메뉴 건너뛰기




Volumn 409, Issue , 2000, Pages 273-308

Surprises in viscous fingering

Author keywords

[No Author keywords available]

Indexed keywords

FINGERTIP; MATHEMATICAL ANALYSIS; VISCOUS FLUID;

EID: 0033927876     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099007788     Document Type: Article
Times cited : (132)

References (108)
  • 2
    • 0000159327 scopus 로고    scopus 로고
    • Instabilities, fingering and Saffman-Taylor problem in filtration combustion
    • ALDUSIN, A. P. & MATKOWSKY, B. J. 1998 Instabilities, fingering and Saffman-Taylor problem in filtration combustion. Combust. Sci. Technol. 133, 293.
    • (1998) Combust. Sci. Technol. , vol.133 , pp. 293
    • Aldusin, A.P.1    Matkowsky, B.J.2
  • 3
    • 0001595618 scopus 로고    scopus 로고
    • Extremum principles for selection in the Saffman-Taylor finger and Taylor-Saffman bubble problems
    • ALDUSIN, A. P. & MATKOWSKY, B. J. 1999 Extremum principles for selection in the Saffman-Taylor finger and Taylor-Saffman bubble problems. Phys. Fluids 11, 1287.
    • (1999) Phys. Fluids , vol.11 , pp. 1287
    • Aldusin, A.P.1    Matkowsky, B.J.2
  • 4
    • 0001484219 scopus 로고
    • Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion limited aggregation
    • ARNEODO, A., COUDER, Y., GRASSEAU, G., HAKIM, V. & RABAUD, M. 1989 Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion limited aggregation. Phys. Rev. Lett. 63, 984.
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 984
    • Arneodo, A.1    Couder, Y.2    Grasseau, G.3    Hakim, V.4    Rabaud, M.5
  • 5
    • 0000806951 scopus 로고
    • A well posed numerical method to track isolated conformal map singularities in Hele-Shaw flow
    • BAKER, G. R., SIEGEL, M. & TANVRER, S. 1995 A well posed numerical method to track isolated conformal map singularities in Hele-Shaw flow. J. Comput. Phys. 120, 348.
    • (1995) J. Comput. Phys. , vol.120 , pp. 348
    • Baker, G.R.1    Siegel, M.2    Tanvrer, S.3
  • 6
    • 0011765413 scopus 로고
    • Velocity selection in the symmetric model of dendritic growth
    • BARBIERI, A., HONG, D. & LANGER, J. 1986 Velocity selection in the symmetric model of dendritic growth. Phys. Rev. A 35, 1802.
    • (1986) Phys. Rev. A , vol.35 , pp. 1802
    • Barbieri, A.1    Hong, D.2    Langer, J.3
  • 7
    • 0000346874 scopus 로고
    • Stabilite d'un deplacement radial non miscible
    • BATAILLE, J. 1968 Stabilite d'un deplacement radial non miscible. Revue Inst. Pe'trole 23, 1349.
    • (1968) Revue Inst. Pe'trole , vol.23 , pp. 1349
    • Bataille, J.1
  • 8
    • 5844299119 scopus 로고
    • Theory of needle crystal
    • BEN AMAR, M. 1988 Theory of needle crystal. Physica D 31, 409.
    • (1988) Physica D , vol.31 , pp. 409
    • Ben Amar, M.1
  • 9
    • 0013264148 scopus 로고
    • Plumes in a Hele-Shaw cell
    • BEN AMAR, M. 1992 Plumes in a Hele-Shaw cell. Phys. Fluids A 4, 2641.
    • (1992) Phys. Fluids A , vol.4 , pp. 2641
    • Ben Amar, M.1
  • 10
    • 0010375086 scopus 로고    scopus 로고
    • Void electro-migration as a moving free boundary problem
    • BEN AMAR, M. 1999 Void electro-migration as a moving free boundary problem. Physica D 134, 275.
    • (1999) Physica D , vol.134 , pp. 275
    • Ben Amar, M.1
  • 11
    • 4244168156 scopus 로고
    • Viscous fingering with adverse anisotropy - A new Saffman-Taylor finger
    • BEN AMAR, M., COMBESCOT, R. & COUDER, Y. 1993 Viscous fingering with adverse anisotropy - a new Saffman-Taylor Finger. Phys. Rev. Lett. 70, 3047.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 3047
    • Ben Amar, M.1    Combescot, R.2    Couder, Y.3
  • 14
    • 11744328200 scopus 로고
    • Stability of viscous fingering
    • BENSIMON, D. 1986 Stability of viscous fingering. Phys. Rev. A 33, 1302.
