Let’s think for a minute about what’s going on with tiny particles in solution, because we chemists spend an awful lot of time dealing with those. These particles vary in size from individual atoms all the way through small molecules, larger biomolecules and polymers, nanoscale engineered particles, micronized powders, etc., but the good news is that fluid and particle behavior is fairly well understood, up to a point.
You’ll want to know the Reynolds number (Re) for your fluid flow situation, which is the (dimensionless) ratio of inertial and viscous forces. Low Re means that viscous forces predominate, and you tend to have laminar flow (think of honey pouring out of a jar), but high-Re situations mean more turbulence, eddies, vortices, chaotic behavior, and so on. If the speed or viscosity of the fluid is changing across the system, then the Reynolds number can be used to predict where the onset of turbulence will be (although this will vary greatly depending on the geometry, such as flow through a tube, over a flat surface, around a spherical obstacle, etc.) That just-starting-into-turbulence regime, I should note, can be a real mathematical no-man’s-land. Getting further into flow will take you into the Navier-Stokes equations, which are simultaneously very useful and rather mysterious: it’s still unproven whether they necessarily have solutions in three dimensions and whether those solutions are mathematically smooth, and there’s a million dollars waiting for you if you can provide a solid answer.
Small particles in the kinds of solutions chemists care about tend to be low-Reynolds-number situations, which is good news. Edit: see this classic treatment of the situation. It’s an open question, though, if small molecules and biomolecules can or do propel themselves through these solutions under reaction conditions, and if so, how you could best prove that. You’d be most likely to see such effects as an increase in the diffusion coefficient, but such “enhanced diffusion” is controversial. It’s been reported, but I get the impression that on the theoretical side there are many competing models, and on the experimental side microscopy results can disagree with the spectroscopic ones, which can also disagree with each other.
There have been reports that Grubbs catalyst molecules display such enhanced diffusion in model systems, which wasn’t quite thought possible at such a small scale and at such low Reynolds numbers. A new paper, though, has a different opinion. The authors (from Univ. New South Wales-Sydney, Western Sydney Univ., and Univ. of Maine) believe that the whole thing is just convection currents in solution. Using a new time-resolved diffusion NMR method, they find a big discrepancy in the early stages of the reaction. The enhanced-diffusion proposal would have the largest effects on the diffusion coefficients at the very onset of the reaction, decreasing as the reaction proceeds. But this work finds that this effect starts off low and takes about 25 minutes to hit its peak, decreasing after that. And the apparent increase of the diffusion coefficient for the Grubbs catalyst species is probably an artifact from it being by far the largest molecular species in the system.
They show the same behavior for another reaction, this one Pd-catalyzed: the time scale is consistent with the development of convection currents. For the Grubbs-catalyzed reaction, this could be driven by the formation of the gaseous by-product, and for the Pd-catalyzed case, though an observed change in temperature. Indeed, the Pd-catalyzed reaction’s changes in diffusion coefficient disappeared entirely when the reaction was run in narrow 3mm NMR tubes rather than the standard-sized ones, which just shouldn’t happen if this were some intrinsic effect of molecular motion.
It looks, then, like the whole concept of “enhanced diffusion” in molecular systems is going to have to prove itself under more stringent conditions. It’s been reported in enzyme behavior as well, and the question is whether that’s real or also is explained by solution currents, instead. A recent paper has calculated that the observed amount of such enhanced diffusion doesn’t seem to make thermodynamic sense, and called for alternative explanations. Perhaps unaccounted-for convection currents are it?