# How does Fick's Law apply to complex diffusion and diffusion within living cells? How can Fick's Law be modified for unsteady-states?

I am trying to understand how diffusion in an unsteady system such as a living cell occurs and if Fick's law can be modified to predict the change in the concentration in the cell over time.

Fick's Law is used to determine the diffusion flux to the concentration in steady state systems and is represented by the equation

$$J = - D \frac{\partial\varphi}{\partial x}$$

where $J$ is the diffusion flux, $D$ is the diffusion coefficient, $x$ is the position/dimension of length, and $\varphi$ is the concentration.

How can Fick's Law and Fick's second law be used to determine how the concentration of a substance within a living cell will change over time? Is this possible? Or is there another equation used in a case like this?

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• I think that the question is too broad, the answers is very context dependent. – user1420303 Aug 30 '16 at 14:24