Effects of Unsteadiness in Membrane Separation of Solutions

Nonstationary diffusion problems are considered within the framework of the homogeneous membrane model for a closed membrane cell and a cross-flow cell with a tangential flow of feed solution and permeate in the absence and presence of convection (as applied to dialysis and any pressure-driven membrane process for separating solutions of neutral substances). Characteristic features of a steady state establishment in each of the three cases considered have been revealed, and simple algebraic formulae have been obtained for calculating the time it takes the process to reach a steady state depending on each of the problem parameters. It has been found that membrane characteristics, such as the diffusion coefficient of solute molecules in the membrane and the magnitude of the potential barrier for diffusing components, have a lesser effect on the process stabilization rate than the thickness of the diffusion layer or the flow regime in the case of convective diffusion. It is the additional surface forces, as well as stirring, that make a decisive contribution to the unsteady-state period of the convective diffusion regime. It has been established that purely diffusion processes (for example, dialysis) are not only slower than convective-diffusion processes, but also reach a steady state more slowly. At the same time, it was revealed that the time to reach a steady state in each process is significantly shorter than the characteristic time of the process itself. This fact provides additional justification for the validity of stationary formulations of the problems studied.