Diffusion Theory: Exploring Particle Motion

[veejay]

while talking abt diffusion, we take it for granted that particles diffuse from a region of high concentration to a region of low concentration.
is there a fundamental/first principle theory that explains this? how do the particles in the high concn. region see the concentration gradient and move towards the low concn. region?

 

[Dr Transport]

Think about the laws of thermodynamics...

The entropy of the system is too low if the particles are completely separated without a barrier in place.

 

[veejay]

Think about the laws of thermodynamics...

The entropy of the system is too low if the particles are completely separated without a barrier in place.

thanks for ur reply. could you explain more abt this or suggest me any references? I'm from electrical engg backgrnd and i dint do that much of thermodynamics.

 

[Dr Transport]

Any thermodynamics text will coverit. I'd suggest Reif.

 

[Modey3]

veejay,

The easiest way to think about diffusion without resorting to the standard chemical potential explanation is think about the random motion of atoms. Diffusion on the atomic level isn't a orderly process. Consider a simple square volume. Gaseous atoms of type A and B populate the volume. The type A atoms are on the right side and the type B atoms are on the left side. When the temperature is raised high enough for diffusion the atoms on both side move randomly. On average the type A atoms will move to the left while the type B atoms will move to the right. This is probably the best explanation for entropy related diffusion. Atoms don't "feel" a concentration gradient like a charged particle feels an electric field unless there is a Gibbs energy of mixing effect.

 

[LydiaAC]

Boltzmann transport equation

Hello Veejay:
You can demonstrate diffusion equation by means of Boltzmann transport equation with the term of "collision" proportional to difference between non-equilibrium and equilibrium distribution functions. If you set the proportionality constant 1/tau as v/lambda and assume that the non-equilibrium distribution function is very close to equilibrium distribution function, you can obtain a relationship between this two distribution functions.
You need to set a unidimensional concentration gradient and no electric field, and solve for the non-equilibrium distribution function. You will have it in terms of velocity, angle between velocity and gradient and equilibrium distribution function. If you assume the equilibrium distribution function as Maxwell-Boltzmann, you can use this expression for obtaining velocity in the standard way.
From velocity, you can obtain current, and this will be a negative constant times the unidimensional derivative of concentration.
The qualitative explanations about diffusion explain why we get a flux from high concentration to low concentration but do not say anything about why this flux is proportional to gradient. The above derivation proves that first Fick´s equation is by no means general and providing other circumstances, diffusion must obey other more complicate equations.
Keeping qualitative, as Modey3 already said, no particle know anything about the gradient, they are only following its random motion. For particles, the configuration in which there are a concentration gradient has a very little probability, but any other specific configuration has exactly the same little probability, so the particles does not know that their configuration is in some way special. For us, their configuration is truly special and when they eventually go to other equally probable configuration we see a big change.
The reason that we can detect a flux is not the behavior of particles but the gradient. The side with less particles has a lower probability to send particles to the other side. The side with more particles has a larger probability to send particles to the other side. The result is that more particles go from high concentration to low concentration than the reverse and the net flux is opposed to gradient.
Lydia Alvarez