Dynamics of osmosis in a porous medium

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 1958 Biochim. Biophys. Acta 27 , 229–246 ( doi:10.1016/0006-3002(58)90330-5 ), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem–Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.

Differential action of plasma and albumin on transcapillary exchange of anionic solute

We tested two hypotheses to account for the reduction in coupling of anionic solute to water flow (solvent drag) in microvessels during perfusion with plasma compared with albumin. Solvent drag is determined by both hydraulic conductivity (Lp) and solute reflection coefficient (sigma). Accordingly, decreased solvent drag during plasma perfusion must be the result of an increase in sigma (hypothesis 1) or reduction of Lp (hypothesis 2) or some combination of both mechanisms. These hypotheses were assessed by measuring Lp, sigma, and diffusive solute permeability (Psd) to the anionic protein alpha-lactalbumin in frog mesenteric exchange microvessels during plasma or albumin perfusion. The solute permeability coefficient to alpha-lactalbumin (Ps alpha-lactalbumin) was lower during exposure to plasma than bovine serum albumin (BSA) [(Ps alpha-lactalbumin)plasma/(Ps alpha-lactalbumin)BSA = 0.31 +/- 0.11 (means +/- SE, n = 9)]. Solute reflection coefficient to alpha-lactalbumin (sigma alpha-lactalbumin) was 0.69 +/- 0.02 in plasma and 0.34 +/- 0.03 in BSA (n = 7). Lp was not significantly influenced by perfusate protein composition (Lp plasma/Lp BSA = 1.02 +/- 0.11; n = 20). These data lead to the conclusion that the actions of plasma are to confer charge selectivity for anionic solute and, to a lesser extent, modify the porous pathways of the microvessel wall. Taken together, these results indicate that porous pathways contribute significantly to macromolecular flux in plasma-perfused vessels.

Modulation of microvessel wall charge by plasma glycoprotein orosomucoid

Haraldsson and Rippe suggested that the circulating glycoprotein orosomucoid (alpha 1-acid glycoprotein) contributes to the net charge on microvessel walls (Acta Physiol. Scand. 129: 127-135, 1987). We tested their hypothesis in individually perfused microvessels of frog mesentery by measuring solute permeability coefficients of two globular proteins (alpha-lactalbumin and ribonuclease) having approximately the same size (Stokes radius, 2 nm) but different charge (-11 and +3, respectively). In vessels perfused with orosomucoid (0.1 and 1 mg/ml) in a Ringer-albumin perfusate, the solute permeability coefficient of alpha-lactalbumin decreased to one-half [0.47 +/- 0.25 (SD)] the value in the absence of orosomucoid, and the solute permeability coefficient of ribonuclease was close to six times as large as alpha-lactalbumin permeability. Both results may be accounted for if orosomucoid increases the net negative charge on microvessel walls in frog mesentery from 11.2 to 28 meq/l. A similar change in microvessel charge would be more than sufficient to account for the decrease in albumin clearance in the presence of orosomucoid reported by Haraldsson and Rippe in rat muscle microvessels.

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and Lp for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.