Diffusion vs Gravity in water: does a dissolved ion tend to "sink"?

Im a french student in geochemistry.

My question might be silly, but I became really too confused to answer it myself. Does gravity affect the diffusion of ions in water ?

Lets imagine a vertical volume of water. There is no temperature gradient. If some NaCl salt is placed (without disturbing the water) at the bottom, it will be dissolved quickely. But then ? : -Na+ and Cl- will start to diffuse as to get their concentrations homogeneous everywhere. There will be an upward flux . - Does gravity want them to remain at the bottom because both of them are heavier than water molecule ? Then it would be a downward flux.. (?)

If these two process occur together, how could I evaluate which is dominant, or what would be the equilibrium ?

I thought I could use something like a Boltzmann distribution ? Like Concentration = $\mathrm{exp}(mgz/kT)$ ? Im not sure though of how to consider an ion (Cl or Na) sinking between water molecules because of gravity

Thanks for help