This mode of operation is achieved when a pure liquid is filtered through a cake of constant thickness at a constant pressure difference. Cake washing by displacement when the washing liquid is located over the cake may be considered to be filtration of washing liquid through a constant cake thickness at constant pressure and flowrate. The rate of washing is related to the rate of filtration during the last stages and may be expressed by Equation 9, where Ap is the pressure at the final moment and V is the filtrate volume obtained during filtration, regardless of the filtration method used (i.e., constant-pressure or constant-rate operation). In the final stages, filtration usually is performed under constant pressure. Then, the rate of this process may be calculated from Equation 19. From filtration constants C and K, at constant pressure for a given system, the filtration rate for the last period is determined. If the washing liquid passes through the filter in the same pore paths as the sludge and filtrate, then the difference between the washing rate and filtration rate for this last period will be mostly due to a difference in the viscosities of the wash liquor and filtrate. Therefore, Equation 19 is applicable using the viscosity of the washing liquid, ftw. Denoting the rate of filtration in the last period as (dV/dx), the washing rate is:
Solid particles undergoing separation from the mother suspension may be captured both on the surface of the filter medium and within the inner pore passages. This phenomenon is typical in the separation of low-concentration suspensions, where the suspension consists of viscous liquids such as sugar liquors, textile solutions or transformer oils, with fine particles dispersed throughout. The penetration of solid particles into the filter medium increases the flow resistance until eventually the filtration cycle can no longer proceed at practical throughputs and the medium must be replaced. In this section standard filtration formulas are provided along with discussions aimed at providing a working knowledge of the filter-medium filtration process.
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