Diffusion (2 species) versus advection (1 species)

Question

Why do we see diffusion with 2 species but advection with a single species if both cases involve molecules spreading to increase entropy?

To take a physical example: Let's say I have a box with two equal-sized sides. Let's consider two scenarios:

1) The left side is full of gas A, the right side has both gas A and B (both sides are at equal pressure). Gas B diffuses toward the left side, against its concentration gradient, until eventually the molecules of both gases are evenly distributed.

2) Both sides are full of A, but the density of A is higher on the right side (i.e. there are more molecules of A on the right side). The higher density means (for an ideal gas) that there is a higher pressure on the right side. So the pressure gradient drives advection of A toward the left side, until eventually the molecules of A are evenly distributed.

Why do we see diffusion with 2 species but advection with 1? Isn't it all just a matter of spreading out molecules to maximize the number of statistical micro-states in the system (to increase entropy)? What is physically different about spreading out 2 types of molecules that it manifests as diffusion whereas the spreading out of a single type of molecule manifests as advection?

In other words, if I am correct that both motions of molecules result from a desire to increase entropy, why do they appear so different?

Could it be that there is indeed diffusion in the single species case, but the diffusion coefficient is so small that we don't include a diffusion term in a continuum mass balance since it is negligible?

Answer 1

So this question is different from Why doesn't the entropy increase when two similar gases mix with each other? but my answer there is the same answer here.

For a single component mixture in equilibrium, there is no way to identify molecules as unique. So if you have a box with a divider in it, you cannot tell a left molecule from a right molecule so you cannot "track" their diffusion in any way. If you somehow made them identical except for tagging them, then you could find diffusion between left and right sides -- but they are no longer identical then.

Your intuition is correct in that a box with a single component will have "diffusion" of molecules from one side to the other. It's just that the state when that happens is completely indistinguishable from the original state. And so from a macroscopic sense, there was no diffusion.

Note also that advection and diffusion are not mutually exclusive. If you had two gasses in a box with a divider and the pressure was higher on one side, you would get flow driven by the pressure gradient in addition to diffusion of the gasses across the original interface.