Dynamics of Microbubbles Oscillating in Rheopectic Fluids Subject to Acoustic Pressure Field

Abstract

In the present work, the dynamics of a single spherical gas bubble surrounded by a rheopectic fluid obeying the Quemada model is numerically investigated while the bubble undergoes oscillatory motion due to acoustic forcing. The generalized form of the Rayleigh–Plesset equation has been used for studying bubble dynamics in Quemada fluids. The integro-differential equation representing the dynamics of the bubble is solved numerically using the finite-element method (FEM) and also the Gauss–Laguerre quadrature (GLQ) method. The effect of rheopexy number (Rx) and viscosity ratio (ξ) are then investigated over a wide range of working parameters. Numerical results show that the rheopectic behavior of the fluid surrounding the bubble can dramatically affect the bubble dynamics. It is predicted that for highly anti-thixotropic fluids, harmonics are affected so much so that the bubble may exhibit chaotic behavior. For instance, at Rx = 0.001 and ξ = 1/81, a one-micron-sized bubble may attain a size almost 30 times of its initial size. The general conclusion is that, in sonography, microbubbles dispersed in rheopectic fluids may indeed be considered as a potent ultrasound contrast agent provided that the fluid is just moderately anti-thixotropic otherwise its chaotic response might damage the adjacent tissues.

Keywords

• gas bubble
• rayleigh–plesset equation
• acoustic pressure
• rheopectic fluid
• quemada model