Nonlinear motion of an oscillating bubble immersed in a magnetic fluid

The motion of a spherical bubble in a ferrofluid subjected to an acoustic pressure field and a magnetic field is examined. The continuous fluid here is a colloidal suspension composed of ferromagnetic particles dispersed in a Newtonian carrier liquid. The constitutive equation for the fluid is based on the standard Maxwell tensor for a symmetric or nonmemory magnetic fluid with uniform permeability. In this case, a new version of the Rayleigh–Plesset equation is formulated considering the magnetic stress contribution of the bubble dynamics. The numerical computation solves a system of ordinary differential equations using a fifth-order Runge–Kutta scheme with adaptive time step. An asymptotic solution of the governing equation is also developed for small values of the nondimensional pressure forcing amplitude and for small values of the magnetic parameter. This theoretical solution is used in order to validate the numerical scheme. A theoretical study of the bubble collapse radius is also presented. The results suggest a strong anisotropic effect on the radial oscillation of the bubble as the magnetic and the hydrodynamic time scales are coupled in the examined dynamics. The bubble oscillatory motion can be controlled and its collapse avoided when a high magnetic field is applied. In this case, the magnetic contribution can control the bubble motion preventing or causing collapse, depending on the magnetic physical parameters: the uniform susceptibility and the magnetic Reynolds number. When the frequency of the acoustic field leads to decoupled time scales, the application of a magnetic field can produce a different scenario of the bubble dynamics. A hydrodynamic linear stability analysis is also presented in order to examine how the bubble motion evolves in time under conditions of different setting of nondimensional parameters, resulting in stable or unstable oscillating modes. The bubble response to an oscillatory magnetic field is also explored in this work. In this regard, new patterns and modes of vibration are identified, including chaotic patterns.