Liquid Permeation Membrane Processes or Dialysis

In membrane processes with liquids, the solute molecules must first be transported or diffuse through the liquid film of the first liquid phase on one side of the solid membrane, through the membrane itself, and then through the film of the second liquid phase. This is shown in Fig. 13.2-la, where Cj is the bulk liquid-phase concentration of the diffusing 

The flux equations through each phase are all equal to each other at steady state and are as follows  

Adding the equations, the internal concentrations c,- and Cj,- drop out, and the final equation is 

In some cases, the resistances in the two liquid films are quite small compared to that of the membrane resistance, which controls the permeation rate. 

Dialysis uses a semipermeable membrane to separate species by virtue of their different diffusion rates in the membrane. The feed solution or dialyzate, which contains the solutes to be separated, flows on one side of the membrane and the solvent or dififusate stream on the other side. Some solvent may also diffuse across the membrane in the opposite direction, which reduces the performance by diluting the dialyzate. 

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