Liquid solid systems

For a solid solution in equilibrium with a liquid, relation (3.3.93) for the equilibrium ratio of species i is 

Here T i is the melting point of species i. For a pure species i at Tmi, fb TmuP) =fli Tmt,P). Exact expressions have been developed for the product of the two remaining ratios. An expression practically useful and based on particular approximations (Smith et al., 2001, pp. 526-531) is 

In the case of leaching of a solid mixture, using expression (3.3.96), one can develop an appropriate expression for the separation factor, Uy, for species i and j being leached out. 

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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]. 

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. 

Thus, the larger the value of (K), the more the solute will be distributed in the stationary phase. (K) is a dimensionless constant and, in gas/liquid and liquidAiquid systems, (Xs) and (Xm) can be measured as mass of solute per unit volume of phase. In gas/solid and liquid/solid systems, (Xs) and (Xm) can be measured as mass of solute per unit mass of phase. 

Nienow, A.W., 1985. The mixer as a reactor Liquid/solid systems. In Mixing in the process industries. Eds. N. Harnby, M.F. Edwards and A.W. Nienow, 1992, 2nd edition. Oxford Butterworth-Heinemann. 

Extraction (sometimes called leaching) encompasses liquid-liquid as well as liquid-solid systems. Liquid-liquid extraction involves the transfer of solutes from one liquid phase into another liquid solvent it is normally conducted in mixer settlers, plate and agitated-tower contacting equipment, or packed or spray towers. Liquid-solid extraction, in which a liquid solvent is passed over a solid phase to remove some solute, is carried out in fixed-bed, moving-bed, or agitated-solid columns. 

Equation (17.7.2.9) was originally used to correlate the minimum fluidisation velocity for gas-solid fluidisation beds but has been successfully employed by Lan and his co-workers42 for adsorbents in the field of direct recovery using liquid-solid systems (Figure 17.4). 

The vast majority of modem liquid chromatography systems involve the use of silica gel or a derivative of silica gel, such as a bonded phase, as a stationary phase. Thus, it would appear that most LC separations are carried out by liquid-solid chromatography. Owing to the adsorption of solvent on the surface of both silica and bonded phases, however, the physical chemical characteristics of the separation are more akin to a liquid-liquid distribution system than that of a liquid-solid system. As a consequence, although most modern stationary phases are in fact solids, solute distribution is usually treated theoretically as a liquid-liquid system. 

Consider a liquid-solid system for which the contact angle is close to 90° (for example, the contact angle for the water-steel system is 70° < 0 < 90° (Grigoriev and Zorin 1982)). The projections of the velocity vector v on x-, y-, z-axes are M = v sin0, v = w = v cos0. For the surface, which is weakly bent, cos 0 v = w. Analogously,... 

Optical systems can be used in multiphase flows at a very low volume fraction of the dispersed phase. Through a refractory index matching of hquid-liquid or liquid-solid systems, it is also possible to measure at high void fractions. However, it is not possible to obtain complete refractory index matching since the molecules at the phase boundary have different optical properties than the molecules in the bulk. Consequently, it is possible to measure at a higher fraction of the dispersed phase with larger drops and particles because of the lower surface area per volume fluid. 

In view of the importance of the particle/bubble contact, it may be assumed that the stress acting on the particles during gas sparging is determined by electrostatic interactions as well as by hydrophobic and hydrophilic interactions, which are determined by the nature of the liquid/solid system. The use of Pluronic as additive leads to the reduction of destruction process [44,47] possibly due to less bubble/floc contact which is also described by Meier et. al. [67]. 

The hydrodynamics in a gas-liquid or gas-liquid-solid system is characterized by the... 

Advances in multiphase reactors for fuel industry are discussed in this work. Downer reactors have some advantages over riser reactors, but suffer from some serious shortcomings. The coupled reactors can fully utilize the advantages of the riser and the downer. For fuel industry that involves gas-liquid-solid system, slurry bed reactors especially airlift reactors are preferred due to their performance of excellent heat control and ease of seale up. For high-pressure processes, the spherical reactor is promising due to its special characteristics. 

Shape selective catalysis as typically demonstrated by zeolites is of great interest from scientific as well as industrial viewpoint [17], However, the application of zeolites to organic reactions in a liquid-solid system is very limited, because of insufficient acid strength and slow diffusion of reactant molecules in small pores. We reported preliminarily that the microporous Cs salts of H3PW12O40 exhibit shape selectivity in a liquid-solid system [18]. Here we studied in more detail the acidity, micropore structure and catal3rtic activity of the Cs salts and wish to report that the acidic Cs salts exhibit efficient shape selective catalysis toward decomposition of esters, dehydration of alcohol, and alkylation of aromatic compound in liquid-solid system. The results were discussed in relation to the shape selective adsorption and the acidic properties. 

In order to confirm further the restriction of the adsorption by the pore in the liquid-solid reaction system, the adsorption of the reactants was measiired at 303 K in the liquid- solid system, at which no reaction took place. Figure 6 provides the time courses of the adsorption of Qrclohexylacetate and isopropylacetate on Cs2.2 and Cs2.5. Both isopropylacetate and cyclohexylacetate adsorbed on Cs2.5 (Figure 6a). The ratio of the adsorption amount was about 1.5 times which is... 

Liquid-liquid-solid system versus liquid-solid system... 

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. 

In catalytic gas-liquid-solid systems mass transfer is more complex. The catalyst particles are present in the liquid phase. The expression for the rate of mass transfer from the gas to the liquid is identical to that for systems without a solid catalyst (Eqn. 5.4-67). However, now also mass transfer from the liquid to the solid surface (external mass transfer) and inside the particle (internal mass transfer) have to be considered. 

