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Fick's first law

The following demonstration is meant to illustrate Fick's 1st Law. Shown is a container containing a fluid. The two sides of the container (A & B) are separated by a permeable barrier. The concentration of the fluid is kept constant on both sides.
Use the sliders to change the width of the barrier, and the concentration of the fluid in sides A and B.
δC = C(A) − C(B))
Use the Show Diffusion button to get an idea of the flux of particles from side to side

\[ J = - D\frac{{\partial C}} {{\partial x}} \]

Barrier width

Side A
Side B
% Concentration A:
% Concentration B:
D = 1

δC =

δx =

δC / δx

 

 

J =

Fick's 1st law is applicable only to situations in which the concentrations at two points are constant.

We can show using numerical analysis that over time, such a system will settle on a state which is predicted by Fick's 1st law

constant concentration
constant concentration
x

Fick's 1st law holds even if the diffusivity changes with position. This is the case when there is temperature gradient across the material. Here the temperature, T, is proportional to x. One may notice though that the graph produced is not linear. This is because the diffusivity D does not change linearly with temperature.
D ∝ exp(-1/T)

constant concentration
constant concentration
x T