Theory of Centrifugal Filtration

Theory of Centrifugal Filtration Theoretical predictions of the behavior of solid-liquid mixtures in a filtering centrifuge are more difficult compared to pressure and gravity filtration. The area of flow and driving force are both proportional to the radius, and the specific... 

During the filter cake-formation period, the filtrate passes radially outward through the filter medium and the bowl. Cake removal from the bowl may take place continuously or batchwise in the latter case, slurry feed to the centrifuge is terminated during the cake removal. The theory of centrifugal filtration is well summarized in the literature [3-5]. 

Particle size, shape, inter-particle forces, zeta potential, liquid surfactant phenomena, and liquid viscosity are important characteristics of a solid-liquid suspending system. Mechanism of flow through porous medium is fundamental to theories of sedimentation, filtration, centrifugation, and expression operations. Most solid-liquid materials are compacti-ble. Unique and strange behavior of pressure filtration of compactible materials has been identified. More attention should be paid for separation of those materials. 

Tiller, F.M., and N.B. Hsyung. 1993. Unifying the theory of thickening, filtration, and centrifugation. Water... 

PRINCIPLES OF CENTRIFUGAL FILTRATION. The basic theory of constant-pressure filtration can be modified to apply to filtration in a centrifuge. The treatment applies after the cake has been deposited and during flow of clear filtrate or freshwater through the cake. Figure 30.18 shows such a cake. In this figure,... 

The design, construction and application of thickeners, centrifuges and filters is a specialised subject, and firms who have expertise in these fields should be consulted when selecting and specifying equipment for new applications. Several specialist texts on the subject are available Svarovsky (2001), Ward (2000) and Wakeman and Tarleton (1998). The theory of sedimentation processes is covered in Volume 2, Chapter 5 and filtration in Chapter 7. 

Theoretical problems with the traditional theory of the parabolic equation relate to the assumption of constant and both of which are functions of the pressure drop across the cake. The pressure drop Ap varies when centrifugal and constant rate pumps are employed. Even in constant pressure filtration, Ap varies with time. At t = 0, there is no cake, and all of the pressnre is absorbed by the medium, as shown in Fignre 22.22. As the cake builds up, the flow rate q drops and the pressure drop across the medium, p, decreases in accord with Equation (22.28) ... 

The theory of constant-pressure filtration discussed in Section 14.2E can be modified and used where the centrifugal force causes the flow instead of the impressed pressure difference. The equation will be derived for the case where a cake has already been deposited as shown in Fig. 14.4-5. The inside radius of the basket is, r,- is the inner radius of the face of the cake, and r is the inner radius of the liquid surface. We will assume that the cake is nearly incompressible so that an average value of a can be used for the cake. Also, the flow is laminar. If we assume a thin cake in a large-diameter centrifuge, then the area A for flow is approximately constant. The velocity of the liquid is... 

It does not matter, from the fundamental point of view, how the pressure drop is generated in the filter. In the case of the centrifugal filters there is an additional phenomenon of the mass forces acting on the Hquid within the cake. The conventional filtration theory must be amended to include this effect (2). 

Mechanism of flow through porous media is fundamental in theoretical study of SLS process, such as filtration, thickening, centrifugation, expression, washing, etc. In the early study, with the development of fluid mechanics, interest was focused on flow in capillaries through incompressible sand beds. The beginning of present day theory can be traced to Hagen (1839), Poiseuille (1840), and Darcy (1856). 

For a particulate application involving SLS, how to choose the best equipment, to use batch or continuous operation, which filter medium to select, and what is the optimum operating conditions are concerns of engineers. Although theories are available for some SLS operations, solutions for equipment selection, process design, and optimization are still very much dependent on test and experience, and are frequently qualitative or semi-qualitative. In this section, strategy and decision networks for selection of SLS equipment, introduction of filter media, centrifugal pumps for filtration operation, and selection of filter aids by cycle analysis will be discussed. 

Studies of molasses provide an illustration. Coalstad1 reported that in spite of improvements in vacuum pans, crystallizers, and centrifuges, the composition of molasses has remained the same for many years. An explanation of this behavior is that when the impurities exceed a critical concentration, they are preferentially adsorbed on the nuclei of sucrose crystals. Because of this, sucrose molecules in solution cannot reach the nuclei and growth of crystals does not occur. When such a molasses solution is further concentrated, the only effect is to cause more impurities to be adsorbed on the nuclei and still further retard growth of crystals. To demonstrate the validity of the theory, Coalstad diluted a sample of molasses from which no further sucrose could be crystallized, and treated the solution with a large quantity of activated carbon. When the filtrate was concentrated, the sucrose crystallized spontaneously. Glycerin... 

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