Chaotic behavior of a single spherical gas bubble surrounded by a Giesekus liquid: A numerical study |
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| Authors: | H Amini Kafiabad K Sadeghy |
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| Institution: | 1. School of Chemistry and Chemical Engineering, Guangxi University, Nanning 530004, China;2. Guangxi Colleges and Universities Key Laboratory of New Technology and Application in Resource Chemical Engineering, Guangxi University, Nanning 530004, China;3. Guangxi Key Laboratory of Petrochemical Resources Processing and Process Intensification Technology, Guangxi University, Nanning 530004, China;4. Department of Biological and Chemical Engineering, Guangxi University of Technology, Liuzhou 545006, China;1. Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada,;2. Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada,;1. L.N. Gumilyov Eurasian National University, Astana, Kazakhstan;2. Institute of Solid State Physics, University of Latvia, Riga, Latvia |
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| Abstract: | In the present work, nonlinear oscillations of a spherical, acoustically driven gas bubble in a Giesekus liquid are examined numerically. A novel approach based on the Gauss–Laguerre quadrature (GLQ) method is implemented to solve the integro-differential equation governing bubble dynamics in a Giesekus liquid. It is shown that, using this robust method, numerical results could be obtained at very high amplitudes and frequencies typical of ultrasound applications. The GLQ method also enabled obtaining results at very high Deborah and Reynolds numbers over prolonged dimensionless times not reported previously. Based on the results obtained in this work, it is concluded that the GLQ method is well suited for bubble dynamics studies in viscoelastic liquids. It is also concluded that the extensional-flow behavior of the liquid surrounding the bubble (as represented by the mobility factor in the Giesekus model) has a strong effect on the chaotic behavior of the bubble, and this is particularly so at high Deborah numbers, high amplitudes and/or high frequencies of the acoustic field. A period-doubling bifurcation structure is predicted to occur for certain values of the mobility factor. |
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