Nonuniformities slight

A gas is not in equilibrium when its distribution function differs from the Maxwell-Boltzman distribution. On the other hand, it can also be shown that if a system possesses a slight spatial nonuniformity and is not in equilibrium, then the distribution function will monotonically relax in velocity space to a local Maxwell-Boltzman distribution, or to a distribution where p = N/V, v and temperature T all show a spatial dependence [bal75]. 

In order to accurately describe such oscillations, which have been the center of attention of modern liquid state theory, two major requirements need be fulfilled. The first has already been discussed above, i.e., the need to accurately resolve the nonlocal interactions, in particular the repulsive interactions. The second is the need to accurately resolve the mechanisms of the equation of state of the bulk fluid. Thus we need a mechanistically accurate bulk equation of state in order to create a free energy functional which can accurately resolve nonuniform fluid phenomena related to the nonlocality of interactions. So far we have only discussed the original van der Waals form of equation of state and its slight modification by choosing a high-density estimate for the excluded volume, vq = for a fluid with effective hard sphere diameter a, instead of the low-density estimate vq = suggested by van der Waals. These two estimates really suggest... 

Weisman and Pei applied their approach to data from tubes with nonuniform axial heat flux. They found the predictive scheme to hold without the need for any nonuniform heat flux correction factor. The accuracy of their prediction was only slightly less than that of the W-3 correlation, Eq. (5-106), for the data they examined. 

Immediate benefits of switching to the larger-volume cell (Fig. 25) include the formation of larger-area deposits, 2-3 cm, versus the 0.1-0.2 cm deposits obtained using the thin layer flow cell. The thicker layer of solution eliminated problems with IR drops, bubbles, and edge effects except at the top of the deposit. Some nonuniformity at the top of the deposit resulted from small variations in the levels of different solutions pumped into the cell. Rinse solution levels, for instance, were always raised to a slightly higher level than the reactant solutions in order to make sure that the reactants were completely removed after each deposition. 

In the photoelectric method, the measured average work function is always less than the true since patches of high work function tend to be excluded from the emission process. Thus, the nonuniform distribution of adsorbate on a patch surface may cause a slight discrepancy in the evaluation of A. Experimentally, the photoelectric method has various limitations. Photocurrents of the order of 10 A. must be measured accurately in the region of vo, and for films of work function greater than 5 v., the threshold frequency lies in the far ultraviolet—a practical disadvantage. Furthermore, the method is inapplicable at pressures in excess of 10 mm. Hg because of ionization of the gas by collision. 

Other surface charge conditions are naturally also possible and indeed necessary to cover the range of physical situations. Zhmud and House [71], for example, have recently solved the linear Poisson-Boltzmann equation to analyze the behavior of the electrical double layer near a surface which is nonuniformly charged with regions of altering ionization ability. The calculations in this case are only slightly more involved than those above. The generalization to curved surfaces has also been undertaken [72]. 

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