Rafael Gabler Gontijo

Numerical simulations of magnetic suspensions with hydrodynamic and dipole-dipole magnetic interactions

This work describes a numerical model to compute the translational and rotational motion of N spherical magnetic particles settling in a quiescent viscous fluid under creeping flow condition. The motion of the particles may be produced by the action of gravitational forces, Brownian thermal fluctuations, magnetic dipole-dipole interactions, external magnetic field, and hydrodynamic interactions. In order to avoid particle overlap, we consider a repulsive force based on a variation of a screened-Coulomb potential mixed with Hertz contact forces. The inertia of the particles is neglected so that a mobility approach to describe the hydrodynamic interactions is used. The magnetic dipoles are fixed with respect to the particles themselves. Thus they can only interact magnetically between them and with an external applied magnetic field. Therefore the effect of magnetic field moment rotation relative to the particle as a consequence of a finite amount of particle anisotropy is neglected in this work. On the oth...

PATTERN IDENTIFICATION ON THE NONLINEAR MOTION OF AN OSCILLATING BUBBLE

The main goal of this article is to study the oscillatory motion of a spherical gas bubble immersed in a Newtonian liquid subjected to a harmonic pressure excitation. We use the classical RayleighPlesset equation to study the radial motion of the bubble undergoing a forcing acoustic pressure field. The second order nonlinear ordinary differential equation that governs the bubble motion is solved through a robust fifth order Runge-Kutta scheme with adaptive time-step. Several interesting patterns are identified. First we develop an asymptotic solution for low amplitudes of excitation pressure to validate our numerical code. Then we develop a bifurcation diagram in order to show how the parameters of the flow modify the vibrational patterns of the bubble. We also train a neural network to identify the vibrational pattern through its FFT data. The combination of neural networks with a bifurcation diagram could be useful for the identification of the flow physical parameters in practical applications. For each pattern we also provide an analysis of the motion of the bubble on the phasespace and interpret physically the system behavior with its FFT. In addition, we analyze nonlinear patterns using standard tools of dynamical systems such as Poincaré sections and calculate the Lyapunov exponents of the system. Based on that, we have identified topological transitions in phase plane using for instance the analysis of Poincaré sections and the solution in the frequency spectrum. We have seen that the mechanisms that dominate the dynamics of the oscillating bubble is the competition of the acoustic field excitation with surface tension forces and momentum diffusion by the action of the surrounding fluid viscosity.