I am thinking about how the velocity of molecules measured from a small region of space might change as the region of inquiry moves closer to the edge of a container. Ultimately I am thinking about MR imaging with velocity phase encoding, which can (in clinical application) resolve voxels in the 1mm$^3$ range (depending on scanner, bore, patient factors and the like).
For instance, if I have a glass container filled with distilled water, sitting still on a table. It is at standard temperature and pressure. If I measure the averaged velocity of all the molecules in the container, there would be a net zero velocity; the water is not jumping out of the container.
That is not to say that the molecules are still; I understand that they will all be moving and interacting per the kinetic model; just that on a macroscopic scale the water is, on average, still. It will have an average velocity of zero and an average speed relative to the temperature and pressure.
As I reduce my region of interest from "the container" down through "1 mL" and smaller towards the minuscule, that average velocity mean of zero will be maintained until statistical variation becomes more apparent, and at the molecular scale it will break down on individual measurements, but still be maintained if averaged over time.
But as I move a region of interest towards the container wall, I wonder if there is anisotropy? That is, as I get towards the wall with the directional component of the velocity become oriented perpendicular to the container wall.
I imagine that there will be several things that happen.
- As you approach the edge, there will be a bias towards the edge from van der waal's forces and affected by the properties of the container (material, it's effects on surface tension I presume)
- Apart from the bias in point 1, molecules heading perpendicular to the wall will be unaffected; molecules heading towards the wall will be reflected (losing some of their kinetic energy); and
- Those on an oblique trajectory will be reflected in the plane parallel to the edge (my nomenclature might be off) again losing some energy, but also having their trajectories altered somewhat by the weak interactions as above
Please feel free to fill me in on the other interactions I am missing.
So I then question myself, if we approach the limit withe our region of interrogation, as we do so will there be a bias in the molecules' velocity perpendicular to the wall?
Will the molecules' velocities (in 2D) go from this?
\ | / \ | / ___\|/___ /|\ / | \ / | \
\ | / | ______\|/______ | /|\ | / | \ |<-- Wall
But still averaging zero on any large scale?
Or will it be biased, having a net velocity away from the container wall, i.e.
\ | \ | / | ______\|/___ | /|\ | / | \ |<-- Wall / |
Or something like this, where there could be an increase in the number
I suppose to clarify I am thinking of long range motion rather than just local motion as discussed here
To extend, how would increasing the pressure (assuming temperature was allowed to equalize) affect this? I presume that the pressure would affect both local motion and long-range motion within the liquid, but mostly in the magnitude domain, not the direction. Similarly for heat, but then also including motion within the molecule itself for non-monatomic molecules.
In summary, does the directional component of the average velocity of molecules in a liquid at rest vary at the edge of a container, does the magnitude or direction (or proportion of molecules heading in a particular direction) component vary anisotropically at the edge of the container, or is there no appreciable difference up to the edge of the container?