{"title":"二维平行粘性流动中的指法","authors":"N. Rakotomalala, D. Salin, P. Watzky","doi":"10.1051/JP2:1997105","DOIUrl":null,"url":null,"abstract":"We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"33 1","pages":"967-972"},"PeriodicalIF":0.0000,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Fingering in 2D Parallel Viscous Flow\",\"authors\":\"N. Rakotomalala, D. Salin, P. Watzky\",\"doi\":\"10.1051/JP2:1997105\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.\",\"PeriodicalId\":14774,\"journal\":{\"name\":\"Journal De Physique Ii\",\"volume\":\"33 1\",\"pages\":\"967-972\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Physique Ii\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/JP2:1997105\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Physique Ii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/JP2:1997105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.