Why is the diffusion coefficient in Fick's law squared?

[jjmclell]

Hi there,

I'm trying to wrap my head around Fick's first law of diffusion (for one dimension):

$$J_{x} = -D \frac{\partial \phi}{\partial x}$$

I understand that $$\phi$$ is the concentration in units amount/volume and that $$x$$ is position on the gradient in units length. What I don't understand is why $$-D$$ is in units area/time. If we're talking one dimensional diffusion, why do we bring area into the equation? Or, put another way, why do we square length in the diffusion coefficient?

Thanks,

jjmclell

 

[Andy Resnick]

It's in units of area/time because it represents the flux of material through a (control) surface