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Figure 1. Direction of gravity force action and filtrate motion in filters: A-cocurrent; B-countercurrent; C-crosscurrent; solid arrow-direction of gravity force action; dashed arrow- direction of filtrate motion; 1-filter plate; 2-cake; 3-sludge; 4-filtrate; 5-clear liquid.

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media.

Cakes containing particles of inorganic substances with sizes in excess of 100 pm may be considered incompressible. Examples of incompressible cake-forming materials are sand and crystals of carbonates of calcium and sodium. The cakes containing particles of metal hydroxides, such as ferric hydroxide, cupric hydroxide, aluminum hydroxide, and sediments consisting of easy deforming aggregates, which are formed from primary fine crystals, are usually compressible. At the completion of cake formation, treatment of the cake depends on the specific filtration objectives. For example, the cake itself may have no value, whereas the filtrate may. Depending on the disposal method and the properties of the particulates, the cake may be discarded in a dry form, or as a slurry. In both cases, the cake is usually subjected to washing, either immediately after its formation, or after a period of drying. In some cases, a second washing is required, followed by a drying period where all possible filtrate must be removed from the cake; or where wet discharge is followed by disposal: or where repulping and a second filtration occurs; or where dry cake disposal is preferable. Similar treatment options are employed in cases where the cake is valuable and all contaminating liquors must be removed, or where both cake and filtrate are valuable. In the latter, cake-forming filtration is employed, without washing, to dewater cakes where a valueless, noncontaminating liquor forms the residual suspension in the cake. To understand the dynamics of the filtration process, a conceptual analysis is applied in two parts. The first half considers the mechanism of flow within the cake, while the second examines the external conditions imposed on the cake and pumping system, which brings the results of the analysis of internal flow in accordance with the externally imposed conditions throughout. The characteristics of the pump relate the applied pressure on the cake to the flowrate at the exit face of the filter medium. The cake resistance determines the pressure drop. During filtration, liquid flows through the porous filter cake in the direction of decreasing hydraulic pressure gradient. The porosity (e) is at a minimum at the point of contact between the cake and filter plate (i.e., where x = 0) and at a maximum at the cake surface (x = L) where sludge enters. A schematic definition of this system is illustrated in Figure 2.

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Figure 2. Important parameters in cake formation.

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