The Rise of Second Harmonics in Forced Oscillation of Gas Bubbles in Thixotropic Fluids

Abstract

In the present work, nonlinear acoustic oscillation of a single spherical gas bubble immersed in an unbounded thixotropic fluid is studied numerically. Using Moore's structural model as the constitutive equation of the liquid surrounding the bubble, the general Rayleigh-Plesset integro-differential equation, which governs bubble dynamics, is solved numerically using the Gauss-Laguerre Quadrature (GLQ) method. It is shown that at sufficiently high pressure amplitudes, typical of medical ultrasound applications, a second harmonics may be observed in the bubble's response.

Pulsatile Flow of Thixotropic Fluids through a Partially-Constricted Tube

“…This fluid model has successfully been used in the past to investigate thixotropic effects in a number of complex flow geometries. [26][27][28] We are particularly interested pulsatile flow. To that end, the paper is organized as follows:…”

“…As previously mentioned, this popular thixotropic fluid model has successfully been used in several numerical studies in recent years. [26][27][28] Now, before attempting to solve the governing equations, ( 1 2 ) a r 1 1 ( 1 2 ) a r 1 1 , …”

Lubricating Flow of Thixotropic Fluids in Slipper-Pad Bearing: A Numerical Study

“…In this fluid model, a drop in viscosity is associated with the structure break-down which is partially eclipsed by a simultaneous structure build-up due to the ever-present Brownian motions. In spite of its apparent simplicity, only simple geometries such as pipe flow 16) , or flow around a spherically growing/collapsing gas bubble 17) have previously been addressed for this particular fluid model. In fact, to the best of our knowledge, flow of thixotropic fluids obeying Moore's model has not previously been studied in complex geometries such as journal bearings.…”

Dynamics of Encapsulated Gas Bubbles Immersed in Thixotropic Fluids

“…In a recent work dealing with free-bubble contrast agents, Ahmadpour et al 9) have shown that second harmonics can also be generated for inelastic fluids provided that the fluid of interest is thixotropic. The present work can be regarded as an extension to their work in that it will be shown that even for encapsulated gas bubbles, the second harmonics can be generated provided that the medium surrounding the bubble is thixotropic.…”

“…To this should be added the fact that in recent years we have acquired some experience working with this simple but robust thixotropic fluid model. 9,11,12) And, due to the qualitative nature of the present work, this thixotropic fluid model was deemed most useful for our simulations.…”