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Numerical study on hydrodynamics of two types of unsteady bubbles in shear-thinning liquids

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Abstract

A volume of fluid method combined with an adaptive grid method was used to study the influence of Galilei (Ga) and Eötvös (Eo) numbers and characteristic parameters (such as rheological index (n) and characteristic time (\(\lambda \))) of shear-thinning liquids on the hydrodynamics of two types of unsteady bubbles. One is the bubble with central breakup behaviors, of which the rise trajectory is a straight line and the shape is symmetrical; however, the shape and centroid velocity cannot reach a steady state. Bubble shape becomes annular after radial expansion, and the centroid velocity has two peaks. The other is the unsteady bubble, of which the rise trajectory is zigzag, but both the shape and rise velocity cannot reach a steady state. The shape of this unstable bubble is flat, which causes periodic vortex shedding at the tail of a bubble. Thus, bubble rise velocity cannot reach a steady state. When the influence of viscous force is relatively weak and Eo is in the range of 50–55, a bubble shows central breakup behaviors. When Eo is low (Eo\(<10\)), effective Morton numbers (Mo\(^{\mathrm{eff}}\)) decrease to the magnitude of \(10^{-7}\) and effective Reynolds numbers meet the condition of Re\(^{\mathrm{eff}}\ge 125.2\), a bubble shows the second type of unsteady characteristics.

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Acknowledgements

We gratefully acknowledge the financial support from the National Natural Science Foundation of China Fund (No. 51376026). We also wish to thank the reviewers and editors for helpful suggestions.

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  1. School of Mechanical Engineering and Rail Transit, Changzhou University, Changzhou, 213164, China

    Bo Hu & Mingjun Pang

  2. Sinopec Shanghai Gaoqiao Petrochemical Co. LTD, Shanghai, 200137, China

    Junrong Dai

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Correspondence to Mingjun Pang.

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Communicated by Song Fu.

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Hu, B., Pang, M. & Dai, J. Numerical study on hydrodynamics of two types of unsteady bubbles in shear-thinning liquids. Theor. Comput. Fluid Dyn. 36, 769–797 (2022). https://doi.org/10.1007/s00162-022-00619-w

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