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 Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell Xu, Xianmin1; Doi, Masao2; Zhou, Jiajia3,4; Di, Yana3,4 2020-09-01 Source Publication PHYSICS OF FLUIDS ISSN 1070-6631 Volume 32Issue:9Pages:10 Abstract We calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele-Shaw cell using Park and Homsy's boundary condition, which accounts for the change of the three dimensional structure in the perimeter zone. We first formulate the problem in the form of a variational problem and discuss the shape change assuming that the bubble takes an elliptic shape. We calculate the shape and the velocity of the bubble as a function of the bubble size, the gap distance, and the inclination angle of the cell. We show that the bubble is flattened as it rises. This result is in agreement with experiments for large Hele-Shaw cells. Published under license by AIP Publishing. DOI 10.1063/5.0016080 Indexed By SCI Language 英语 Funding Project National Key R&D Program of China[2018YFB0704304] ; National Key R&D Program of China[2018YFB0704300] ; National Natural Science Foundation of China[11971469] ; National Natural Science Foundation of China[11421110001] ; National Natural Science Foundation of China[21774004] ; National Natural Science Foundation of China[11771437] WOS Research Area Mechanics ; Physics WOS Subject Mechanics ; Physics, Fluids & Plasmas WOS ID WOS:000568836500002 Publisher AMER INST PHYSICS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/52182 Collection 中国科学院数学与系统科学研究院 Corresponding Author Xu, Xianmin Affiliation 1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC,ICMSEC, Beijing 100190, Peoples R China2.Beihang Univ, Ctr Soft Matter Phys & Its Applicat, 37 Xueyuan Rd, Beijing 100191, Peoples R China3.Beijing Normal Univ, Inst Math Res, Div Sci & Technol, BNU HKBU United Int Coll, Zhuhai 519087, Peoples R China4.UIC, Zhuhai 519087, Peoples R China Recommended CitationGB/T 7714 Xu, Xianmin,Doi, Masao,Zhou, Jiajia,et al. Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell[J]. PHYSICS OF FLUIDS,2020,32(9):10. APA Xu, Xianmin,Doi, Masao,Zhou, Jiajia,&Di, Yana.(2020).Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell.PHYSICS OF FLUIDS,32(9),10. MLA Xu, Xianmin,et al."Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell".PHYSICS OF FLUIDS 32.9(2020):10.
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