Heterogeneities, effect

For heterogeneous propellants, the current situation is much less satisfactory. The complexity of the combustion process was discussed in Section 7.7. To employ a result like equation (66) directly is questionable, although attempts have been made to evaluate parameters like A and B of equations (67) and (68) from complicated combustion models for use in response-function calculations [81], [82]. Relatively few theories have been addressed specifically to the acoustic response of heterogeneous propellants [82]. Applications of time-lag concepts to account for various aspects of heterogeneity have been made [60], [83], a simplified model—including transient variations in stoichiometry—has been developed [84], and the sideways sandwich model, described in Section 7,7, has been explored for calculating the acoustic response [85], There are reviews of the early studies [7] and of more recent work [82], 

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From Eq. (33) it follows that, in the case of very large homogeneous domains, even very small heterogeneity effects should completely destroy any phase transition connected with the adsorbate condensation. This result is quite consistent with the theoretical predictions stemming from the random field Ising model [40,41]. 

In Fig. 14 the points for Cu, Ag, and Au are also shown. In view of the large heterogeneity effect on the value of for these metals, the points are those for the (110) face which, however, shows behavior close to that of a polycrystalline surface.6 While these metals will be discussed in a separate plot, they are also shown here to highlight the relationship with the sp-metals. 

Patella V, Ciccarelli A, Lamparter-Schummert B. de Paulis A, Adt M, Marone G Heterogeneous effects of protamine on human mast cells and basophils. Br J Anaesth 1997 78 724. 

The above list of effects reveals that transport and its environment do not suffer from a single problem, but from several heterogeneous effects caused by different modes and affecting different population groups or environmental sectors with individual... 

Extracting Information ABOUT Surface Heterogeneity Effect on Heterogeneous Reactions Using Multifractal Scaling... 

Extracting Information about Surface Heterogeneity Effect on Heterogeneous... 371... 

Kevorkian et al.68 pyrolyzed CH4 in a shock tube at 1656-1965°C. and observed first-order decomposition with an activation energy of 93 ( 10%) kcal. These observations were said to be free of heterogeneous effects and to support, but not to confirm reaction (9) as the initial step. In another shock-tube study, Skinner and Ruehrwein126 found an activation energy for CH4 decomposition of 101 kcal. and concluded that the initial step is reaction (10), based largely on the similarity of the activation energy to the endothermicity of the reaction. 

These observations suggest that the heterogeneous effect in the S02-modenite system represents an extreme case, so much so that chemisorp-tive bonds may be stipulated (probably between the S02 and the cations). These effects would, of course, involve energy emission and show up in the calorimetric measurements. However, the specificity of the adsorption would tend to show a relatively temperature-insensitive isotherm in the low-pressure region, thus rendering the isosteric techniques of obtaining heats of adsorption/chemisorption ineffective. 

More recently, Sole391 studied the system to determine the extent, if any, of heterogeneous reaction. By means of differential calorimetry, he compared the heat transferred to the vessel walls with that transferred to a probe in the center of the vessel. He found that heterogeneous effects could be completely disregarded. 

Jeffers, P.M., P. Coty, S. Luczak, and N.L. Wolfe. 1994. Halocarbon hydrolysis rates - A search for ionic strength and heterogeneous effects. J. Environ. Sci. Health. A29 821-831. 

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