Bulk diffusion limitations

There is no doubt that the coefficient of the third term on the right hand side of this equation is much larger than the coefficient of the second term at the bulk diffusion limit, and this justifies our original form (5,29). However, on constructing from and using equation (5,32) and its... 

It remains to check Chat our supposedly general equations (11.20) -(11.23) reduce to the previously obtained limiting forms at the extremes of bulk diffusion and Knudsen diffusion. The bulk diffusion limit is easily obtained by letting — and assuming that for all r, s,... 

Effective diffusion coefficient, in porous medium at bulk diffusion limit, 14... 

Both diffusional flame calculations and detailed spatial mapping indicate that the nondispersed injection mode produces a vapor cloud that is characterized by diffusionally controlled combustion and bulk heating while subjecting the droplets to near isothermal conditions. The soot produced in this cloud is strongly influenced by bulk diffusion limitations and as such represents a bulk soot formation extreme. It was found that fuel changes had little effect on the overall soot yield due to this diffusion control. Lower gas temperatures and richer conditions were found to favor soot formation under bulk sooting conditions, probably due to a decrease in the oxidation rate of the soot. 

Concluding we should point out that Burton, Cabrera and Frank [4.35, 4.53] (see also Lorenz [4.54, 4.55]) have solved also the problem of stationary surface diffusion towards steps with circular symmetry. The theory of the more complex case of combined surface diffusion and bulk diffusion limitations can be found in the works of Fleischmann and Thirsk [4.48], Damjanovich and Bockris [4.50] and Gilmer et al. [4.56]. Note, however, that all these theoretical considerations do not accoimt for difficulties coimected with the so-called Ehrlich-Schwoebel barrier [4.57-4.62]. Elastic [4.63, 4.64] and entropic [4.65] interactions between growing steps are also neglected. 

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