Things that are moving want to keep moving in a straight line. It takes a force toward the middle of the circle to keep them moving in a circle, which is exerted by the outer wall of the centrifuge. So the particles all get pressed against the outer wall with enough force to cause the constant-magnitude acceleration that keeps them going in a circle.
You know what else is a force causing a constant-magnitude acceleration? Gravity. The particles can’t tell the difference between centrifuge walls and gravity, because they don’t look around, they only feel forces.
So the particles all act like they’re being pulled to the outer wall by gravity. And because they’re freely moving particles of different densities, they also experience buoyancy as they would under gravity. The denser particles “sink” to the outside, and the less dense ones “float” to the inside in the opposite direction of what they think is gravity.
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