    • (1986) Phys. Rev. A , vol.33 , pp. 1302
    • Bensimon, D.1
  • 16
    • 0025213667 scopus 로고
    • Two dimensional dendritic growth at arbitrary Peclet number
    • BRENER, E. & MELNIKOV, V. I. 1990 Two dimensional dendritic growth at arbitrary Peclet number. J. Phys. Paris 51, 157.
    • (1990) J. Phys. Paris , vol.51 , pp. 157
    • Brener, E.1    Melnikov, V.I.2
  • 17
    • 84855585199 scopus 로고
    • The motion of long bubbles in tubes
    • BRETHERTON, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166.
    • (1961) J. Fluid Mech. , vol.10 , pp. 166
    • Bretherton, F.P.1
  • 18
    • 0037596834 scopus 로고
    • Analysis of the boundary conditions for Hele-Shaw bubbles
    • BURGESS, D. & FOSTER, M. R. 1990 Analysis of the boundary conditions for Hele-Shaw bubbles. Phys. Fluids A 2, 1105.
    • (1990) Phys. Fluids A , vol.2 , pp. 1105
    • Burgess, D.1    Foster, M.R.2
  • 19
    • 0033940025 scopus 로고    scopus 로고
    • The singular perturbation of surface tension in Hele-Shaw flows
    • CENICEROS, H. & HOU, T. Y. 2000 The singular perturbation of surface tension in Hele-Shaw flows. J. Fluid Mech. 409, 251-272.
    • (2000) J. Fluid Mech. , vol.409 , pp. 251-272
    • Ceniceros, H.1    Hou, T.Y.2
  • 20
    • 0001121256 scopus 로고
    • The instability of slow immiscible viscous liquid-liquid displacements in permeable media
    • CHUOKE, R. L., MEURS, P. VAN & POEL, C. VAN DER 1959 The instability of slow immiscible viscous liquid-liquid displacements in permeable media. Trans. AIME 216, 188.
    • (1959) Trans. AIME , vol.216 , pp. 188
    • Chuoke, R.L.1    Van Meurs, P.2    Van Der Poel, C.3
  • 21
    • 0000634182 scopus 로고
    • Selection of Saffman-Taylor fingers in the sector geometry
    • COMBESCOT, R. & BEN AMAR, M. 1991 Selection of Saffman-Taylor fingers in the sector geometry. Phys. Rev. Lett. 67, 453.
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 453
    • Combescot, R.1    Ben Amar, M.2
  • 22
    • 0038509134 scopus 로고
    • Selection in the Saffman-Taylor bubble and assymmetrical finger problem
    • COMBESCOT, R. & DOMBRE, T. 1988 Selection in the Saffman-Taylor bubble and assymmetrical finger problem. Phys. Rev. A 38, 2573.
    • (1988) Phys. Rev. A , vol.38 , pp. 2573
    • Combescot, R.1    Dombre, T.2
  • 25
    • 0040490387 scopus 로고
    • Dynamics of a complex interface
    • CONSTANTIN, P. & KADANOFF, L. 1991 Dynamics of a complex interface. Physica D 47, 450.
    • (1991) Physica D , vol.47 , pp. 450
    • Constantin, P.1    Kadanoff, L.2
  • 26
    • 0000851461 scopus 로고
    • Global solutions for small data to the Hele-Shaw problem
    • CONSTANTIN, P. & PUGH, M. 1993 Global Solutions for small data to the Hele-Shaw problem. Nonlinearity 6, 393.
    • (1993) Nonlinearity , vol.6 , pp. 393
    • Constantin, P.1    Pugh, M.2
  • 27
    • 85051955879 scopus 로고    scopus 로고
    • Existence and uniqueness for a class of nonlinear higher order partial differential equations in the complex plane
    • Submitted
    • COSTIN, O. & TANVEER, S. 1999 Existence and uniqueness for a class of nonlinear higher order partial differential equations in the complex plane. Submitted to Commun. Pure Appl. Maths.
