The 1st law of diffusion

Assume the concentration of dissolved material changes by a constant amount along one dimension of a container, defined as the x direction, and for simplicity does not change along the other two directions. Thus the concentration, c is expressed as (where G is a constant):

[1]    c = G x

The red line in the Figure below represents this equation. The change of concentration along x (the derivative or gradient or slope of the red line in the Figure) is thus G. Material will flow in the direction of lower x (in the minus x direction) to even out the distribution. It was observed by the German physiologist, Adolph Fick, (1829-1901) that J, the flow per unit area across a surface perpendicular to the x axis, was a constant times the concentration gradient:

[2]    J = - D G ; or in general, when the concentration gradient isn't a constant = - D dc/dx

Where D is the diffusion constant, and equation [2] is also known as Fick's law. The SI units of the variables in [2] are:

c in Kg / m³
x in m
t in sec
J in Kg / m² sec

substitution into [2] shows the units of D are m² / sec.