The Kinetics of Membrane Processes. II. Theoretical Pressure-Time Relationships for Permeable Membranes

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Abstract
The rate equations developed in Part I for the flow of solvent and solute through a permeable membrane have been extended to the case in which the flow is measured by the rise and fall in a capillary inserted into the more concentrated solution. The differential equation obtained for this case has been integrated to give an explicit relationship between the height of rise in the capillary and the time. The equation is shown to give the height‐time relationship in the form found by experiment. It is shown that the osmotic pressure obtained with a semipermeable membrane is a special case of the more general theory of diffusion through membranes permeable to both solvent and solute. The possibility of positive and negative values of P, i.e., of initial rise or fall respectively in the capillary, is discussed, and the significance of these cases evaluated in terms of the molar volumes and permeation constants of solvent and solute.

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