Fick's Second Law of Diffusion
Diffusivity is not dependent on time. It is dependent on temperature (and material). Fick's second law holds because the diffusivity, $D$, is constant with respect to depth, $x$, and time, $t$, so it is treated as a constant in the equation.

$$\frac{\partial c_{x}}{\partial t}=\frac\partial{\partial x}\left(D\frac{\partial c_{x}}{\partial x}\right) = D\left(\frac{\partial^2c_x}{\partial x^2}\right)$$

Fick's second law of diffusion applies to non steady state diffusion, which concentration at a depth $x$, $c_x$ is a function of time.