Substituting in equation (10.1):
dV KAzkP d t fivV
This is a general equation relating rate of filtration to pressure drop, cross-sectional area of the filter and filtrate retained. Equation 10.2 can be integrated for filtration at constant pressure.
Integrating equation (10.3):
Now in equation (10.4), AP is constant, /x is generally equal to 1, v can be determined by laboratory investigation and A2 remains approximately constant. Thus there is a linear relationship between V2 and t. By carrying out small-scale filtration trials it is therefore possible to obtain a value for K. It is then possible to reapply the equation for large-scale filtration calculations.
Although it is also possible to derive the equation for the pressure necessary to maintain a constant filtration rate, it has little practical application. The pressure is made up of two components. Firstly the pressure needed to pass the constant volume through the filter resistance and, secondly, an increasing pressure component which is proportional to the resistance from the increasing cake depth. This filtration procedure would be complex to perform practically, and other methods of filtration are used to achieve constant flow rates, e.g. vacuum drum filters.
It is common practice to use filter aids when filtering bacteria or other fine or gelatinous suspensions which prove slow to filter or partially block a filter. Kieselguhr (diatr maceous earth) is the most widely used material. It has a voidage of approximately 0.85, and, when it is mixed with the initial cell suspension, improves the porosity of a resulting filter cake leading to a faster flow rate. Alternatively, it may be used as an initial bridging agent in the wider pores of a filter to prevent or reduce blinding. The term 'blinding' means the wedging of particles which are not quite large enough to pass through the pores, so that an appreciable fraction of the filter surface becomes inactive.
The minimum quantity of filter aid to be used in filtration of a broth should be established experimentally. Kieselguhr is not cheap, and it will also absorb some of the filtrate, which will be lost when the filter cake is disposed. The main methods of using the filter aid are:
1. A thin layer of kieselguhr is applied to the filter to form a precoat prior to broth filtration.
2. The appropriate quantity of filter aid is mixed with the harvested broth. Filtration is started, to build up a satisfactory filter bed. The initial raffinate is returned to the remaining broth prior to starting the true filtration.
3. When vacuum drum filters are to be used which are fitted with advancing knife blades, a thick precoat filter is initially built up on the drum (later section in this chapter).
In some processes such as microbial biomass production, filter aids cannot be used and cell pretreatment by flocculation or heating must be considered (see later section in this chapter). In addition it is not normally practical to use filter aids when the product is intracellular and its removal would present a further stage of purification.
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