    • (1999) Commun. Pure Appl. Maths.
    • Costin, O.1    Tanveer, S.2
  • 28
    • 0000081494 scopus 로고
    • Narrow fingers in the Saffman-Taylor instability
    • COUDER, Y., GERARD, N. & RABAUD, M. 1986 Narrow fingers in the Saffman-Taylor Instability. Phys. Rev. A 34, 5175.
    • (1986) Phys. Rev. A , vol.34 , pp. 5175
    • Couder, Y.1    Gerard, N.2    Rabaud, M.3
  • 29
    • 0001422167 scopus 로고
    • Interface dynamics and the motion of complex singularities
    • DAI, W. S., KADANOFF, L. & ZHOU, S. 1991 Interface dynamics and the motion of complex singularities. Phys. Rev. A 43, 6672.
    • (1991) Phys. Rev. A , vol.43 , pp. 6672
    • Dai, W.S.1    Kadanoff, L.2    Zhou, S.3
  • 30
    • 0000069302 scopus 로고
    • Finger break-up in Hele-Shaw cells
    • DEGREGORIA, A. J. & SCHWARTZ, L. W. 1985 Finger break-up in Hele-Shaw cells. Phys. Fluids 28, 2313.
    • (1985) Phys. Fluids , vol.28 , pp. 2313
    • DeGregoria, A.J.1    Schwartz, L.W.2
  • 31
    • 0004940163 scopus 로고
    • Saffman-Taylor fingers with anisotropic surface tension
    • DORSEY, A. T. & MARTIN, O. 1987 Saffman-Taylor fingers with anisotropic surface tension. Phys. Rev. A 35 3989.
    • (1987) Phys. Rev. A , vol.35 , pp. 3989
    • Dorsey, A.T.1    Martin, O.2
  • 32
    • 0000694313 scopus 로고
    • Evolution d'une interface par capillarite' et diffusion de volume
    • DUCHON, J. & ROBERT, R. 1984 Evolution d'une interface par capillarite' et diffusion de volume. Ann l'Inst. H. Poincare' 1, 361.
    • (1984) Ann L'inst. H. Poincare' , vol.1 , pp. 361
    • Duchon, J.1    Robert, R.2
  • 33
    • 22044444067 scopus 로고    scopus 로고
    • A Hele-Shaw problem and the second Painleve' transcendent
    • FOKAS, A. S. & TANVEER, S. 1998 A Hele-Shaw problem and the second Painleve' transcendent. Math. Proc. Camb. Phil. Soc. 124, 169.
    • (1998) Math. Proc. Camb. Phil. Soc. , vol.124 , pp. 169
    • Fokas, A.S.1    Tanveer, S.2
  • 34
    • 0000280217 scopus 로고
    • Unsteady filtration with a free surface
    • in Russian
    • GALIN, L. A. 1945 Unsteady filtration with a free surface. Dokl. Akad. Nauk. SSSR 47, 246 (in Russian).
    • (1945) Dokl. Akad. Nauk. SSSR , vol.47 , pp. 246
    • Galin, L.A.1
  • 37
    • 33749026600 scopus 로고
    • The flow of water
    • HELE-SHAW, H. J. S. 1898 The flow of water. Nature 58, 34.
    • (1898) Nature , vol.58 , pp. 34
    • Hele-Shaw, H.J.S.1
  • 38
    • 34250022330 scopus 로고
    • Channelling in packed columns
    • HILL, S. 1952 Channelling in packed columns. Chem. Engng Sci. 1, 247.
    • (1952) Chem. Engng Sci. , vol.1 , pp. 247
    • Hill, S.1
  • 40
    • 0023242924 scopus 로고
    • Viscous fingering in porous media
    • HOMSY, G. M. 1987 Viscous fingering in porous media. Ann. Rev. Fluid Mech. 19, 271.
    • (1987) Ann. Rev. Fluid Mech. , vol.19 , pp. 271
    • Homsy, G.M.1
  • 41
    • 35949010597 scopus 로고
    • Bubbles in the Hele-Shaw cell: Pattern selection & tip perturbations
    • HONG, D. C. & FAMILY, F. 1988 Bubbles in the Hele-Shaw cell: pattern selection & tip perturbations. Phys. Rev. A 37, 2724.
