Abstract
and we must therefore plot f(S2, T21 a)1 f(SI, Til a) as a function of D instead of G O (S2)/G O (SI). Now T2 and Tl indicate the average radii, respectively, at t2 and fl. A plot of f(s) for various values of Tlx is given in Fig. 2 , to show the general behavior of f(s). From this graph it can be seen that for concentrations which are likely to matter, Go(s) can be used instead of f(s) if Tlx::S;1O-2 . Here T can be as small as 10-4 cm, in which case the stationary flow approximation can be used for particles 10-2 cm from the original interface. At concentrations smaller than those covered in the graph f(s, 0.01) and Go(s) may differ appreciably. The larger the value of s, the larger the ratio of f(s, 0.01) to JOURNAL OF APPLIED PHYSICS Go(s) becomes. For large values of s, however, both of these functions are extremely sensitive to the value of s, since they both contain a factor e-•'. (At low concentrations G can be approximated by (1/ 1l')(1/ s)e-•'.) A small change in D and hence in s can cause a large change in this exponential. It can be shown on this basis that an error of less than 2 percent in the evaluation of D will be made by using Go(s) instead of f(s, 0.01) for s>3.0.
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