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On the viscous motion of a small particle in a rotating cylinder. (English) Zbl 1043.76059
From the summary: The dynamics of a non-neutrally buoyant particle moving in a rotating cylinder filled with a Newtonian fluid is examined analytically. The particle is set in motion from the centre of the cylinder due to the acceleration caused by the presence of a gravitational field. The problem is formulated in Cartesian coordinates, and a relevant fractional Lagrangian equation is proposed. This equation is solved exactly by recognizing that the eigenfunctions of the problem are Mittag-Leffier functions. Virtual mass, gravity, pressure, and steady and history drag effects at low particle Reynolds numbers are considered, and the balance of forces acting on the particle is studied for realistic cases. The presence of lift forces, both steady and unsteady, is taken into account. Results are compared to the exact solution of Maxey-Riley equation for the same conditions.
MSC:
76U05Rotating fluids
76T20Suspensions