Browsing by Subject "Bifurcation diagrams"

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Open Access
Chaotic behavior of gas bubble in non-Newtonian fluid: A numerical study
(2013) Behnia, S.; Mobadersani F.; Yahyavi, M.; Rezavand, A.
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. © 2013 Springer Science+Business Media Dordrecht.
Open Access
Effect of magnetic field on the radial pulsations of a gas bubble in a non-Newtonian fluid
(Elsevier Ltd, 2015) Behnia, S.; Mobadersani F.; Yahyavi, M.; Rezavand, A.; Hoesinpour, N.; Ezzat, A.
Dynamics of acoustically driven bubbles' radial oscillations in viscoelastic fluids are known as complex and uncontrollable phenomenon indicative of highly active nonlinear as well as chaotic behavior. In the present paper, the effect of magnetic fields on the non-linear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. The constitutive equation [Upper-Convective Maxwell (UCM)] was used for modeling the rheological behaviors of the fluid. 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. It was found that the magnetic field parameter (B) can be used for controlling the nonlinear radial oscillations of a spherical, acoustically forced gas bubble in nonlinear viscoelastic media. The relevance and importance of this control method to biomedical ultrasound applications were highlighted. We have studied the dynamic behavior of the radial response of the bubble before and after applying the magnetic field using Lyapunov exponent spectra, bifurcation diagrams and time series. A period-doubling bifurcation structure was predicted to occur for certain values of the parameters effects. Results indicated its strong impact on reducing the chaotic radial oscillations to regular ones. © 2015 Elsevier Ltd. All rights reserved.