Nonstationary diffusion through a membrane separating two finite volumes of stirred or unstirred solutions

Abstract

The decay of the osmotic pressure with time is treated theoretically and experimentally for the case of a solute with low molecular weight permeating through a membrane. The influence of the boundaries of the external phases has been taken into account. The solutions of the diffusion equations for the composite system yield the solute concentration as a function of position and time everywhere in the system. Expressions are derived for the experimental osmotic pressure (i.e. the pressure needed to make volume flow through the membrane vanish) with the external solutions either stirred or unstirred and including a number of experimentally interesting initial conditions. For sufficiently large values of time, even in the unstirred situation, these expressions predict a simple exponential decay with time, reflecting that the system has arrived at a quasi-stationary state. The pressure-time curves were measured with a high-speed osmometer equipped with a cellulose membrane separating two unstirred solutions of glycerol trioctadecanoate in toluene. A single curve allows the determination of at least two transport parameters: the reflection coefficient σ and the membrane diffusion coefficient D. It is shown that without loss of accuracy a simplified evaluation of these parameters is possible by using only the simple exponential part of the decay curve.