Solid-liquid separation expression

It was shown in Chapter 2 that the simplest models of solid-liquid separation are those based of the Carman-Kozeny equation for filtration in whieh the bed permeability (filtrability), F, may be expressed by... 

The nature and sizing of equipment depends on the economic values and proportions of the phases as well as certain physical properties that influence relative movements of liquids and particles. Pressure often is the main operating variable so its effect on physical properties should be known. Table 11.1 is a broad classification of mechanical processes of solid-liquid separation. Clarification is the removal of small contents of worthless solids from a valuable liquid. Filtration is applied to the recovery of valuable solids from slurries. Expression is the removal of relatively small contents of liquids from compressible sludges by mechanical means. 

Solid-liquid separation systems generally consist of four stages including pretreatment, solid concentration in thickeners, solid separation in filters or centrifuges, and post-treatment by expression and washing operations. There are different types of SLS equipment served for different functions in relation to the four stages. Product specification, characteristics of solid-liquid suspension, solid settling velocity, rate of cake... 

This chapter is written with three objectives in mind. First, the importance of the size and concentration of the particles to be treated in determining the eflFectiveness of some solid-liquid separation processes is evaluated. Second, past theories are used to examine how particle sizes and concentrations are altered by these treatments. Third, interrelationships among the individual unit processes that comprise a complete treatment system are investigated to provide a base for an integral treatment plant design. These aims are undertaken using a typical water treatment system as employed in practice to remove turbidity from surface water supplies. Before addressing these objectives, it is useful to review some mathematical expressions of particle size distributions, and to identify some important properties of these functions. 

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. 

Solid-Liquid Separation Equipment (Thickeners, Clarifiers, FUters, Centrifuges, and Expression)... 

Instrumental techniques for measurement of particle size distribution of powders have had a tremendous advancement in recent times. Numerous methods and procedures have been developed at a steady pace over the years, and there is the possibility of covering the wide spectrum from nanosystems, to ultrafine powders, and to coarse particulate assemblies. Many instruments offer nowadays quick, reliable results for a wide variety of powders and particulate systems, and for a number of applications. There is still, however, the need to understand the basic principles under which sophisticated instruments operate, as well as to resource to direct measurements under some circumstances. Some of the most modern instrumental techniques are based on an indirect measurement and carry out transformations among the different ways of expressing particles size distributions, that is, by number, surface, or mass. Sometimes it is advisable to avoid transformations because instruments assume a constant shape coefficient on such transformation, which is not necessarily the case, and overestimation or underestimations of size of certain particles may arise. Also, in very specific applications, or in cases of basic or applied research, is better to measure directly the most relevant particle size and particle size distribution. For example, if research is carried out in modeling of solid-liquid separations, a direct measurement of the Stokes equivalent diameter would be most appropriate. The aim of the exercise is to measure the particle size distribution of a sample of medium-sized dolomite, and compare the results with those of the Andreasen Pipette method. 

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. 

Pressure between solid walls separated by ultra-thin liquid film is then expressed as follows ... 

You can represent the enthalpy change that accompanies a phase change—from liquid to solid, for example—just like you represented the enthalpy change of a chemical reaction. You can include a heat term in the equation, or you can use a separate expression of enthalpy change. 

Expression is the separation of liquid from a two-phase solid-liquid system by compression of the system under conditions that permit the liquid to escape, while the solid is retained between the compressing surfaces. Expression serves the same purposes as filtration but is distinguished from the latter in that the pressure is applied by movement of the retaining walls instead of pumping the material into a fixed space. Expression is usually employed to separate systems that are not easily pumped. It is also used instead of filtration when a more thorough removal of liquid from the cake is desired. The usual equipment for expression is a hydraulic press. Most of the common vegetable oils are produced by expression, In the expl in-... 

The equilibrium process describing the adsorption and desorption of a solute / in a liquid-solid chromatographic separation can be expressed by... 

If the dielectric properties are known, the expression represents a complete solution to the interaction problem, provided Aat a liquid separating the two interacting solid surfaces is itself not perturbed in structure by the surfaces. These forces can be calculated and measured. We make the following remarks. The assumption of two-body forces is completely misleading and qualitatively erroneous for condensed media interactions. The sum in the 11 expression above includes contributions from all frequencies. 

In water solution containing small particles (i.e., suspended solids or turbidity) and non-surface-active solutes, when air is bubbled through it, little or no particles will be removed by any adsorptive bubble separation process. This is because the particles have virtually no natural affinity for air bubbles and hence there is no adhesion when contact is made. This particular phenomena may be explained by the contact angle between a particle and an air bubble. Consider the case of the three-phase fine of contact between a smooth, rigid, solid phase, a liquid phase and a gas phase. The equilibrium contact angle can be expressed in terms of the average surface tensions (i.e., interfacial tensions, dyne/cm) of the liquid-gas solid-liquid (r j ), and solid-gas (r ) interfaces, by the well-known Young s equation ... 

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. 

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