The sessile drop method has several drawbacks. Several days elapse between each displacement, and total test times exceeding one month are not uncommon. It can be difficult to determine that the interface has actually advanced across the face of the crystal. Displacement frequency and distance are variable and dependent upon the operator. Tests are conducted on pure mineral surfaces, usually quartz, which does not adequately model the heterogeneous rock surfaces in reservoirs. There is a need for a simple technique that gives reproducible data and can be used to characterize various mineral surfaces. The dynamic Wilhelmy plate technique has such a potential. This paper discusses the dynamic Wilhelmy plate apparatus used to study wetting properties of liquid/liquid/solid systems important to the oil industry. 

The wetting behavior of liquid/liquid/solid systems is not only dependent on the two liquid phases, but upon the interaction of the solid surface with these liquids (see Equation 1). An example is in the wetting cycles for glass and PTFE in a hexadecane/water system. 

In addition, there are a few examples of heterogeneous nonaqueous sonochemistry, in both liquid-liquid and liquid-solid systems. Two recent reports have utilized ultrasonic agitation in place of or along with phase transfer catalysis for the preparation of dichlorocarbene from aqueous NaOH/CHCl3 (166), and for N-alkylation of amines with alkyl halides (167). Along the same lines, several papers have appeared in which... 

Note that for liquid solid systems, Eq. (20) should also include the short-range lubrication forces and the effects of other forces such as the virtual mass force. But this is beyond the scope of this chapter. 

A turbine type agitator is commonly used for liquid-solid systems. Mixing rates depend on the forces required to suspend all solid particles. Minimum levels can be determined for (1) lifting the particles, and (2) for suspending them in an homogeneous manner [200]. Similar requirements apply to liquid-liquid systems. For cases where two poorly miscible fluids of about equal volume are used in the reaction, the mixer is placed at the interface. For a bench-scale experimental system of about 2 liters capacity, the minimum rotational speed to obtain well-dispersed system is 300 to 400 rpm [201], depending on the type of mixer. This rotational value decreases as the vessel volume increases. 

Numerous studies have been made of the hydrodynamics and other aspects of the behavior of gas-liquid-solid systems, in particular of trickle beds, and including absorption and extraction in packed beds. A selection of correlations of these parameters is presented in problem P8.03.02. They tell something of what is going on in three-phase reactors. 

Microbes were frequently found to synthesise surface-active molecules in order to mobilise hydrophobic organic substrates. These biosurfactants, which are either excreted by the producing organisms or remain bound to their cell surfaces, are composed of a hydrophilic part making them soluble in water and a lipophilic part making them accumulate at interfaces. With respect to their physical effects, one can distinguish two types of biosurfactants firstly, molecules that drastically reduce the surface and interfacial tensions of gas-liquid, liquid-liquid and liquid-solid systems, and, secondly, compounds that stabilise emulsions of nonaqueous phase liquids in water, often also referred to as bioemulsifiers. The former molecules are typically low-molar-mass... 

The strongly basic properties of potassium hydroxide are apparent from the work of Dietrich and Lehn (1973) who reported that the liquid-solid system KOH/THF/[2.2.2]-cryptand was capable of generating the anions of weak carbon acids such as triphenylmethane [142], diphenylmethane [143], and fluorene. The same anions could be generated using NaNH2 instead of KOH. 

Lee and Chang (1978) have compared the ability of linear polyethers, crown ethers, and quaternary ammonium compounds to catalyse oxidations with KMn04 under liquid-liquid and liquid-solid conditions. In the presence of acetic acid as a scavenger for the KOH produced, the products of olefin oxidation were carboxylic acids, diones, diols and ketols. The three different classes of catalysts exhibited about the same activity in liquid-solid systems. 

Chemical reactions on solid surfaces can be realized in gas-solid and liquid-solid systems. In both cases the reaction takes place on the surface of the solid matrix, and therefore the molecules to be reacted need to get in contact with the reactive surface. Several transport regimes and interaction mechanisms define the mass transfer efficiency. They can be summarized as follows [6] ... 

ZANKER, A. In Separation Techniques Vol 2 Gas Liquid Solid Systems (McGraw-Hill, 1980), p. 178. Hydrocyclones dimensions and performance. 

General behaviour of gas solids and liquid solids systems... 

Average values of heat-transfer coefficients to liquid-solids systems 97-99 have been measured using small electrically heated surfaces immersed in the bed. The temperature of the element is obtained from its electrical resistance, provided that the temperature coefficient of resistance is known. The heat supplied is obtained from the measured applied voltage and resistance and is equal to V2/R, where V is the voltage applied across the element, and R is its resistance. 

Heat transfer coefficients for a number of gas-solids systems were measured by Richardson and Shakiri 112 using an electrically heated element 25 mm square over a range of pressures from sub-atmospheric (0.03 MN/m2) to elevated pressures (up to 1.5 MN/m2). The measuring technique was essentially similar to that employed earlier for liquid-solids systems, as described in Section 6.5.2. 

Fluidised beds may be divided into two classes. In the first, there is a uniform dispersion of the particles within the fluid and the bed expands in a regular manner as the fluid velocity is increased. This behaviour, termed particulate fluidisation, is exhibited by most liquid-solids systems, the only important exceptions being those composed of fine particles of high density. This behaviour is also exhibited by certain gas-solids systems over a very small range of velocities just in excess of the minimum fluidising velocity—particularly where the particles are approximately spherical and have very low free-falling velocities. In particulate fluidisation the rate of movement of the particles is comparatively low, and the fluid is predominantly in piston-type flow with some back-mixing, particularly at low flowrates. Overall turbulence normally exists in the system. 

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