Heterogeneous Case

In practice, container walls are usually present, and the liquid is rarely free from dust particles, adsorbed gas, absorbed gas, and foreign ions. Heterogeneous nucleation refers to the formation of nuclei on a foreign object. 

Vapor bubble on a flat surface. The foregoing shape exists if the liquid wets the solid poorly. 

As for the work of forming a nucleus, consider the simple case of the effect of a foreign solid surface. If the vapor and the liquid both wet the foreign surface, the work will be less than for the homogeneous case. This decrease will result in an increased rate of nucleation per nucleation site at the same superheat. 

Assume that a bubble forming on a solid is a segment of a sphere, as shown in Fig. 19. This shape corresponds to a volume of minimum free energy. The contact angle /9 is greater than 90° for a system such as water on wax. It is usually less than 90° for systems such as water on metal. The reversible work of formation (F3) is 

The work of forming a bubble of critical size, a nucleus, is 

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If the nucleation is random, we will have the homogeneous case if it is specific (with foreign or phase boundary walls), we have the heterogeneous case, vis-... 

The Heterogeneous Case. Hachiya et al. (1984) and Hayes and Leckie (1986) used the pressure-jump relaxation method to study the adsorption kinetics of metal ions to oxide minerals. Their results support in essence the same adsorption mechanism as that given for homogeneous complex formation. 

Although no direct evidence was available, Ben-Taarit et al. advanced a tentative mechanism for propylene oxidation [2]. As only heterogeneous or mixed oxides catalyze the formation of acrolein, the behavior of Cu+ y zeolite is similar to the heterogeneous case. On the contrary, on Rh +Y, acetone was selectively produced [2]. This is now in line with the behavior of Rh salts in... 

The work Wx of creating a cluster of x monomers will now be considered. This involves changing x superheated liquid molecules into a vapor cluster and will depend on whether the cluster forms within the liquid mass (homogeneous case) or whether it forms on the surface of a wall or foreign inclusion (heterogeneous case). 

Inspection of Table 18.3 reveals that in principle any reaction catalyzed by orga-nometallic catalysts is amenable to running in a CMR. Further, enanhoselechvities seem to be just as high in the non-heterogenized case. The space-time yields achieved, often in excess of 1 kg (L d) 1, point to the potentially very favorable volumetric productivities of a CMR configuration. 

Huber, M., Rettler, I., Bernasconi, K., Wyss, M., and Hohl, D., Lamellar ichthyosis is genetically heterogenous — cases with normal keratinocyte transglutaminase, J. Invest. Dermatol., 105, 653, 1995. 

Within the framework of the transition state theory [112,113], the observed activation energy, Eobs, for a monomolecular catalytic process in the heterogeneous case is Eobs = E0 + A//ads [act. complex], where E0 is the energy of the reaction without a catalyst and A//.lds act. complex] is the adsorption enthalpy of the activated complex [114], In the monomolecular cracking of n-alkanes catalyzed by... 

Figure 7. Eleotroosmotic streamlines at the midplane of a 50pm T-shaped micromixer for the a) homogeneous case with = -42 mV, b) heterogeneous case with six offset patches on the left and right channel walls. All heterogeneous patches are represented by the crosshatched regions and have a = + 42mV. The applied voltage is (baoD = 500 V/cm.

Figure 8. 3D species concentration field for a 50pm x 50pm T-shaped micromixer resulting from die flow fields shown in Figure 7. (a) homogeneous case, and (b) heterogeneous case with offset patches. Species diffiisivity is SxlO mVs and zero electrophoretic mobility are assumed. 

Typical results from this study are shown in Fig. 2. Here the breakthrough curves at the target are shown for both cases. As can be seen, the breakthrough in the heterogeneous case is much faster than would have been expected if calculated using homogeneous case assumptions. The consequence for the practical safety assessment of a pollution incident are self evident. 

A rate expression, n, as a function of concentration and temperature, for each of the nr reactions is required to complete the problem description. Equations 7.1 and 7.2 can be used for any reaction within the reactor as long as the plug-flow conditions are satisfied. These balances are applicable to reactions that are homogeneous or heterogeneous the heterogeneous case is referred to as a fixed-bed reactor. 

So was the case of the heterogeneous linear homopolymerization of MMA in SC-CO2, also addressed in Chapter 15 (Figs 15.7, 15.8, and 15.9), and copolymerization with crosslinking in SC-CO2 (Fig. 15.10). The only change in those heterogeneous cases was that additional equations... 

In spite of the great number of investigations on CP-driven chemical deposition of metal particles there have been almost no attempts to address the mechanism of this process, either in homogeneous or heterogeneous cases. In a homogeneous system with dispersed metal ions and CP species, the process most probably includes continuous formation of metal nuclei that provide a catalytic surface for further reduction of metal ions and give rise to autocatalytic growth [254]. 

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