Asset Details
Do you wish to reserve the book?
A Direct Derivation of Fick’s Law for Multicomponent Diffusion
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
A Direct Derivation of Fick’s Law for Multicomponent Diffusion
Do you wish to request the book?
A Direct Derivation of Fick’s Law for Multicomponent Diffusion
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
A Direct Derivation of Fick’s Law for Multicomponent Diffusion
2022
Overview
Fick’s law applicable to isothermal solid-solid
n
-component diffusion couples has been recently derived by the author directly from the continuity equation. The derivation is briefly reviewed in this paper and general expressions applicable to the determination of interdiffusion coefficients,
D
~
ij
n
(
i
,
j
=
1
,
2
,
…
n
-
1
)
, are developed for isothermal, diffusion couples with constant molar density. Explicit expressions for ternary and quaternary interdiffusion coefficients,
D
~
ij
3
(
i
,
j
=
1
,
2
)
and
D
~
ij
4
(
i
,
j
=
1
,
2
,
3
)
, are also presented. These expressions developed for the calculation of both main and cross interdiffusion coefficients at a section
x
include various partial derivatives of
[
(
J
~
i
)
·
(
x
-
x
o
)
]
(
i
=
1
,
2
,
…
n
-
1
)
with respect to individual concentrations
C
j
, where
J
~
i
is the interdiffusion flux of component
i
based on a laboratory-fixed frame and
x
o
is the Matano plane for the couple. In this paper the analysis is applied to the concentration profiles theoretically calculated for an isothermal, binary diffusion couple characterized by a constant interdiffusion coefficient
D
~
to illustrate the validity of the analysis. A parabolic representation of the derivative,
d
[
(
J
~
i
)
·
(
x
-
x
o
)
]
/
d
C
i
(
i
=
1
,
2
)
that is involved in the expression for
D
~
, is also developed as a function of
x
, and such representation has been shown to be useful for the calculation of
D
~
for the binary diffusion couple. The parabolic representation of the terms employed for the determination of the binary
D
~
is presented for the first time in this study.
Publisher
Springer US,Springer Nature B.V
Subject