    • (1988) Phys. Rev. A , vol.37 , pp. 2724
    • Hong, D.C.1    Family, F.2
  • 42
    • 0000772855 scopus 로고
    • Analytic theory for the selection of Saffman-Taylor fingers
    • HONG, D. C. & LANGER, J. S. 1986 Analytic theory for the selection of Saffman-Taylor fingers. Phys. Rev. Lett. 56, 2032.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 2032
    • Hong, D.C.1    Langer, J.S.2
  • 43
    • 0008283862 scopus 로고
    • Removing the stiffness from interfacial flows with surface tension
    • HOU, T. Y., LOWENGRUB, J. S. & SHELLEY, M. J. 1994 Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114, 312.
    • (1994) J. Comput. Phys. , vol.114 , pp. 312
    • Hou, T.Y.1    Lowengrub, J.S.2    Shelley, M.J.3
  • 45
    • 0022733938 scopus 로고
    • Fingering in Hele-Shaw cells
    • HOWISON, S. D. 1986 Fingering in Hele-Shaw cells. J. Fluid Mech. 167, 439.
    • (1986) J. Fluid Mech. , vol.167 , pp. 439
    • Howison, S.D.1
  • 46
    • 84971920974 scopus 로고
    • Complex variable methods in Hele-Shaw moving boundary problems
    • HOWISON, S. D. 1992 Complex variable methods in Hele-Shaw moving boundary problems. Eur. J. Appl. Maths 3, 209.
    • (1992) Eur. J. Appl. Maths , vol.3 , pp. 209
    • Howison, S.D.1
  • 47
    • 0033911790 scopus 로고    scopus 로고
    • A note on the two-phase Hele-Shaw problem
    • HOWISON, S. D. 2000 A note on the two-phase Hele-Shaw problem. J. Fluid Mech. 409, 243-249.
    • (2000) J. Fluid Mech. , vol.409 , pp. 243-249
    • Howison, S.D.1
  • 48
    • 0019569274 scopus 로고
    • Fundamentals of dendritic solidification - I. Steady state tip growth
    • HUANG, S. C. & GLICKSMAN, M. E. 1981 Fundamentals of dendritic solidification - I. Steady state tip growth. Acta Metall. 29, 701.
    • (1981) Acta Metall. , vol.29 , pp. 701
    • Huang, S.C.1    Glicksman, M.E.2
  • 49
    • 0001309752 scopus 로고
    • Temperature field around a spheroidal, cylindrical and acicular crystal growing in a supercooled melt
    • in Russian
    • IVANTSOV, G. P. 1948 Temperature field around a spheroidal, cylindrical and acicular crystal growing in a supercooled melt. Dokl. Akad. Nauk. SSSR 58, 569 (in Russian).
    • (1948) Dokl. Akad. Nauk. SSSR , vol.58 , pp. 569
    • Ivantsov, G.P.1
  • 50
    • 0031320751 scopus 로고    scopus 로고
    • Numerical solutions of sink flow in the Hele-Shaw cell with small surface tension
    • KELLY, E. D. & HINCH, E. J. 1997 Numerical solutions of sink flow in the Hele-Shaw cell with small surface tension. Eur. J. Appl Maths 8, 533.
    • (1997) Eur. J. Appl Maths , vol.8 , pp. 533
    • Kelly, E.D.1    Hinch, E.J.2
  • 51
    • 0011738614 scopus 로고
    • Steady state dendritic crystal growth
    • KESSLER, D., KOPLIK, J. & LEVINE, H. 1986 Steady state dendritic crystal growth. Phys. Rev. A 33, 3352.
    • (1986) Phys. Rev. A , vol.33 , pp. 3352
    • Kessler, D.1    Koplik, J.2    Levine, H.3
  • 52
    • 0024000989 scopus 로고
    • Patterned selection in fingered growth phenomena
    • KESSLER, D., KOPLIK, J. & LEVINE, H. 1988 Patterned Selection in fingered growth phenomena. Adv. Phys. 37, 255.
    • (1988) Adv. Phys. , vol.37 , pp. 255
    • Kessler, D.1    Koplik, J.2    Levine, H.3
  • 53
    • 35949019873 scopus 로고
    • The theory of Saffman-Taylor fingers
    • KESSLER, D. & LEVINE, H. 1985 The theory of Saffman-Taylor fingers. Phys. Rev. A 32, 1930.
