Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

Abstract

In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.

Topological analysis of the periodic structures in a harmonically driven bubble oscillator near Blake's critical threshold: Infinite sequence of two-sided Farey ordering trees

“…The simple initial value problem solver, applied here, has been used for decades to investigate the bifurcation structure of various bubble oscillators with a variety of control parameters. The interested reader is referred to the publications [1,[33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Classification of the bifurcation structure of a periodically driven gas bubble

“…The accumulated knowledge of this nonlinear behavior has been summarized in many reviews [18][19][20] and papers [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The most important findings are the existence of period-doubling cascades in the bifurcation structure [1,21,30,31,35], the appearance of resonance horns in the amplitude-frequency plane of the driving [24,27,34] or the alternation of chaotic and periodic windows [21,23,33].…”

Numerical study on a polymer-shelled microbubble submerged in soft tissue

“…Lauterborn and his colleagues [43][44][45] have made great contributions by introducing the method of chaos physics to a model of a driven spherical gas bubble in water to determine its dynamic properties, especially its resonance behavior and bifurcation structure. Also, based on the previous works, the chaotic behavior of free bubbles observed both theoretically and experimentally [46][47][48][49][50], but this is not investigated for the case of UCAs, and it will be helpful to survey from this point of view because the method of chaos physics provides extensive knowledge about rich nonlinear dynamical systems. Moreover, neglecting liquid compressibility is not suitable for high-pressure amplitudes where the wall velocity of the agent is equal to the speed of sound in liquid [31], so the effects of liquid compressibility on the microbubble dynamics should be considered [40,41].…”