can some one explain gradient and counter gradient diffusion to me.

how do we model them???

Gradient diffusion says that the variable "moves" from areas of high concentration to areas where the concentration is lower. So if you've got, say, a region of high temperature (hot brick) in a domain (bucket of water), the temperature will fall in the hot region and increase in the rest of the domain. If you let it go for a "long time", temperature everywhere will be the same, i.e. the gradient will fall to zero. In short, the (energy) flux will point down the gradient.

Remember, gradient diffusion is a model for the flux (in my example, a heat flux): "what happens when I have a hot body and a cold body" kind of situation.

In some circumstances, the above is not the case: the flux actually goes in the opposite direction. In that case, coming back to my example, you would have a cold water further heating up the hot brick. This model is, of course, unstable on its own, but you get such effects when you study things that are not really diffusion, like turbulence and try to model them in a diffusion-like manner.

Enjoy,

Hrv

ok thanks.

so how do we model non-gradient diffusion???

In my views, the gradient is necessasry condtion for diffusion to occur. If there is no gradient, then there will not be any diffusion. So the question of non-gradient diffusion does not exist.

Hrvoje's second example was not "non-gradient", it was counter-gradient. So, yes, a gradient is a necessary condition for diffusion, but the issue is the direction of the diffusion (and whether it is physically plausible).

ok.

so how do we model counter gradient diffusion?

and why might we get it?

and should we model it...is it important???