Simulation of the Sedimentation of a Falling Oblate

TL;DR

This paper numerically investigates the complex dynamics of a falling oblate ellipsoid in viscous fluid, revealing steady, periodic, and chaotic motions influenced by physical parameters, with detailed analysis of trajectories and sensitivities.

Contribution

It introduces a detailed 3D numerical simulation of oblate fall dynamics using a constrained-force technique, exploring various motion regimes and sensitivities to initial conditions.

Findings

Identified steady, periodic, and chaotic fall regimes.

Chaotic motion characterized by a Lyapunov exponent of approximately 0.052.

Trajectory sensitivity to initial orientation in chaotic regime.

Abstract

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 \cite{Kai}, \cite{Kaih} and \cite{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. \cite{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 $\lambda = 0.052 \pm 0.005$. A phase space comparing to the results of ref \cite{Nori}, is shown.