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Abstract

The theory of liquid diffusive flow through graded membrane under applied pressure difference is developed and demonstrated on four simple models. The grading of the membrane, caused by a gradient of chemical composition or physical structure, results in a gradient of liquid uptake (hydration) which in turn is reduced by the compacting pressure existing in the membrane during the permeation experiment. The hydration established in equilibrium between the swelling tendency and compacting pressure determines the local permeability. It has different values K+ = K for opposite flow direction. The total membrane permeability 〈K〉, however, depends on the current direction only in the case that the relative depression of local hydration, and hence of permeability by pressure, is not uniform but has a gradient. In mathematical formulation, the directionality of membrane requires the local permeability to be an irreducible function of location and pressure p, continuously increasing or decreasing with x. Th permeability of the membrane is higher if the driving pressure is applied at the side of the membrane with higher relative reduction of hydration and permeability by compacting pressure.