The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient
2021 ◽
Vol 16
◽
pp. 59-67
Keyword(s):
In this work it is considered the Fick’s second law in a context in which the diffusion coefficient depends on the concentration. It is employed the Kirchhoff transformation in order to simplify the mathematical structure of the Fick’s second law, giving rise to a more convenient description. In order to provide a general protocol, the diffusion coefficient will be assumed a piecewise constant function of the concentration. Exact formulas are presented for both the Kirchhoff transformation and its inverse, in such a way that there is no limit of accuracy. Some numerical examples are presented with the aid of a semi-implicit procedure associated with a finite difference approximation.
2013 ◽
Vol 18
(3)
◽
pp. 325-345
◽
Keyword(s):
2011 ◽
Vol 01
(02)
◽
pp. 134-138
◽
2018 ◽
Vol 168
(1)
◽
pp. 29-41
◽
2021 ◽