polykin.transport.diffusion¤
profile_constc_semiinf ¤
profile_constc_semiinf(
t: float, x: float, D: float
) -> float
Concentration profile for transient diffusion in semi-infinite medium.
For a semi-infinite medium, where the concentration is initially \(C_0\) everywhere, and the surface concentration is maintained at \(C_s\), the normalized concentration is:
where \(x\) is the distance from the surface, \(t\) is the time, and \(D\) is the diffusion coefficient.
References
- J. Crank, "The mathematics of diffusion", Oxford University Press, 1975, p. 32.
PARAMETER | DESCRIPTION |
---|---|
t
|
Time (s).
TYPE:
|
x
|
Distance from surface (m).
TYPE:
|
D
|
Diffusion coefficient (m²/s).
TYPE:
|
RETURNS | DESCRIPTION |
---|---|
float
|
Fractional accomplished concentration change. |
Examples:
Determine the fractional concentration change after 100 s in a thick polymer film (diffusivity: 1e-10 m²/s) at a depth of 0.1 mm below the surface.
>>> from polykin.transport import profile_constc_semiinf
>>> profile_constc_semiinf(t=1e2, x=0.1e-3, D=1e-10)
0.4795001221869535
Source code in src/polykin/transport/diffusion.py
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