Why do particles gather in the center of a stirred pot of water?

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When water is stirred in a circular motion, particles tend to gather at the center due to the centrifugal force created by the flow. This force pushes the particles outward, but as the water settles, the particles are drawn back towards the center where the flow is weaker. The phenomenon is related to secondary flow dynamics, which explains how particles behave in a rotating fluid. Additionally, a similar effect occurs with helium balloons in a moving vehicle, where they shift forward due to buoyancy and acceleration. Understanding these fluid dynamics can clarify why particles behave this way in stirred water.
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I have a pot with water and some large particles lying on the bottom. When I stirr the water in a circular motion and then let the particles settle, they all gather in the center of the pot. Why is that so?
 
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Thanks for the solution!

Btw, that reminds me of another simpler effect: Apparently when a van with helium balloons accelerates, the ballons move to the front :) Bouyancy I suppose.
 

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