Solid-liquid filtration theory

This chapter summarizes the solid-liquid separation operations commonly used for the pretreatment of drying operations. We focus on the practical aspects of cake filtration, centrifngal filtration, and mechanical expression. The choice of equipment depends on the objective of the separation, the properties of the slurry, and the scale of prodnction. The details of solid-liquid separation theories are omitted. The reader is referred to the references for further information. 

While research has developed a significant and detailed filtration theory, it is still so difficult to define a given liquid-solid system that it is both faster and more accurate to determine filter requirements by performing small-scale tests. Filtration theoiy does, however, show how the test data can best be correlated, and extrapolated when necessary, for use in scale-up calculations. 

In this subsection, basic design theory for preliminary sizing and specifying equipment are reviewed. Some sample design calculations are included. References cited at the end of tlie chapter can be consulted for more detailed information and design methods. For solid-liquid separation methods, the reader should refer to Liquid Filtration, 2" edition, by N. P. Cheremisinoff, Butterworth-Heinemarui Publishers (1998). 

Sedimentation classifiers, 76 619-620 in depth filtration theory, 11 339 in particle size measurement, 78 142-144 in solid-liquid separation, 76 656-657 Sedimentation rate... 

Tiller, F.M., Filtration Theory Today, Chem. Eng., 73,13, 151, 1966. Svarovsky, L., Advanced in Solid Liquid Separations I, Chem. Eng., 86,... 

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. 

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... 

Expression is the separation of a liquid from a two-phase solid-liquid system by compression, due to movanent of the retaining wall rather than the pumping of the solid-liquid system into a fixed chamber as in filtration. In filtration, the original mixture is sufficiently fluid to be pumpable in expression, the material may appear either entirely sani-solid or slurry. Based on an expression theory [6,7], the time for expression is also proportional to the square of cake thickness. 

Yim S.S. and Kwon Y.D., 1997. A unified theory on solid-liquid separation Filtration, expression, sedimentation, filtration by centrifugal force, and cross flow filtration, Korean J. Chem. Eng., 14, 354-358. 

Fouling layers, in general, are compressible, that is they become more compact as the extent of their compression increases. Solid compressive pressure is responsible for the compression of a fouling layer according to basic filtration theory [46]. In traditional filtration theory, the derivation of the drag equations of filtration for rigid particle slurries assume that particles are in point contact mode and that compression attends instantaneously. Under this assumption, a force balance can be obtained between liquid pressure over the entire cross-section and the solid compressive pressure on the total mass within the porous layer as ... 

Chapter 4 is devoted to the description of stochastic mathematical modelling and the methods used to solve these models such as analytical, asymptotic or numerical methods. The evolution of processes is then analyzed by using different concepts, theories and methods. The concept of Markov chains or of complete connected chains, probability balance, the similarity between the Fokker-Plank-Kolmogorov equation and the property transport equation, and the stochastic differential equation systems are presented as the basic elements of stochastic process modelling. Mathematical models of the application of continuous and discrete polystochastic processes to chemical engineering processes are discussed. They include liquid and gas flow in a column with a mobile packed bed, mechanical stirring of a liquid in a tank, solid motion in a liquid fluidized bed, species movement and transfer in a porous media. Deep bed filtration and heat exchanger dynamics are also analyzed. 

---