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# Inward migration of tea leaves in rotating fluid flow

Rigid particles maintain circular motion by balancing the outward (centrifugal) force by an inward (centripetal) force. When a light rigid particle follows the motion of a rotating fluid, such as a tea leaf in a cup containing water that is rotated by a stirrer, it flows inwards towards the center of the cup. The forces on the tea leaf are determined by two different methods both producing the same result. The shape of the water-air interface is predicted by expressing the slope of the interface as a function of radius and rotational velocity. The larger the radius, the higher the interface as measured from the base of the cup. Euler equation is then used to determine the pressure on the two faces of the tea leaf. The face closer to the center of the cup (smaller radius) faces lower pressure. The face farther from the center of the cup (larger radius) faces higher pressure. This pressure differential across the two faces of the tea leaf accompanies a force that is large enough to overcome the centrifugal force on the particle. Therefore, the tea leaf migrates inwards contradicting our intuitive understanding of the rotational motion of rigid particles. This finding has applications for industrial flows and was inspired by class work on pressure and viscous forces and applying Newton's second law to fluid motion. In particular, the project "Relating ThermoFluids to Life" encouraged development of these ideas.