Fick’s Law

Definition

Fick’s First Law

It is considered that the concentration gradient of elements in mineral and rock resulted from an evidence of diffusion, and the nonequilibrium state was frozen in them. The mobile element found the concentration gradient in material is useful as the tracer to estimate the timescale. The tracer diffuses in a manner to decrease the concentration gradient from the material surface. In such cases, the flux density of species, i, in the three dimensions is given by

$$ {J}_i=-{D}_i\rho \nabla {C}_i $$

(1)

where D_i is the diffusion coefficient, ρ is the density, and ∇C_i is the mass fraction concentration gradient. In one dimension, Eq. 1 becomes

$$ {J}_i=-{D}_i\rho \left(\frac{\partial {C}_i}{\partial x}\right) $$

(2)

Fick’s Second Law

Equation 2 is written with the consideration of the conservation of mass. It can be shown that

$$ \frac{\partial {C}_i}{\partial t}=\frac{\partial }{\partial x}\left({D}_i\frac{\partial {C}_i}{\partial x}\right) $$

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