## Filtration

Filtration is one of the most common processes used at all scales of operation to separate suspended particles from a liquid or gas, using a porous medium which retains the particles but allows the liquid or gas to pass through. Gas filtration has been discussed in detail elsewhere (Chapters 5 and 7). It is possible to carry out filtration under a variety of conditions, but a number of factors will obviously influence the choice of the most suitable type of equipment to meet the specified requirements at minimum overall cost, including:

1. The properties of the filtrate, particularly its viscosity and density.

2. The nature of the solid particles, particularly their size and shape, the size distribution and packing characteristics.

3. The solids: liquid ratio.

4. The need for recovery of the solid or liquid fraction or both.

5. The scale of operation.

6. The need for batch or continuous operation.

7. The need for aseptic conditions.

8. The need for pressure or vacuum suction to ensure an adequate flow rate of the liquid.

### Theory of filtration

A simple filtration apparatus is illustrated in Fig. 10.7, which consists of a support covered with a porous filter cloth. A filter cake gradually builds up as filtrate passes through the filter cloth. As the filter cake increases in thickness the resistance to flow will gradually increase. Thus, if the pressure applied to the surface of the slurry is kept constant the rate of flow will gradually diminish. Alternatively, if the flow rate is to be kept constant the pressure will gradually have to be increased. The flow rate may also be reduced by blocking of holes in the filter cloth and closure of voids between particles, if the particles are soft and compressible. When particles are compressible it may not be feasible to apply increased pressure.

Flow through a uniform and constant depth porous bed can be represented by the Darcy equation:

Rate of flow dV ~dt

where /x = liquid viscosity,

L — depth of the filter bed, A P = pressure differential across the filter bed,

A = area of the filter exposed to the liquid, K = constant for the system. K itself is a term which depends on the specific surface area ,? (surface area/unit volume) of the particles making up the filter bed and the voidage 2 when they are packed together. The voidage is the amount of filter-bed area which is free for the filtrate to pass through. It is normally 0.3 to 0.6 of the cross-sectional area of the filter bed. Thus K (Kozeny's constant) can be expressed as

Unfortunately, s and 2 are not easily determined.

In most practical cases L is not readily measured but can be defined in terms of:

V = volume of filtrate passed in time t and v = volume of cake deposited per unit volume of filtrate.

Then

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