    • (1985) Phys. Rev. A , vol.32 , pp. 1930
    • Kessler, D.1    Levine, H.2
  • 54
    • 0343767426 scopus 로고
    • Stability of finger patterns in Hele-Shaw cells
    • KESSLER, D. & LEVINE, H. 1986a Stability of finger patterns in Hele-Shaw Cells. Phys. Rev. A 33, 2632.
    • (1986) Phys. Rev. A , vol.33 , pp. 2632
    • Kessler, D.1    Levine, H.2
  • 55
    • 0142235768 scopus 로고
    • Stability of dendritic crystals
    • KESSLER, D. & LEVINE, H. 1986b Stability of dendritic crystals. Phys. Rev. Lett. 57, 3069.
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 3069
    • Kessler, D.1    Levine, H.2
  • 56
    • 0007823408 scopus 로고
    • Discrete set selection of Saffman-Taylor fingers
    • KESSLER, D. & LEVINE, H. 1987 Discrete set selection of Saffman-Taylor fingers. Phys. Fluids 30, 1246.
    • (1987) Phys. Fluids , vol.30 , pp. 1246
    • Kessler, D.1    Levine, H.2
  • 57
    • 0001454630 scopus 로고
    • Asymptotics beyond all orders in a model of crystal growth
    • KRUSKAL, M. & SEGUR, H. 1991 Asymptotics beyond all orders in a model of crystal growth. Stud. Appl. Maths 85, 129.
    • (1991) Stud. Appl. Maths , vol.85 , pp. 129
    • Kruskal, M.1    Segur, H.2
  • 58
    • 0342896415 scopus 로고    scopus 로고
    • Dendritic crystal growth for weak undercooling
    • KUNKA, M. D., FOSTER, M. R. & TANVEER, S. 1997 Dendritic crystal growth for weak undercooling. Phys. Rev. E. 56, 3068.
    • (1997) Phys. Rev. E. , vol.56 , pp. 3068
    • Kunka, M.D.1    Foster, M.R.2    Tanveer, S.3
  • 59
    • 0039114881 scopus 로고    scopus 로고
    • Dendritic crystal growth for weak undercooling, Part II: Surface energy effects on nonlinear evolution
    • KUNKA, M. D., FOSTER, M. R. & TANVEER, S. 1999 Dendritic crystal growth for weak undercooling, Part II: Surface energy effects on nonlinear evolution. Phys. Rev. E 59, 673.
    • (1999) Phys. Rev. E , vol.59 , pp. 673
    • Kunka, M.D.1    Foster, M.R.2    Tanveer, S.3
  • 60
    • 0023330485 scopus 로고
    • The nonlinear growth of a gravitationally unstable interface in a Hele-Shaw cell
    • MAXWORTHY, T. 1987 The nonlinear growth of a gravitationally unstable interface in a Hele-Shaw cell. J. Fluid Mech. 177, 207.
    • (1987) J. Fluid Mech. , vol.177 , pp. 207
    • Maxworthy, T.1
  • 61
    • 0000698993 scopus 로고
    • Experimental study of interface instability in a Hele-Shaw cell
    • MAXWORTHY, T. 1989 Experimental study of interface instability in a Hele-Shaw Cell. Phys. Rev. A 39, 5863.
    • (1989) Phys. Rev. A , vol.39 , pp. 5863
    • Maxworthy, T.1
  • 63
    • 0019374495 scopus 로고
    • The effect of surface tension on the shape of fingers in a Hele-Shaw cell
    • MCLEAN, J. W. & SAFFMAN, P. G. 1981 The effect of surface tension on the shape of fingers in a Hele-Shaw cell. J. Fluid Mech. 102, 455.
    • (1981) J. Fluid Mech. , vol.102 , pp. 455
    • McLean, J.W.1    Saffman, P.G.2
  • 64
    • 0000893452 scopus 로고
    • Selection of steady states in the two dimensional symmetric model of dendritic growth
    • MEIRON, D. 1986 Selection of steady states in the two dimensional symmetric model of dendritic growth. Phys. Rev. A 33, 2704.
