Does gravity affect Brownian Motion?

[dedocta]

TL;DR Summary

Brownian motion of free falling ISS vs Brownian Motion on Earth

I know passive diffusion rates behave differently on the International Space Station relative to Earth (video of a contained flame experiment burning up there.) However, does the random walk of pollen particles etc. have slowed velocity in comparison to that on Earth? Has been bugging me for a while, as I was wondering how our biology deals with slower Brownian mtion if so...

 

[mpresic3]

Chandrasekhar wrote an excellent paper on Stochastic Problems in Physics and Astronomy in 1943. You can find his paper in N. Wax's Book in Dover, "Selected Papers..." To make a long story short, in an early chapter, Chandrasekar demonstrates the exponential atmpsphere is the steady state solution for a falling particle with viscous damping rebounding from a fixed surface (the ground). The nice feature of the paper is that it also demonstrates the transient (i.e. time dependent) solution showing how the equilibrium solution is approached. Wax's book has many good papers along these lines.

 

[TeethWhitener]

Summary:: Brownian motion of free falling ISS vs Brownian Motion on Earth

video of a contained flame experiment burning up there.

That has less to do with diffusion differences and more to do with the fact that convection operates differently in microgravity. Basically, hot air rises in a gravitational field because it is less dense than cold air. In microgravity, this buoyant force doesn’t exist or is much smaller, so that the hot carbon dioxide generated by a flame does not rise away from the flame to make way for fresh air to sustain the reaction.

Summary:: Brownian motion of free falling ISS vs Brownian Motion on Earth

However, does the random walk of pollen particles etc. have slowed velocity in comparison to that on Earth? Has been bugging me for a while, as I was wondering how our biology deals with slower Brownian mtion if so...

You can model this straightforwardly by adding a gravity term to the Langevin equation
$$\dot{\mathbf{v}}=-\gamma\mathbf{v}+\sigma\mathbf{\xi}(t)-\mathbf{g}$$
Gravity will pull denser particles in the direction of the gravitational source, but if the noise term is large (at higher T, for instance), or the drag term is large (at higher density, for instance), then gravity will become irrelevant.

 

[mpresic3]

update on my earlier post. N.B. the page 57 of the Chadrasekhar paper concerning gravity effects on Brownian motio