What is the principle behind centrifugation?

Question

What is the principle behind centrifugation?

I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite grasp how particles (in the non subatomic sense) with different density should be affected differently.

Quite coarsely, I would expect to write down Newton's second law, but then the mass would simplify and the acceleration of every particle would be the same, regardless of mass.

Is friction the answer? Or am I missing something silly?

Answer 1

You are missing buoyant force. Let us take a simple example when you pour some dirt in water and shake after some time more dense object settle.Why ? Because of buoyant force $$F=mg-V_{obj}d_{fluid}g$$ $$a=g-\frac{d_{fluid}}{d_{obj}}g$$ Hence the less dense object remain suspended for a long time.

In the same way, in centrifuge there is outward acceleration same a $g$(due to centrifugal force) but greater in magnitude and buoyant force due to that.Hence dense particles moves away from the axis and less dense particles towards the axis.
Although to an "inertial observer" the spinning centrifuge does not produce a "real force" it does increase the pressure within the fluid,but to an observer "in the test tube" it is same as increasing the gravitational force.

Answer 2

You've got particles suspended in a liquid. There is brownian motion due to the temperature of the liquid. Each particle feels gravity, but it also feels the brownian motion. (Also the viscosity of the liquid.) The smaller the particle, the smaller its mass, so the less is the force of gravity on it, to the point where the particles come down too slowly to wait for, like years.

You can increase the "gravity" by spinning it in a centrifuge. Then the particles will "settle", but at rates determined by their size and/or density. That makes them segregate into layers.

Answer 3

The acceleration for different masses is not the same as is the velocity. Newton's 2nd law in the rotating frame would include the viscous force along with the centrifugal force and hence, mass would not be immaterial.Moreover,all particle in the rotating liquid quickly attain their critical velocities which is strongly dependent on the densities.