Shape stability of a gas bubble in a soft solid

Area of Science:

• Soft Matter Physics
• Acoustics
• Materials Science

Background:

• Understanding bubble cavitation in soft materials is crucial for applications like sonoprocessing and biomedical ultrasound.
• The behavior of bubbles in viscoelastic media, particularly their shape stability, presents a fundamental challenge.
• Existing models often simplify the complex viscoelastic properties of soft solids.

Purpose of the Study:

• To analytically investigate the shape stability of bubbles in a nonlinear elastic, Kelvin-Voigt viscoelastic medium.
• To develop a predictive model for bubble oscillations and compare it with experimental data.
• To elucidate the influence of viscoelastic properties on bubble shape instability.

Main Methods:

• Utilized perturbation methods to derive a model for bubble dynamics.
• Developed coupled evolution equations for bubble radius and non-spherical mode amplitudes.
• Analyzed parametric instability using natural frequency and Mathieu equation for non-spherical modes.

Main Results:

• The theoretical model accurately predicts experimental observations of bubble shape oscillations in gelatin gels.
• Viscosity was found to increase the damping rate, thereby suppressing shape instability.
• Shear modulus increases the natural frequency, influencing the unstable modes of bubble oscillation.

Conclusions:

• The developed model provides a robust framework for predicting bubble shape instability in viscoelastic soft matter.
• Viscoelastic properties significantly impact bubble dynamics, with viscosity and shear modulus playing distinct roles.
• This research offers a potential method for measuring viscoelastic properties of soft materials via bubble oscillation experiments.