    • (1986) Phys. Rev. A , vol.33 , pp. 2704
    • Meiron, D.1
  • 65
    • 0001594883 scopus 로고    scopus 로고
    • Selection of the Saffman-Taylor finger width in the absence of surface tension: An exact result
    • MINEEV-WEINSTEIN, M. 1998 Selection of the Saffman-Taylor finger width in the absence of surface tension: an exact result. Phys. Rev. Lett. 80, 2113.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 2113
    • Mineev-Weinstein, M.1
  • 66
    • 4243284590 scopus 로고
    • Class of non-singular exact solutions for Laplacian pattern formation
    • MINEEV-WEINSTEIN, M. & PONCE-DAWSON, S. 1994 Class of non-singular exact solutions for Laplacian pattern formation. Phys. Rev. E 50, 24.
    • (1994) Phys. Rev. E , vol.50 , pp. 24
    • Mineev-Weinstein, M.1    Ponce-Dawson, S.2
  • 67
    • 0023390334 scopus 로고
    • Velocity selection for needle crystals in the 2-D one-sided model
    • MISBAH, C. 1987 Velocity selection for needle crystals in the 2-D one-sided model. J. Phys. Paris 48 1265.
    • (1987) J. Phys. Paris , vol.48 , pp. 1265
    • Misbah, C.1
  • 69
    • 84903717133 scopus 로고
    • Two-phase displacement in Hele-Shaw cells: Theory
    • PARK, C. W. & HOMSY, G. M. 1985 Two-phase displacement in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291.
    • (1985) J. Fluid Mech. , vol.139 , pp. 291
    • Park, C.W.1    Homsy, G.M.2
  • 70
    • 0019683481 scopus 로고
    • Radial fingering in a Hele-Shaw cell
    • PATERSON, L. 1981 Radial fingering in a Hele-Shaw cell. J. Fluid Mech. 113, 513.
    • (1981) J. Fluid Mech. , vol.113 , pp. 513
    • Paterson, L.1
  • 72
    • 0018997574 scopus 로고
    • Penetration of fluid into a Hele-Shaw cell: The Saffman-Taylor experiment
    • PITTS, E. 1980 Penetration of fluid into a Hele-Shaw cell: the Saffman-Taylor experiment. J. Fluid Mech. 97, 53.
    • (1980) J. Fluid Mech. , vol.97 , pp. 53
    • Pitts, E.1
  • 74
    • 0023439567 scopus 로고
    • Interface conditions for two-phase displacement in Hele-Shaw cells
    • REINELT, D. A. 1987a Interface conditions for two-phase displacement in Hele-Shaw cells. J. Fluid Mech. 183, 219.
    • (1987) J. Fluid Mech. , vol.183 , pp. 219
    • Reinelt, D.A.1
  • 75
    • 0001677455 scopus 로고
    • The effect of thin film variations and transverse curvature on the shape of fingers in a Hele-Shaw cell
    • REINELT, D. A. 1987b The effect of thin film variations and transverse curvature on the shape of fingers in a Hele-Shaw cell. Phys. Fluids 30, 2617.
    • (1987) Phys. Fluids , vol.30 , pp. 2617
    • Reinelt, D.A.1
  • 76
    • 0006066135 scopus 로고
    • PhD thesis, Department of Applied Mathematics, California Institute of Technology
    • ROMERO, L. A. 1982 The fingering problem in a Hele-Shaw cell. PhD thesis, Department of Applied Mathematics, California Institute of Technology.
    • (1982) The Fingering Problem in a Hele-Shaw Cell
    • Romero, L.A.1
  • 77
    • 0022888394 scopus 로고
    • Viscous fingering in a Hele-Shaw cell
    • SAFFMAN, P. G. 1986 Viscous fingering in a Hele-Shaw cell. J. Fluid Mech. 173, 73.
    • (1986) J. Fluid Mech. , vol.173 , pp. 73
    • Saffman, P.G.1
  • 78
    • 33645094290 scopus 로고
    • Exact solutions for the growth of fingers from a flat interface between two fluids in a porous medium or Hele-Shaw cell
    • SAFFMAN, P. G. 1959 Exact solutions for the growth of fingers from a flat interface between two fluids in a porous medium or Hele-Shaw cell. Q. J. Mech. Appl. Maths 12, 146.
