Section 7.3 Liquid-Solid

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Thus, to encourage wetting, 7sl and 7lv should be made as small as possible. This is done in practice by adding a surfactant to the liquid phase. The surfactant adsorbs to both the liquid-solid and liquid-vapor interfaces, lowering those interfacial tensions. Nonvolatile surfactants do not affect 7sv appreciably (see, however. Section X-7). It might be thought that it would be sufficient merely to lower ytv and that a rather small variety of additives would suffice to meet all needs. Actually it is equally if not more important that the surfactant lower 7sL> and each solid will make its own demands. 

The liquid-solid interface, which is the interface that is involved in many chemical and enviromnental applications, is described m section A 1.7.6. This interface is more complex than the solid-vacuum interface, and can only be probed by a limited number of experimental techniques. Thus, obtaining a fiindamental understanding of its properties represents a challenging frontier for surface science. 

Richard C. Bennett, B.S., Ch.E., Registered Professional Engineer, Illinois Member, American Institute of Chemical Engineers (AIChE) President of Crystallization Technology, Inc. Former President of Swenson Process Equipment, Inc. (Section 18, Liquid-Solid Operations and Equipment)... 

Chad McCleary, EIMCO Process Equipment Company, Process Consultant (Section 18, Liquid-Solid Operations and Equipment)... 

The expression gas-liquid fluidization, as defined in Section III,B,3, is used for operations in which momentum is transferred to suspended solid particles by cocurrent gas and liquid flow. It may be noted that the expression gas-liquid-solid fluidization has been used for bubble-column slurry reactors (K3) with zero net liquid flow (of the type described in Sections III,B,1 and 1II,V,C). The expression gas-liquid fluidization has also been used for dispersed gas-liquid systems with no solid particles present. 

Section 8 deals with reactions which occur at gas—solid and solid—solid interfaces, other than the degradation of solid polymers which has already been reviewed in Volume 14A. Reaction at the liquid—solid interface (and corrosion), involving electrochemical processes outside the coverage of this series, are not considered. With respect to chemical processes at gas-solid interfaces, it has been necessary to discuss surface structure and adsorption as a lead-in to the consideration of the kinetics and mechanism of catalytic reactions. 

Table 5.4-3 summarizes the design equations and analytical relations between concentration, C/(, and batch time, t, or residence time, t, for a homogeneous reaction A —> products with simple reaction kinetics (Van Santen etal., 1999). Balance equations for multicomponent homogeneous systems for any reaction network and for gas-liquid and gas-liquid-solid systems are presented in Tables 5.4-7 and 5.4.8 at the end of Section 5.4.3. 

The flow pattern of fluids in gas-liquid-solid (catalyst) reactors is often far from ideal. Special care must be taken to avoid by-passing of the catalyst particles near the reactor walls, where the packing density of the catalyst pellets is lower than in the centre of the bed. By-passing becomes negligible if the ratio of reactor to particles diameter is larger than 10 a ratio of 20 is recommended. Flow maldistributions might be serious in the case of shallow beds. Special devices must be used to equalize the velocity over the cross-section of the reactor before reactants are introduced onto the catalyst bed. 

Prior to the development of modern SPE formats, liquid-solid partitioning with charcoal, silica, Florisil, and/or alumina was common to aid in the removal of lipids in the determination of nonpolar pesticides, but these sorbents are less useful in the cleanup of semi-polar and polar pesticides owing to the large elution volumes needed. Applications of modern SPE are discussed in Section 3.2. 

For the remainder of this chapter, we discuss results for various studies of interfacial solvation dynamics. We first discuss studies at liquid liquid interfaces at planar interfaces and in microheterogeneous media in Section II. In Section III, we discuss solvation dynamics at liquid solid interfaces. In Section IV, we review theoretical models and simulations of solvation dynamics at liquid interfaces. Finally, we conclude with a discussion of future studies. 

As discussed in Section II.A, Eisenthal and coworkers have studied the related problem of isomerization at liquid-solid interfaces. They used time-resolved second harmonic generation to investigate the barrierless photoisomerization of malachite green at the silica-aqueous interface using femtosecond time-resolved second harmonic generation [26]. They found that the photoisomerization reaction proceeded but was an order of magnitude slower at the water-silica interface than in bulk solution. 

In liquid-solid extraction (LSE) the analyte is extracted from the solid by a liquid, which is separated by filtration. Numerous extraction processes, representing various types and levels of energy, have been described steam distillation, simultaneous steam distillation-solvent extraction (SDE), passive hot solvent extraction, forced-flow leaching, (automated) Soxh-let extraction, shake-flask method, mechanically agitated reflux extraction, ultrasound-assisted extraction, y -ray-assisted extraction, microwave-assisted extraction (MAE), microwave-enhanced extraction (Soxwave ), microwave-assisted process (MAP ), gas-phase MAE, enhanced fluidity extraction, hot (subcritical) water extraction, supercritical fluid extraction (SFE), supercritical assisted liquid extraction, pressurised hot water extraction, enhanced solvent extraction (ESE ), solu-tion/precipitation, etc. The most successful systems are described in Sections 3.3.3-3.4.6. Other, less frequently... 

Cyclones can be used for the classification of solids, as well as for liquid-solid, and liquid-liquid separations. The design and application of liquid cyclones (hydrocyclones) is discussed in Section 10.4.4. A typical unit is shown in Figure 10.3. 

Thickeners, thickeners are primarily used for liquid-solid separation (see Section 10.4). When used for classification, the feed rate is such that the overflow rate is greater than the settling rate of the slurry, and the finer particles remain in the overflow stream. 

The term two-phase flow covers an extremely broad range of situations, and it is possible to address only a small portion of this spectrum in one book, let alone one chapter. Two-phase flow includes any combination of two of the three phases solid, liquid, and gas, i.e., solid-liquid, gas-liquid, solid-gas, or liquid-liquid. Also, if both phases are fluids (combinations of liquid and/or gas), either of the phases may be continuous and the other distributed (e.g., gas in liquid or liquid in gas). Furthermore, the mass ratio of the two phases may be fixed or variable throughout the system. Examples of the former are nonvolatile liquids with solids or noncondensable gases, whereas examples of the latter are flashing liquids, soluble solids in liquids, partly miscible liquids in liquids, etc. In addition, in pipe flows the two phases may be uniformly distributed over the cross section (i.e., homogeneous) or they may be separated, and the conditions under which these states prevail are different for horizontal flow than for vertical flow. 

Denote the superficial liquid-solids velocity ratio (.L/pfA)/(S/psA) by N, and let (S/psut) =At. which is the minimal cross-sectional area if the solids were to flow at their terminal velocity, up in the absence of fluid flow, and can, therefore, be called terminal cross-sectional area. Then Eq. (2) can be reduced to a dimensionless form in terms of a reduced area, A, defined as follows... 

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