Three-phase systems, determination

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

These should normally be used in a box form for better mounting, uniformity and metal utilization. The method of determining the reactance for single- and three-phase systems is the same as for rectangular sections (Figure 28.20(a)). 

In this work it has been demonstrated that parallel fixed bed reactor system facilitates experimentation of heterogeneous catalysts in three-phase systems. The residence times and Reynolds numbers were determined. The Reynolds numbers were veiy... 

Solvents and solids, as well as water constituents, can have varying influences on kLa, depending not only on their properties but also on the hydrodynamics of the system (as discussed in Section B 3.2). Therefore, the kLa and the alpha-factor (ratio of kLa in the three-phase-system to the one in water) in the three-phase system under operating conditions similar to the ozonation experiments should always be determined. 

The driving force for the mass transfer of the solute in the three-phase system can be determined with the solvent/water partition coefficient, just as the partition coefficient for gas/liquid phases, the Henry s Law constant, is used to determine the driving force for the mass transfer of ozone. A solute tends to diffuse from phase to phase until equilibrium is reached between all three phases. This tendency of a solute to partition between water and solvent can be estimated by the hydrophobicity of the solute. The octanol/water partition coefficient Kow is a commonly measured parameter and can be used if the hydrophobicity of the solvent is comparable to that of octanol. How fast the diffusion or transfer will occur depends not only on the mass transfer coefficient in addition to the driving force but also on the rate of the chemical reaction as well. 

Simple sequential processes frequently do not yield particles with the planned architectures. This is because of the complexity of emulsion polymerizations and because a system in which different polymers coexist with water will tend to rearrange toward the composition with the lowest overall surface energy. Theoretical descriptions of such phenomena [17-19] are based on the concept that the final state of the system consisting of polymer I, polymer 2, and water (labeled phase 3) depends on the three interfacial tensions yi2, Y2i and y2.i. and the corresponding interfacial areas. The equilibrium state of the three phases is determined by the minimum value of the surface free energy, Gy. 

In the case of adsorption of a vapor by a porous material, a three phase system in terms of SAS is produced pore/adsorbed film or capillary condensed vapor/solid. Since the s.l.d. of H2O and D2O are known while the pore space s.l.d. equals to zero, contrast matching conditions are achieved if an appropriate mixture of H2O/D2O that has the same s.l.d. as the solid is used as the adsorbate. In this case the adsorbed film as well as the condensed cluster of pores will cease to act as scatterers, and only the remaining empty pores will produce measurable scattering. In terms of SANS, contrast matching reduces the solid/film/pore system to a binary one [1]. By determining a number of scattering curves corresponding to the same sample equilibrated at various relative pressures, for both the adsorption and desorption branches of the adsorption isotherm, a correlation of the two methods could be possible. If the predictions of the Kelvin equation are in accordance with the SAS analysis, a reconstruction of the adsorption isotherm can be obtained from the SAS data [2]. 

Thus, to determine the thermodynamic properties per unit mass of a single-component, two-phase mixture, we need to specify the equivalent of one single-phase state variable (the one degree of freedom) and one variable that provides information on the mass distribution. The additional specification of one extensive property is needed to determine the total mass or size of the system. Similarly, to fix the thermodynamic properties of a single-component, three-phase mixture, we.need not specify any single state variable (since the triple point is unique), but two variables that provide information on the distribution of mass between the vapor, liquid, and solid phases and one extensive variable to determine the total mass of the three-phase system. 

Experimental Examples. An example may be given of the applicability of the forementioned theories to a complex but well defined morphology. It is well known that in commercial high impact polystyrene (HIPS) the dispersed rubber phase, the gel, is filled with up to 75% occluded polystyrene (PS) (15, 16). In principle, we have a three-phase system Keskkula and Turley (17) succeeded in isolating the gel and determining its dynamic mechanical... 

The specific mixing power can also be determined from (9.335) by experimentally determining the rate of a mass transfer or the heat released in the process. For instance, the dissolution of solid materials is limited by mass transfer and could be used for calculation of mass transfer coefficients and specific mixing power. An example illustrating how the calculations could be performed for a three-phase system will be presented in the following section. 

We determine first the equilibrium temperatures and pressures for coexistence. Conde and Vega in their work [31] performed similar calculations using long NPT MD trajectories (up to 1 ps). They waited for complete crystallization or complete melting of the initial three-phase system at several fixed temperatures. We follow another approach looking directiy for the phase coexistence conditions. 

In a three phase system with two components, Gibb s phase rule dictates that only one degree of freedom exists. Therefore, for a defined pressure there is only one temperature at which the three phases coexist. In order to determine this equilibrium temperature using MD simulations, many simulations are conducted for a range of temperatures at the same pressure. One can then... 

In order to design an extraction unit, the rate-limiting step in the extraction process has to be determined. As explained in Section 14.4 and Fig. 14.3, the film model can be used to describe extraction in the three-phase system. The overall mass transfer flux of monomer in this extraction process is given by Eq. (14)... 

Phenomena at the gas-liquid and at the liquid-solid interfaces are governed by properties of the gas, the liquid and the solid such as density, viscosity, surface tension, wettability... These properties are numerous to characterize a three phase system which therefore shall be very difficult to simulate by another one let us for instance mention here the non validity for organic systems of the physical kinetics correlations determined with aqueous systems. Moreover, the interfacial phenomena and the significant physico-chemical properties to be considered are far being well known for instance, the foaming ability of organic liquids is not determined univocally by their density. 

---