## Principles of Membrane Processes

Membrane separation, electrodialysis, reverse osmosis, ultrafiltration and other such processes are playing an increasingly important role in waste water treatment.

A membrane is defined as a phase that acts as a barrier between other phases. It can be a solid, a solvent-swollen gel or even a liquid. The applicability of a membrane for separation depends on differences in its permeability to different compounds.

Table 10.1 gives a survey of membrane separation processes and their principal driving forces, applications and their useful ranges.

Figure 10.1 shows the relation between the membrane permeability and the size of various impurities in waste water. The selection of membrane process is, as seen from this figure, a questionof which impurities are required to be removed from the waste water.

Osmosis is defined as a spontaneous transport of a solvent from a dilute solution to a concentrated solution across a semi-permeable membrane. At a certain pressure - the so-called osmotic pressure - equilibrium is reached. The osmotic pressure varies with concentration and temperature, and depends on the properties of the solution. For water, the osmotic pressure is given by:

where n = the number of moles of solute V = the volume of water R = the gas constant T = the absolute temperature

This equation describes an ideal state and is valid only for dilute solutions. For more concentrated solutions the equation must be modified by the van't Hoff factor by using an osmotic pressure coefficient:

For most electrolytes the osmotic pressure coefficient is less than unity and will usually decrease with increasing concentrations. This means that equation (10.1) is usually conservative and predicts a higher pressure than is observed. If the pressure is increased above the osmotic pressure on the solution side of the membrane, as shown in Fig. 10.2, the flow is reversed. The solvent will then pass from the solution into the solvent. This is the basic concept of reverse osmosis. Reverse osmosis can be compared with filtration, as it also involves the moving of liquid from a mixture by passing it through a filter.

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