The derivative of this expression with respect to q is:
On some rearranging of terms, we obtain:
Equation 61 states that the intensity of increase in total resistance with increasing filtrate amount is proportional to resistance to the 3/2 power. In this case, the total resistance increases less sensitively than in the case of total pore blockage.
As follows from Equations 56 and 62:
Substituting Equation 55 for C and using Equation 48 for B, the above expression becomes:
Note that for constant Win, parameter K'' is proportional to the ratio of the settled volume of cake in the pores to the filtrate volume obtained, and is inversely proportional to total pore volume for a unit area of filter medium.
Replacing W by dq/dt in Equation 57, we obtain:
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