Void, fraction

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

Knudsen diffusion coefficient for the test gas in a micropore. represents the total void fraction and c that part of of the void fraction... 

Here c denotes the void fraction and T a tortuosity factor, while G... 

Most of the voltage savings in the air cathode electrolyzer results from the change in the cathode reaction and a reduction in the solution ohmic drop as a result of the absence of the hydrogen bubble gas void fraction in the catholyte. The air cathode electrolyzer operates at 2.1 V at 3 kA/m or approximately 1450 d-c kW-h per ton of NaOH. The air cathode technology has been demonstrated in commercial sized equipment at Occidental Chemical s Muscle Shoals, Alabama plant. However, it is not presentiy being practiced because the technology is too expensive to commercialize at power costs of 20 to 30 mils (1 mil = 0.1 /kW). 

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

The same procedure may be applied in principle to design of forced-recirculation reboilers with shell-side vapor generation. Little is known about two-phase flow on the shell side, out a reasonable estimate of the fric tion pressure drop can be made from the data of Diehl and Unruh [Pet Refiner, 36(10), 147 (1957) 37(10), 124 (1958)]. No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms. Tnese may be roughly estimated by assuming homogeneous flow. 

The values of p, and/or <7 must be known in order to use Eqs. (12-26) and (12-27). The value of a is difficult to estimate without experimental data. When the void fraction is known, a can sometimes be estimated from the following relationships ... 

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