Bubble dynamics in a Hele-Shaw channel and velocity selection without surface tension
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| Main Authors: | , , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866929534276730880 |
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| author | Vasconcelos, Giovani L. Cordeiro, Luan P. Brum, Arthur A. Mineev-Weinstein, Mark |
| author_facet | Vasconcelos, Giovani L. Cordeiro, Luan P. Brum, Arthur A. Mineev-Weinstein, Mark |
| contents | Inviscid bubble dynamics in a viscous fluid, moving with velocity $V$ far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. The well-posed (after a Tikhonov regularization) dynamical system provides an extensive list of unsteady closed form solutions due to integrability. A new (rational) class of solutions is obtained and added to the logarithmic class found earlier (Phys. Rev. E 89, 061003(R), 2014). The only attractor selects the observable bubble shape and velocity $U = 2V$ from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results illustrate the most salient aspects of the bubble dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_04327 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Bubble dynamics in a Hele-Shaw channel and velocity selection without surface tension Vasconcelos, Giovani L. Cordeiro, Luan P. Brum, Arthur A. Mineev-Weinstein, Mark Fluid Dynamics Pattern Formation and Solitons Inviscid bubble dynamics in a viscous fluid, moving with velocity $V$ far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. The well-posed (after a Tikhonov regularization) dynamical system provides an extensive list of unsteady closed form solutions due to integrability. A new (rational) class of solutions is obtained and added to the logarithmic class found earlier (Phys. Rev. E 89, 061003(R), 2014). The only attractor selects the observable bubble shape and velocity $U = 2V$ from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results illustrate the most salient aspects of the bubble dynamics. |
| title | Bubble dynamics in a Hele-Shaw channel and velocity selection without surface tension |
| topic | Fluid Dynamics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/1910.04327 |