Hello everyone,

I was trying to model concentration gradients in a flow-free diffusion chamber using COMSOL. I wanted see what would be the effect of gravity on the concentration gradients that I obtain as a result of pure diffusion. I thought that I can add the effect of such drag force to the diffusion equation by calculating the terminal velocity that particles would have in the solution due to gravity.

By using Stoke's Drag Force Formula for spherical particles:

Fdrag = Fgravity

6*π*µ*R*Vt = m*g

Vt = (m*g) / (6*π*µ*R)

Where

µ = Dynamic viscosity of the solution

R = Stokes radius of the particle

Vt = Terminal velocity of the particle

I have added the terminal velocity that I found as a constant velocity field, and solved the new model. As one may predict, as the particle size decreases the effect of gravitational field becomes negligible. However, would this concept still work for very small particles? For example, can I use this for the accumulation of Na+ ions in the period 100.000 years? Is there are bottom limit for Stoke's drag assumption in terms of particle size?

I found a similar topic on StackExchange, where, interestingly, the terminal velocity of the particle in the solution was defined as

Vt = (m*g) / µ

https://physics.stackexchange.com/questions/173800/diffusion-vs-gravity-in-water-does-a-dissolved-ion-tend-to-sink

Do you have any idea why it might have been defined like that independent of the particle size?

Thanks.