By Professor Dr. M. H. Jacobs (auth.)
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Extra resources for Diffusion Processes
While equations (28) and (29) enable all cases to be dealt with which involve measurements of concentrations at different levels and times, it has already been mentioned that the commonest closedsystem methods depend upon chemical determinations at the end of the experiment of the quantities of the diffusing substance contained in layers of finite thickness. The equations necessary to evaluate this type of experimental data are very readily derived. It is obvious that the amount of substance contained in an elementary layer lying between x and x dx is uAdx, where A is the area of the layer, and where u can be obtained from equation (28).
With finite systems, this relation will of course not be obtained when the initial layers of solution and water are of unequal thickness. While equations (28) and (29) enable all cases to be dealt with which involve measurements of concentrations at different levels and times, it has already been mentioned that the commonest closedsystem methods depend upon chemical determinations at the end of the experiment of the quantities of the diffusing substance contained in layers of finite thickness. The equations necessary to evaluate this type of experimental data are very readily derived.
It has sometimes been objected (BROOKS and BROOKS 1932) that since partition is an equilibrium phenomenon it cannot properly be used for the purpose of predicting rates of diffusion. In reply, however, it may be pointed out, as has been done by COLLANDER and BARLUND, OSTERHOUT and others, that the rate of diffusion across a non-aqueous phase depends on the difference rather than on the ratio of the concentrations of the diffusing substance on the two sides of this phase. If, therefore, the concentrations of the diffusing substance in the two aqueous media be C1 and c2 , respectively, and the partition coefficient between the non-aqueous medium and water be 5, the effective concentration gradient across the interposed layer, under equilibrium or nearly equilibrium conditions, must be 5 c1 -;; 5 C2 - in other words, the partition effect will multiply the gradient that would otherwise exist by 5 and, other things being equal, will increase the rate of diffusion to the same to much interesting information: GRAHAM (1861), CHABRY (1888), VOIGTLANDER (1889), REFORMATSKY (1891), PRINGSHEIM (1895a, b),HAGENBACH (1898), CALUGAREANU and HENRI (1901), NELL (1905), BECHHOLD and ZIEGLER (1906a, b), MEYER (1906), DUMANSKI (1908), YEGOUNOW (1906, 1908), 6HOLM (1913), VANZETTI (1914), FURTH and BUBANOVIC (1918a, b), FURTH, BAUER and PIESCH (1919), GRAHAM and GRAHAM (1918), STILES (1920, 1921, 1923), STILES and ADAIR (1921), ADAIR (1920), TRAUBE and SHIKATA (1923), AUERBACH (1924), MANN (1924).