Theory of filtration

Filterability of slurries depends so markedly on small and unidentified differences in comhlions of formation and aging that no correlations of this behavior have been made. In fact, the situation is so discouraging that some practitioners have dismissed existing filtration theory as virtually worthless for representing filtration behavior. Qualitatively, however, simple filtration theory is directionally valid for modest scale-up and it may provide a structure on which more complete theory and data can be assembled in the future. 

As filtration proceeds, a porous cake of solid particles is built up on a porous medium, usually a supported cloth. Because of the fineness of the pores the flow of liquid is laminar so it is represented by the equation 

The resistance R is made up of those of the filter cloth Rf and that of the cake which may be assumed proportional to the weight of the cake. Accordingly, 

R and a are constants of the equipment and slurry and must be evaluated from experimental data. The simplest data to analyze are those obtained from constant pressure or constant rate tests for which the equations will be developed. At constant pressure Eq. (11.2) is integrated as 

The constants Rf and a are derivable from the intercept and slope of the plot of against K Example 11.1 does this. If the constant pressure period sets in when t = Iq and V=Vq, Eq. (11.4) becomes 

Vacuum drum filter F G E high to med. — medium high medium medium high high medium 

A plot of the left hand side against V H- Vq should be linear. At constant rate of filtration, Eq. (11.2) can be written 

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The theory of filtration of aerosols from a gas stream is much more involved than the sieving action which removes particles in a liquid medium. Figure 29-1 shows three of the mechanisms of aerosol removal by a filter. In practice, the particles and filter elements are seldom spheres or cylinders. 

Models have been developed for this drainage process which are based upon theories of filtration. The Kozeny-Karmen equation is the most common rate expression used as a model for this filtration process. It can be expressed as ... 

Ives, K. J. Proc. Int. Water Supply Assn. Eighth Congress, Vienna. Vol. 1. (Intematl. Water Supply Assn., London, 1969). Special Subject No. 7. Theory of Filtration. 

Tiller, F. M. and Chum-Dar Tsai. 1986. Theory of filtration of ceramics I, Slip casting. J. Amer. Ceram. Soc. 69(12) 882-87. 

The theory of filtration is a direct application of principles of Brownian diffusion discussed previously. The objective of the theory is to provide a framework for cal-... 

Electrostatic. Virtually all colloids in solution acquire a surface charge and hence an electrical double layer. When particles interact in a concentrated region their double layers overlap resulting in a repulsive force which opposes further approach. Any theory of filtration of colloids needs to take into account the multi-particle nature of such interactions. This is best achieved by using a Wigner-Seitz cell approach combined with a numerical solution of the non-linear Poisson-Boltzmann equation, which allows calculation of a configurational force that implicitly includes the multi-body effects of a concentrated dispersion or filter cake. 

Aldushin, A. P., New results in the theory of filtration combustion. Combust. Flame, 94,308 (1993). 

Aldushin, A. R, Merzhanov, A. G., and Sepliarskii, B. S., Theory of filtration combustion of metals. Combust. Explos. Shock Waves, 12,285 (1976b). 

Naidenov, V. I. and Polyanin, A. D., On some nonlinear convective-heat effects in the theory of filtration and hydrodynamics, Physics Doklady, Vol. 29, No. 11, 1984. 

Properties of clays and clayey rocks, and also the processes in them depend on a number of factors. Then the mathematical simulation of the properties and processes, as one of the methods of their examination, is a rather difficult problem. Physically it is clear that the speciflc properties of clay rocks (low permeability, plasticity in moist condition) are caused by the existence of clay minerals in their composition, and these properties are a manifestation of surface capacities, which exist between particles of the clay minerals, which are included in the composition of clays. The most useful conception of the activity of surface capacities is the conception of disjoining pressure between colloid particles, Mitchell (1976). In this work we provide a description of the physical and mechanical clay properties and transport processes in them. The description is based on methods of theory of filtration consolidation. Nikolaevskiy (1996), and also on the theory of stability of lyophobic colloids (theory of Deijaguin-Landau-Verwey-Overbeeck, or DLVO theory), which uses the conception of disjoining pressure. 

The theories of filtration by a fibrous filter relate only to the initial... 

Tiller FM, Hsyung NB (1991) Theory of filtration of ceramics, 2. Slip casting on radial surfaces. J Am Ceram Soc 74 210-218... 

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