Effectiveness factor liquid-solid

Additional Factors Affecting Evaporation Times. For liquid drops containing solids, which lower the normal vapor pressure of the liquid, the net effect of the solids is to increase the time for complete evaporation, Marshall (1954). The presence of solids introduces an additional complication associated with the changing droplet surface temperature during the evaporation process. This gives rise to longer evaporation times. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Al-Dahhan and Dudukovic, 1996 Dudukovic et al., 1999). This way, more solid-liquid contact points over which the liquid flows are created and the bed porosity is reduced, especially near the reactor wall. Following a proper procedure for packing a trickle bed with catalyst particles and fines decouples the apparent kinetics from hydrodynamics, which is highly desirable. The addition of lines is not the same as reducing the particle size of the catalyst, as in the latter case the particle effectiveness factor is smaller. 

The effectiveness factor is very low, indicating that intraparticle mass transfer resistance is very significant. The gas-liquid mass transfer resistance is also important, as expected. On the other hand, the liquid-solid mass transfer resistance is negligible. As a result, the rate of reaction in the slurry reactor is about 50 times higher than that in the trickle-bed. Therefore, in cases of such high rates of reaction, the slurry reactor is a better choice, although the gas-liquid mass transfer and the filtration of the catalyst may be a problem. 

The design of a gas-liquid-solid reactor is very much dependent upon the size of the solid particles chosen for the reaction and the anticipated value of the effectiveness factor is one of the most important considerations. Generally, the smaller the particle size the closer the effectiveness factor will be to unity. Particles smaller than about 1 mm in diameter cannot, however, be used in the form of a fixed bed. There would be problems in supporting a bed of smaller particles the pressure drop would be too great and perhaps, above all, the possibility of the interstices between the particles becoming blocked too troublesome. There may, however, be other good reasons for choosing a fixed-bed type of reactor. 

The pseudohomogeneous reaction term in Equation (11.42) is analogous to that in Equation (9.1). We have explicitly included the effectiveness factor rj to emphasis the heterogeneous nature of the catalytic reaction. The discussion in Section 10.5 on the measurement of intrinsic kinetics remains applicable, but it is now necessary to ensure that the liquid phase is saturated with the gas when the measurements are made. The void fraction s is based on relative areas occupied by the liquid and solid phases. Thus,... 

An appropriate model for trickle-bed reactor performance for the case of a gas-phase, rate limiting reactant is developed. The use of the model for predictive calculations requires the knowledge of liquid-solid contacting efficiency, gas-liquid-solid mass transfer coefficients, rate constants and effectiveness factors of completely wetted catalysts, all of which are obtained by independent experiments. 

Solid phase micro-extraction (SPME) allows isolation and concentration of volatile components rapidly and easily without the use of a solvent. These techniques are independent of the form of the matrix liquids, solids and gases can be sampled quite readily. SPME is an equilibrium technique and accurate quantification requires that the extraction conditions be controlled carefully. Each chemical component will behave differently depending on its polarity, volatility, organic/water partition coefficient, volume of the sample and headspace, speed of agitation, pH of the solution and temperature of the sample (Harmon, 2002). The techniques involve the use of an inert fiber coated with an absorbant, which govern its properties. Volatile components are adsorbed onto a suitable SPME fiber (which are usually discriminative for a range of volatile components), desorbed in the injection chamber and separated by a suitable GC column. To use this method effectively, it is important to be familiar with the factors that influence recovery of the volatiles (Reineccius, 2002). 

Products formed in plant cells are usually intracellular storage products and must therefore be released from the cells if the product is to be continuously collected in the medium. This is especially important in immobilized cell systems. There are several environmental factors that will allow for release of products such as modifications in the media pH (35) and addition of solvents that permeabilize the cells Q, 36). It has also been demonstrated that operation in two-phase reactors, where the products are extracted into the nonaqueous phase, can be effective. Both liquid-liquid (37) and liquid-solid (38) systems have been used. The continuous release of products in this manner would also favor their continuous production since the storage capacity of the cells would not become limiting. 

Satterfield150 considers a special case of the above equation, in which the gas-phase resistance is neglected (i.e., the second term on the right-hand side of the above equation is zero) and the catalyst effectiveness factor is assumed to be unity. In this case, a series of measurements of AG/R for various catalyst loadings permits a plot of AG/R versus 1/m to be established. The intercept yields the gas-liquid mass-transfer coefficient and the slope yields a combination of the intrinsic rate constant and the liquid- solid mass-transfer coefficient. 

If a transport parameter rc — CS/CL is defined, where Cs is the concentration of C at the catalyst surface, then Peterson134 showed that for gas-solid reactions t)c < rc, where c is the catalyst effectiveness factor for C. For three-phase slurry reactors, Reuther and Puri145 showed that rc could be less than t)C if the reaction order with respect to C is less than unity, the reaction occurs in the liquid phase, and the catalyst is finely divided. The effective diffusivity in the pores of the catalyst particle is considerably less if the pores are filled with liquid than if they are filled with gas. For finely divided catalyst, the Sherwood number for the liquid-solid mass-transfer coefficient based on catalyst particle diameter is two. 

Increasing the pressure of the gaseous reactant not only increases the amount present in the gas phase but also increases gas/liquid transport and the solubility of the gas in the liquid phase. This, in turn, facilitates liquid/solid transport of this species. All of these factors increase the availability of the gaseous reagent to the catalyst. Fig. 5.11 shows a typical plot for the relationship between hydrogen pressure and the reaction rate at a fixed catalyst quantity and agitation rate.28 At lower values an increase in pressure promotes an increase in rate but above a given value further increases in pressure have little or no effect on the rate. In the... 

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

Loop Reactors For some gas-liquid-solid processes, a recirculating loop can be an effective reactor. These involve a relatively high horsepower pumping system and various kinds of nozzles, baffles, and turbulence generators in the loop system. These have power levels anywhere from 1 to 10 times higher than the power level in a typical mixing reactor, and may allow the retention time to be less by a factor of 1 to 10. 

The retention model developed by Eon and Guiochon [7,8] to describe the adsorption effects at both gas-liquid and liquid-solid interfaces, which was later modified by Mdckel et al. [6] to account for the retention at chemically bonded reversed-phase materials in HPLC, is not applicable to ion chromatography. But if the dependence of the capacity factors of various inorganic anions on the column temperature is studied, certain parallels with HPLC are observed. The linear dependences shown in Fig. 3-2 are obtained for the ions bromide and nitrate when the In k values are plotted versus the reciprocal temperature (van t Hoff plot). However, in the case of fluoride, chloride, nitrite, orthophosphate, and sulfate, the k values were found to be constant within experimental error limits in the temperature range investigated. Upon linear regression of the values in Table 3-1, the following relations are derived for bromide and nitrate ... 

The choice of operation modes and, if applicable, suitable imaging environments depend on many factors, including the type of polymer system to be analyzed and the type of information that is required. Biologically relevant materials or effects that are intrinsic to the liquid—solid interface, for instance, require, of course, AFM under liquid. For a number of experiments, these almost trivial considerations dictate the choice and we refer to the hands-on sections in the corresponding chapters for more detailed information. 

When a solid has been solubilized in the liquid prior to the introduction of the compressed gas, the volumetric expansion is accompanied by a decrease of the liquid solvent strength, which causes the solid to precipitate as ultra fine particles. The physicochemical properties of the solute of interest strongly influence the choice of a solvent/antisolvent pair. The antisolvent should have appreciable mutual solubility with the solvent and should have little or no affinity for the solute. As will be seen, the solute-solvent affinity is also an effective factor that can strongly influence the morphology of the end product. 

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