosis; D009997:Osmotic Pressure; D012996:Solutions
D012996:Solutions