Effect of Filtration Rate on Throughput

For any type of pressure filtration, the filtration rate per unit area or flux (J) will be proportional to the pressure drop (AP) across the membrane or filter (i.e., the driving force) divided by the resistance to flow. The resistance term consists of two parts the resistance of the cake which accumulates on the upstream surface of the membrane (Rc) and the resistance contributed by the membrane itself (Rm). 

The resistance of the membrane, (Rm) is easily determined by the resistance to flow observed with ultrapure water and should be a constant for a given membrane operating with a specified fluid and temperature. 

The resistance of the cake of accumulated particulates, Rc, is more complicated it is a variable which increases as filtration proceeds resulting in a progressively lower filtration rate at constant pressure. This is due to the continually increasing thickness of the cake and its compaction under the pressurized conditions of filtration. If Rm is defined as above, Rc must also include the effect of pore plugging within the membrane. 

the flux declines as the throughput increases. Inverting equation (12) 

If one assumes that the limiting resistance to flow is that due to accumulated particulates on the membrane or within the pores, equation (12) becomes  

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