Simulation of the Sedimentation of a Falling Oblate

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We present a numerical investigation of the dynamics of one falling oblate ellipsoid particle in a viscous fluid, in three dimensions, using a constrained-force technique Kai, Kaih and Esa. We study the dynamical behavior of the oblate for a typical downward motion and obtain the trajectory, velocity, and orientation of the particle. We analyze the dynamics of the oblate generated when the height of the container, the aspect-ratio, and the dynamical viscosity are changed. Three types of falling motions are established: steady-falling, periodic oscillations and chaotic oscillations. In the periodic regime we find a behavior similar to the case of falling flat strips reported in ref. Belmonte. In the chaotic regime the trajectory of the oblate is characterized by a high sensitivity to tiny variations in the initial orientation. The Lyapunov exponent is λ= 0.052 ± 0.005. A phase space comparing to the results of ref Nori, is shown.