Do denser objects generally move down towards the "centre" (where $F_g = 0$) of a gravitational field relative to a less dense object?

Question

Background( What I think is happening for fluids)

Hello, I am high school student currently investigating buoyancy.

Consider a dense liquid such as honey added to a less dense liquid such as water. In this case, I would presume that there is force upwards(buoyant force) due to the difference in pressure. For the less dense liquid, the resulting acceleration is higher than the resulting acceleration on the denser liquid as a consequence of Newton's second law as the mass of the dense object is large relative to the force acting on it( which is proportional to the volume occupied by the fluid) The dense object has a net force downwards due to gravity while the buoyant force is larger than the force of gravity on the less dense object. This is what I presume to be why a dense fluid sinks when immersed in a less dense fluid.

Question

Consider now a jar containing two types of solids spheres, one denser than the other, all of uniform size ( about the size of a marble) and shape(spherical). They are randomly distributed. The jar is shaken vigorously while maintaining its upright position. Do the marbles sort themselves according to density with the densest marbles on the bottom? If so why?

I don't see a plausible mechanism for this myself, so I would assume not, but the conclusion seems counterintuitive, that a system of fluids would act differently from a system containing solids.

Answer 1

A large number of small marbles confined to a jar can be treated as a fluid when you are shaking it vigorously. When marbles of different densities are present, Archimedes principle applies here, and the denser (heavier) marbles tend to go down. Also, it is energetically favourable for the system to have its more massive components lower down. Unlike fluids, the marbles in a jar do not have enough vibrational energy for diffusion, it requires external agitation.

As for the mechanism, more massive marbles exert a higher force on the marbles below them. Depending on the angle of contact, this force would have components that would push the lighter marbles away from their path. Just like moving through a crowd requires you to be strong, running down the jar requires the marble to be denser. After a while of shaking, you would only find denser marbles at the bottom.