Dialysis
 
 Dialysis is the transport of a solute through a membrane under the influence of a difference in the concentrations (or activities) of the solute in the solutions separated by the membrane. The separation of solutes is induced by differences in their transport by diffusion through the membrane matrix. A diffusable low-molecular-weight solute can thus be separated from a solution containing nondiffusable large macromolecules. The rate of dialysis is directly proportional to the membrane area and inversely proportional to the membrane thickness. Since the 1960s, the principal clinical use of this technique has been the treatment of patients with kidney disease.
 Nonclinical applications of dialysis techniques for the separation of solutes with molecular weights ranging from 100 to 100,00 Da may be on a small laboratory scale or with larger-scale commercial units for the recovery of alkai or in food processing applications. Dialysis is also important in biotechnology, as it provides a technique whereby products can be separated from fragile shear-sensitive or heat-sensitive solutions. A number of variants of the technique exist. These may be divided into batch and continuous processes. The simplest batch process is one in which a semipermeable membrane tubing made from cellulose and sealed at one or both ends contains the solution of interest. The tubing is suspended in a buffer solution or water. Small molecules contained within the solution bounded by the membrane diffuse into the surrounding buffer solution. The transfer of the substance across the membrane obeys Fick's law, if we assume that chemical equilibrium is established between the membrane and solution. If no water transfer occurs, and the mass transfer coefficient is constant along the diffusion path, the amount of substance transferred through the membrane W may be expressed as 

Where D is the overall dialysis coefficient of the substance, A the membrane area, and DC the logarithmic mean bulk concentration difference across the membrane based on the initial and final values.
A variation of equilibrium dialysis is reverse dialysis, in which the fluid contained in the semipermeable membrane tube is placed into a water-soluble polymer, such as polyethylene glycol. This causes the water to diffuse out of the membrane tube and concentrates the macromolecule within the tube.
For batch dialysis, where mass transfer is not at steady state, the transfer rate is given by 

Where k is the dialysis rate constant, t the time, m the volume of the feed ratio to diffusate, C₀ the concentration of the feed, and C the concentration of the dialysate.
Equilibration of the low-molecular-weight solutes or electrolytes by this technique can be speeded up by ensuring that the area of membrane contact is large relative to the volume of solution being dialysed. Since any molecule from the solution held within the membrane has to pass through the stagnant fluid film or boundary layer on either side of the membrane, as well as across the membrane itself, the overall dialysis rate may be enhanced by the minimization of the stagnant layers. This can be achieved by the introduction of a stirrer into the system, or by frequent changes of the dialysis fluid.
 The transfer rate is also dependent on temperature. Biological materials such as proteins usually need to be dialyzed in the cold to minimize bacterial growth or protein denaturation. Under such conditions, the transfer of molecules will be reduced compared with that at room temperature.
If the solution requiring to be dialyzed is available in a sufficiently large quantity, continuous methods that use a countercurrent flow configuration to maintain a large difference in the solute concentration across the membrane may be used. For such systems, which are similar to those used in the treatment of renal failure, the amount of solute transferred across the module, if we assume that the membrane is the primary barrier to diffusion, may be expressed as 

Where Q is the flow rate of the solute undergoing dialysis, C_in and C_out are the concentrations at the inlet and outlet, k and A are as previously defined, and DC is the log mean concentration difference between the dialysis fluid and the fluid being dialyzed.
 Many substances bind to proteins or plasma. The solute transfer referred to above relates to an unbound solute. However, a bound solute will be in equilibrium with the unbound solute, the extent of the binding being governed by the solute association constant. The effect of this will be that there will be an overestimate of the concentration driving force present. As free solute is removed, there will be unbinding of the solute with the effect of understating the concentration driving force.
 In a single-pass situation, ie, where the dialyzing fluid flows to waste and the solute undergoing dialysis is recirculated, the solute exchange rate within the module used for dialysis is expressed in terms of dialysance D, defined as 

The generalized concentration driving force will be determined by the Donnan factor a, defined as the ratio of the ionic concentrations in the dialysis fluid and in the solute undergoing dialysis at equilibrium. If the solute is noncharged, a = 1, and the measurement of the transport rates may occur by the use of a single pass flow configuration on the dialyzate side, while the fluid being dialyzed is recirculated. In such a flow configuration, provided that the volume being dialyzed V is unchanged, the concentration at time t, C_t, may be expressed in terms of the removal rate k and the initial concentration C₀ by