So why don't we just get a liquid that is heavier than quartz so that the gold will settle and all the light gravels will just float off like a piece of wood?
It is possible to find liquids that are of a high enough density that rock minerals will float up on the surface and the heavy minerals will sink to the bottom.
Bromoform is such an organic heavy liquid with a density of 2.84. It is too poisonous and too pricey to use in a production situation. It is however quite useful in a laboratory for mineral separations.
How about having an upward rising column of water where the gold can settle and the rocks floated off?
This can work if the particle sizes have been close screened
Due to edge effects and difficulty of keeping the flow constant across the water bed and feed rate and consistancy it is not a practical solution.
Seldom will we find a situation where we may take direct advantage of the falling velocities of different solids, Most of the time separation occurs in moving streams of water.
This adds another realm to separation technology. Lift, drag and bagnold's forces now come into play. Bernoulli, Reynolds and many other scientists and engineers have spent a great deal of time working out the interplay of these forces. I will deal very lightly with the math, in fact I would like to avoid the math altogether.
You may see in this animation of a sluice box that flows may become very complicated.
When fluids move they flow in two very different regimes. With slow flow and smooth surfaces fluids flow in whats called laminar flow. This means that if you look closely enough at the fluid, you can treat the speed of flow like laminae, or pages in a book. At a surface the first layer attached to the surface does not move at all, the next layer moves a little, the next a little faster, and so on. All the layers flowing smoothly.
At higher flow speeds or on rough surfaces the water flow becomes turbulent, such as the sluice above.
Water flow will create lift and drag forces on the particles in the bed. As the water cannot move in the bed and there is higher velocity water on the top of the particle. Lift forces like on an airplane wing are caused on the particle.
With very slow flows there is no particle movement on the bed. As the velocity increases there will start to be some movement and jostling of the grains.
When the velocity increases, more lift and drag forces cause the odd particle to "saltate".
A particle will all of a sudden jump from the bed and land further downstream. This particle has expierienced a high shear at the bed surface and this has induced enough lift to allow the particle to jump from the surface.When the particle enters the stream flow it accelerates to the same speed as the stream, the lift disappears and the particle settles to the surface. In these high shear areas these forces are refered to as Bagnolds forces. This force is interesting as the effect is stronger on large particles. It may be observed next time you are at the seashore watching waves wash over the sand.
When water is flowing faster it no longer flows in a smooth state, it becomes turbulent. Eddys and vortices form in the flow and if there is enough energy in the flow, and the flow is rough enough, air will become entrained. Air bubbles get sucked down from the surface. This entrained air is disastrous to fine gold recovery. If any of these bubbles touches a gold particle they will stick and decrease the effective specific gravity of the gold. If enough bubbles stick to a gold particle it will become light enough to float and depart to the tailings. Not a good thing.