    • (1959) Q. J. Mech. Appl. Maths , vol.12 , pp. 146
    • Saffman, P.G.1
  • 79
    • 84948508246 scopus 로고
    • Lecture notes in physics
    • ed. Burridge et al. Springer
    • SAFFMAN, P. G. 1982 Fingering in a Porous Medium (ed. Burridge et al.) Lecture Notes in Physics. Springer.
    • (1982) Fingering in a Porous Medium
    • Saffman, P.G.1
  • 80
    • 0001383598 scopus 로고
    • The penetration of a fluid into a porous medium of Hele-Shaw cell containing a more viscous fluid
    • SAFFMAN, P. G. & TAYLOR, G. I. 1958 The penetration of a fluid into a porous medium of Hele-Shaw cell containing a more viscous fluid. Proc. R. Soc. Lond. A 245, 312.
    • (1958) Proc. R. Soc. Lond. A , vol.245 , pp. 312
    • Saffman, P.G.1    Taylor, G.I.2
  • 82
    • 0343767381 scopus 로고
    • Quantitative test of solvability theory for the Saffman-Taylor problem
    • SARKAR, S. & JASNOW, D. 1987 Quantitative test of solvability theory for the Saffman-Taylor problem. Phys. Rev. A 35, 4900.
    • (1987) Phys. Rev. A , vol.35 , pp. 4900
    • Sarkar, S.1    Jasnow, D.2
  • 83
    • 0001434111 scopus 로고
    • Stability of Hele-Shaw flows - The wetting-layer effect
    • SCHWARTZ, L. W. 1986 Stability of Hele-Shaw flows - the wetting-layer effect. Phys. Fluids 29, 2086.
    • (1986) Phys. Fluids , vol.29 , pp. 2086
    • Schwartz, L.W.1
  • 84
    • 0007723052 scopus 로고
    • Simulation of Hele-Shaw cell fingering with finite capillary number effects included phys
    • SCHWARTZ, L. W. & DEGREGORIA, A. J. 1987 Simulation of Hele-Shaw cell fingering with finite capillary number effects included Phys. Rev. A 35, 276.
    • (1987) Rev. A , vol.35 , pp. 276
    • Schwartz, L.W.1    DeGregoria, A.J.2
  • 85
    • 0005103108 scopus 로고
    • Universality in selection with local perturbations in the Saffman -Taylor problem
    • SHAW, B. E. 1989 Universality in selection with local perturbations in the Saffman -Taylor problem. Phys. Rev. A 40, 5875.
    • (1989) Phys. Rev. A , vol.40 , pp. 5875
    • Shaw, B.E.1
  • 86
    • 35949017843 scopus 로고
    • On velocity selection and the Saffman-Taylor problem
    • SHRAIMAN, B. I. 1986 On velocity selection and the Saffman-Taylor problem. Phys. Rev. Lett. 56, 2028.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 2028
    • Shraiman, B.I.1
  • 87
    • 0001378829 scopus 로고
    • Singularities in nonlocal interface dynamics
    • SHRAIMAN, B. I. & BENSIMON, D. 1984 Singularities in nonlocal interface dynamics. Phys. Rev. A 30, 2840.
    • (1984) Phys. Rev. A , vol.30 , pp. 2840
    • Shraiman, B.I.1    Bensimon, D.2
  • 88
    • 0030239360 scopus 로고    scopus 로고
    • Singular effects of surface tension in a smoothly evolving Hele-Shaw flow
    • SIEGEL, M., TANVEER, S. & DAI, W. S. 1996 Singular Effects of surface tension in a smoothly evolving Hele-Shaw flow. J. Fluid Mech. 323, 201.
    • (1996) J. Fluid Mech. , vol.323 , pp. 201
    • Siegel, M.1    Tanveer, S.2    Dai, W.S.3
  • 89
    • 0000624863 scopus 로고
    • Film draining and the Saffman-Taylor problem
    • TABELING, P. & LIBCHABER, A. 1986 Film draining and the Saffman-Taylor problem. Phys. Rev. A 33, 794.
    • (1986) Phys. Rev. A , vol.33 , pp. 794
    • Tabeling, P.1    Libchaber, A.2
  • 90
    • 0023331242 scopus 로고
    • An experimental study of the Saffman-Taylor instability
    • TABELING, P., ZOCCHI, G. & LIBCHABER, A. 1987 An experimental study of the Saffman-Taylor instability. J. Fluid Mech. 177, 67.
