Ruth filtration equation

Ruth, B. F. Ind. Eng. Chem. 27 (1935) 708 and 806. Studies in filtration. III. Derivation of general filtration equations. IV. Nature of fluid flow through filter septa and its importance in the filtration equation. 

In cake filtration, once a layer of solid particles has formed on the filter medium, its surface becomes the actual filter medium. As the solids get deposited they add to the thickness of the cake whereas the clear liquid passes through. The cake is therefore composed of a bulky mass of particles, among which irregular small channels run. The flow of liquid through the channels is always laminar and can be described by the following Ruth s filtration equation ... 

Based on the above equation, several investigators notably Ruth, Sperry, Lewis, Carman and Bonilla, developed the filtration equations under the conditions of both constant pressure and constant filtration rate . The general form of the equation developed was as follows. 

Ruth et alS4-7) have made measurements on the flow in a filter cake and have concluded that the resistance is somewhat greater than that indicated by equation 7.1. It was assumed that part of the pore space is rendered ineffective for the flow of filtrate because of the adsorption of ions on the surface of the particles. This is not borne out by Grace18 or by Hoffing and Lockhart(9) who determined the relation between flowrate and pressure difference, both by means of permeability tests on a fixed bed and by filtration tests using suspensions of quartz and diatomaceous earth. 

Ruth, B. F. and Kempe, L. Trans. Am. Inst. Chem. Eng. 33 (1937) 34. An extension of the testing methods and equations of batch filtration practice to the field of continuous filtration. 

Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-54) may be integrated for a constant rate of slurry feed to the filter to give the following equations, in which filter-medium resistance is treated as the equivalent constant-pressure component to be deducted from the rising total pressure drop to give the variable pressure through the filter cake [Ruth, Ind. Eng. Chem., 27, 717 (1935)] ... 

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