Bubble dynamics: Long-time behavior and interaction in viscous liquids |
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| Authors: | Alexandre Wolf Rao M A Masood Antonio Delgado Cornelia Rauh |
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| Institution: | 1. FAU Erlangen-Nürnberg, Institute of Fluid Mechanics (LSTM), Cauerstraße 4, 91058 Erlangen;2. TU Berlin, Department of Food Biotechnology and Food Processing Engineering, Königin-Luise-Straße 22, 14195 Berlin |
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| Abstract: | A mathematical two-phase model is used to numerically investigate physical and rheological effects on small, individual bubbles in high-viscosity liquids under pressure impact. It is found out that bubbles remain stable over time at high viscosity and surface tension. The steady case is considered and connected to the stability behavior of the bubble. An upper bound for the bubble radius is derived and the new equilibrium state of the bubble can be predicted by means of stability theorems of differential equations. Finally, the interaction of a limited number of well separated bubbles in an Hele-Shaw flow is mathematically analyzed to visualize and physically interpret their trajectories. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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