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Concentration-Dependent Diffusion in One Dimension Hiroshi FUJITA'k

By Received September


The method of moments is applied to problems of one-dimensional diffusion involv-ing a general concentration-dependent diffusion coefficient. The general procedure of application is illustrated for the case in which a solute diffuses into a plane sheet of uniform thickness from a surrounding solution; for simplicity, it is assumed that both surfaces of the sheet.attain a state of equilibrium with the surrounding solution instan-taneously when the sheet is immersed in it. To simplify the mathematics only the zeroth and first moment equations are used in all the problems treated in this study. The gene-ral procedure is first applied to the case in which the diffusion coefficient is independent of concentration, in order to check the reliability of the method; excellent agreements are found with the exact solution in all respects examined, except for the behavior at suf-ficiently small values of time. The method is then applied to the diffusion coefficient varying linearly with concentration, again with a satisfactory agreement with the numeri-cal and graphical solutions obtained by previous workers for this particular case. Ap-proximate solutions are obtained, using the method of moments, for one-dimensional dif-fusion problems in a semi-infinite medium involving diffusion coefficients dependent bot

Year: 2015
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