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 diffusate stream on the other side. Some solvent may diffuse across the membrane in the opposite direction, which reduces the performance by diluting the dialyzate.

In practice it is used to seperate species that differ appreciably in size, which have a reasonably large difference in diffusion rates. Solute fluxes depend on the concentration gradient in the membrane. Hence, dialysis is characterized by low flux rates, in comparison to other membrane processes, such as reverse osmosis and ultrafiltration, membrane processes that depend on applied pressure.

A common type of equipment configuration used in liquid membrane processes is the flat plate, which is similar to a filter press. Vertical solid membranes are placed in between alternate liquor and solvent feed frames, with the liquor to be dialyzed being fed to the bottom and the solvent to the top of these frames. The dialyzate and the diffusate are removed through channels located at the top and bottom of the frames, respectively. The most important type consists of many small tubes or very fine hollow fibers arranged in a bundle like a heat exchanger. This type of unit has a very high ratio of membrane area to volume of the unit.

The artificial kidney is an important example of a liquid permeation process. In this application for purifying human blood, the principle solutes removed are the small solutes urea, uric acid, creatinine, phosphates and excess amounts of chloride. A typical membrane used is cellophane, which is about 0.025 mm thick, which allows small solutes to diffuse but retains the large proteins of the blood. During the hemodialysis, blood is passed on one side of the membrane while an aqueous dialyzing fluid flows on the other side. Solutes such as urea, uric acid, NaCl and so on, which have elevated concentrations in the blood, diffuse across the membrane to the dialyzing aqueous solution, which contains certain concentrations of solutes such as potassium salts and so on to ensure that concentrations in the blood do not drop below certain levels. In one configuration the membranes are stacked in the form of a multilayered sandwich with blood flowing by one side of the membrane in a narrow channel and the dialyzing fluid by the other side in alternate channels.

To calculate the rate of removal of urea at steady state from the blood in a cuprophane (cellophane) membrane dialyzer, the following equations can be used:

	               c1-c2
   Na    =     --------------------
               1/Kc1 + 1/Pm + 1/Kc2

where	Na is the flux of urea across the cuprophane membrane
	c1 is the concentration of urea in the blood
	c2 is the concentration of urea in the dialyzing fluid
	Kc1 is an estimated mass transfer coefficient on the blood side of the membrane
	Kc2 is an estimated mass transfer coefficient on the dialyzing side of the membrane
	Pm is the permeability of the cuprophane membrane, which is a property of the membrane

The rate of removal = Na x A

where	A is the area of the membrane

Geankoplis, Christie. Transport Processes and Unit Operations. Prentice Hall, Englewood 
	Cliffs, New Jersey. pp. 754-758.