The same way that just letting it settle in earth’s gravity does, but faster.
If you let an oil water mix sit long enough undisturbed, it will separate, because they are of different densities. The more dense substance will settle to the bottom and the less dense substance will settle at the top, because the earth’s gravity pulls harder on the dense material per unit volume. Much like if I have packing peanuts and steel balls in a box and lightly shake it.
The centrifuge spins. When we spin a container whatever is inside it “wants” to go in a straight line, but that’s not possible when it is in a container. From inside the container it seems like a force is pulling it to the outside. The faster the container spins, the more this apparent force is. This apparent force in centrifuges gets very high, kind of like if the force of gravity was multiplied by 10 or more. Thus speeding up the process that would normally take a long time in earth’s gravity.
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