Hele-Shaw Flows: Historical Overview

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Saffman-Taylor experiments Experiments showed: • the instability of an interface moving towards a more viscous fluid; • Growth of a single long finger. BIRS, Canada, July 2007 – p. 69
Conformal formulation Saffman-Taylor exact solution: Imz π −π The function f(ζ,t) = Q t −log ζ +2(1 −λ) log(1+ζ). maps 2πλ the unit disk U minus (−1, 0] onto the phase domain Ω(t). Ω(t) Re z BIRS, Canada, July 2007 – p. 70
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Hele-Shaw Flows: Historical Overvie
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Henri Selby Hele-Shaw ... an exampl
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1871-1876 At the age of 17 he finis
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1885-1904 In 1885 Hele-Shaw was inv
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1906-1941 Upon returning from South
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1906-1941 Upon returning from South
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1906-1941 Hele-Shaw took a very act
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1906-1941 One of his greatest contr
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1906-1941 Hele-Shaw was a man of gr
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1906-1941 Hele-Shaw was a man of gr
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Hele-Shaw’s inventions Two greate
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Hele-Shaw’s inventions • Specia
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Hele-Shaw’s inventions H. S. Hele
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Hele-Shaw’s inventions Further de
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Hele-Shaw Prizes • Hele-Shaw Priz
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Stream-line Flow Methods The most n
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Stream-line Flow Methods In 1897 He
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Experiment by Reynolds O. Reynolds
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Experiment by Reynolds O. Reynolds
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Hele-Shaw Cell Hele-Shaw got the Go
Page 45 and 46: Hele-Shaw Papers • Experiments on
Page 47 and 48: USSR CONTRIBUTION BIRS, Canada, Jul
Page 49 and 50: Stokes-Leibenzon Model Leonid Samui
Page 51 and 52: Stokes-Leibenzon Model x3 h 0 x1,x3
Page 53 and 54: Stokes-Leibenzon Model Ω(t) 0 y
Page 55 and 56: Stokes-Leibenzon Model Ω(t) 0 y
Page 57 and 58: Free Boundary Problem • ∆p = Q
Page 59 and 60: P. Ya. Polubarinova-Kochina Pelagey
Page 61 and 62: P. Ya. Polubarinova-Kochina In 1921
Page 63 and 64: P. Ya. Polubarinova-Kochina In 1958
Page 65 and 66: L. A. Galin Lev Alexandrovich Galin
Page 67 and 68: Hele-Shaw problem P. Ya. Polubarino
Page 69 and 70: Papers • P. Ya. Polubarinova-Koch
Page 71 and 72: P. P. Kufarev Pavel Parfenievich Ku
Page 73 and 74: Kufarev’s exact solutions 1947-19
Page 75 and 76: Kufarev’s exact solutions 1947-19
Page 77 and 78: The proof of local existence BIRS,
Page 79 and 80: Flows in Porous Media Random struct
Page 81 and 82: Examples of Porous Media Rock, BIRS
Page 83 and 84: Darcy’s Low Henry Philibert Gaspa
Page 85 and 86: Oil Recovery BIRS, Canada, July 200
Page 87 and 88: Microscopic Image Beginning of reco
Page 89 and 90: Fingering Phenomenon Modelling by t
Page 91 and 92: UK CONTRIBUTION BIRS, Canada, July
Page 93 and 94: Saffman-Taylor Finger Mathematical
Page 95: Philip G. Saffman Philip Geoffrey S
Page 99 and 100: Selection Problem This proposal was
Page 101 and 102: Richardson: Modern Period BIRS, Can
Page 103 and 104: MODERN PERIOD 1981-PRESENT • Nowa
Page 105 and 106: Evolution Geometry Björn Gustafsso
Page 107 and 108: Other Models Witten, Sander, Hastin
Page 109 and 110: Multi-dimensional flows, PDE Caffar
Page 111 and 112: Integrable Systems (2000-2007) P.Wi
Page 113 and 114: Integrable Systems (2000-2007) The
Page 115 and 116: Recommended Reading Two monographs:
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