Filtration basic theory

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,... 

Traditionally, the average specific cake and medium resistances have been deterrnined from constant pressure experiments and the solution of the basic filtration equation for constant pressure which relates filtrate volume to time. This relationship is, in theory, paraboHc but deviations occur in practice. 

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). 

Metal hydride element is a complex physical item, which can be described by the continuum theory equations. There are three basic processes i) process of hydrogen filtration through a porous hydride matrix and heat-conducting inserting, ii) processes of heat application and heat abstraction from a space of hydrogenation and iii) chemical processes accompanying hydrogen sorption - desorption. 

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. 

Flow normal to a right circular cylinder is the basic model for the theory of aerosol filtration by fibrous and cloth filters, and of particle collection by pipes and rods in a flow (Fig. 3.1). The aerosol concentration at large distances from the surface is uniform at one particle radius from the surface, the concentration vanishes. 

A better understanding of the basic principles of ultrafiltration has permitted the development of much more efficient equipment and corresponding commerical applications. A detailed consideration of the theory of ultrafiltration was published by Porter (134), who dealt specifically with the problem Of concentration polarization. As shown in Figure 4.4, the movement of particles toward the membrane results in the formation of a concentrated sol layer of high viscosity. This can reduce the flux or rate of filtration to a small fraction of that of the liquid medium in the absence of colloid. The resistance to flow is not due to plugging of pores, or even to an actual solid layer (gel) of close-packed colloidal particles. In has been observed... 

The filtration theory presented here is only very basic and the assumptions on which it is built are often too simplistic. This so-called classical filtration... 

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 ... 

The selection of a membrane for a particular type of separation is usually determined by its average pore size e.g., 10-100 yam is useful for conventional filtration, 0.1-10 yam for microfiltration, 50-1000 A for ultrafiltration, and less than 50 A for reverse osmosis, gas separation, and pervaporation, as depicted in Fig. 33.2. The latter are also described as nonporous membranes and depend on molecular interactions between the permeant and the membrane itself to affect separation. The basic terminology and theory of membrane-based separation systems are similar for both gases and liquids and are therefore treated together in this section. 

The reaction of hexahydropyrroloindole (HPI) (46) with thiols to give the corresponding 2-thioether-tryptophan compounds has been further investigated (464). Reaction of cysteine with HPI (1.2 equiv) in 25% tri-fluoroacetic acid produces quantitatively tryptathionine, an amino acid contained in the toxic peptides of Amanita phalloides (see Section VI.2.4.). Reduced ribonuclease, a protein containing 8 cysteine residues per molecule, was treated with HPI, and the modified protein purified by gel filtration. The completeness of the reaction was confirmed by hydrolysis with /7-toluenesulfonic acid (233) and analysis of the hydrolyzate. A value of 7.6 (theory 8) residues per mole of protein of oxindolylalanine, the product of hydrolysis of the tryptathionine residues (431) (see Section III.4.2.), was obtained. This new reaction of cysteine residues should be of value in peptide synthesis, providing a simple method for linking tryptophan and cysteine as a basic step in the chemical synthesis of the peptides of Amanita phalloides. 

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