Nonspherical oscillations of an encapsulated magnetic microbubble

TL;DR

This study models nonspherical oscillations of magnetic microbubbles coated with a polymer, analyzing stability, natural frequencies, and the effects of magnetic fields and material properties on oscillation behavior.

Contribution

It introduces a membrane theory-based model for magnetic microbubble oscillations, focusing on axisymmetric deformations and stability analysis under magnetic influence.

Findings

Second mode dominates within the stability region.

Magnetic susceptibility and initial radius increase oscillation amplitude.

Magnetic field does not affect the stability region for exponential stability.

Abstract

This paper presents a model for nonspherical oscillations of encapsulated bubbles coated with a polymer infused with magnetic particles, developed using membrane theory for thin weakly magnetic membranes. According to this theory, only the applied magnetic field significantly contributes to the Maxwell stress and membrane is under generalized plane stress. The study focuses on axisymmetric deformations of bubbles under symmetrically arranged magnetic coils. Non-spherical oscillations of the bubble are restricted to the linear regime, with the second mode dominating within the pressure range of the stability region. The pressure-frequency stability region is computationally determined, and its variation with different material properties and applied magnetic field is analyzed. The natural frequency of each mode is estimated using boundary layer approximation. Time-series analysis of the second mode amplitude reveals a significant oscillation amplitude relative to the bubble radius. Estimation using the model indicates that the interface magnetic susceptibility and initial bubble radius enhance the amplitude of second-mode oscillations. Computational findings suggest that the applied magnetic field does not influence the stability region for exponential stability.