    • (1987) J. Fluid Mech. , vol.177 , pp. 67
    • Tabeling, P.1    Zocchi, G.2    Libchaber, A.3
  • 91
    • 0000132672 scopus 로고
    • The effect of surface tension on the shape of a Hele-Shaw cell bubble
    • TANVEER, S. 1986 The effect of surface tension on the shape of a Hele-Shaw cell bubble. Phys. Fluids 29, 3537.
    • (1986) Phys. Fluids , vol.29 , pp. 3537
    • Tanveer, S.1
  • 92
    • 0001677450 scopus 로고
    • New solutions for steady bubbles in a Hele-Shaw cell
    • TANVEER, S. 1987a New solutions for steady bubbles in a Hele-Shaw cell. Phys. Fluids 30, 651.
    • (1987) Phys. Fluids , vol.30 , pp. 651
    • Tanveer, S.1
  • 93
    • 0001677454 scopus 로고
    • Analytic theory for the selection of symmetric Saffman-Taylor finger
    • TANVEER, S. 1987b Analytic theory for the selection of symmetric Saffman-Taylor finger. Phys. Fluids 30, 1589.
    • (1987) Phys. Fluids , vol.30 , pp. 1589
    • Tanveer, S.1
  • 94
    • 0001677449 scopus 로고
    • Analytic theory for the linear stability of Saffman-Taylor finger
    • TANVEER, S. 1987c Analytic theory for the linear stability of Saffman-Taylor finger. Phys. Fluids 30, 2318.
    • (1987) Phys. Fluids , vol.30 , pp. 2318
    • Tanveer, S.1
  • 95
    • 0011462119 scopus 로고
    • Analytic theory for the selection of a two dimensional needle crystal at arbitrary Peclet number
    • TANVEER, S. 1989 Analytic theory for the selection of a two dimensional needle crystal at arbitrary Peclet number. Phys. Rev. A 40, 4756.
    • (1989) Phys. Rev. A , vol.40 , pp. 4756
    • Tanveer, S.1
  • 96
    • 0007235268 scopus 로고
    • Analytic theory for the selection of Saffman-Taylor finger in the presence of thin-film effects
    • TANVEER, S. 1990 Analytic theory for the selection of Saffman-Taylor finger in the presence of thin-film effects. Proc. R. Soc. Lond. A 428, 511.
    • (1990) Proc. R. Soc. Lond. A , vol.428 , pp. 511
    • Tanveer, S.1
  • 97
    • 0003378155 scopus 로고
    • Viscous displacement in a Hele-Shaw cell
    • ed. H. Segur, S. Tanveer & H. Levine. Plenum
    • TANVEER, S. 1991 Viscous Displacement in a Hele-Shaw cell. In Asymptotics Beyond all orders (ed. H. Segur, S. Tanveer & H. Levine). Plenum.
    • (1991) Asymptotics Beyond All Orders
    • Tanveer, S.1
  • 98
    • 0027507009 scopus 로고
    • Evolution of Hele-Shaw interface for small surface tension
    • TANVEER, S. 1993 Evolution of Hele-Shaw interface for small surface tension. Proc. R. Soc. Lond. A 343, 155.
    • (1993) Proc. R. Soc. Lond. A , vol.343 , pp. 155
    • Tanveer, S.1
  • 99
    • 0029656926 scopus 로고    scopus 로고
    • Asymptotic calculation of three-dimensional thin-film effects on unsteady Hele-Shaw fingering
    • TANVEER, S. 1996 Asymptotic calculation of three-dimensional thin-film effects on unsteady Hele-Shaw fingering. Phil. Trans. R. Soc. Lond. A 354, 1065.
    • (1996) Phil. Trans. R. Soc. Lond. A , vol.354 , pp. 1065
    • Tanveer, S.1
  • 100
    • 0003775791 scopus 로고
    • Stability of bubbles in a Hele-Shaw cell
    • TANVEER, S. & SAFFMAN, P. G. 1987 Stability of bubbles in a Hele-Shaw cell. Phys. Fluids 30, 2624.
    • (1987) Phys. Fluids , vol.30 , pp. 2624
    • Tanveer, S.1    Saffman, P.G.2
  • 101
    • 0000409950 scopus 로고
    • A note on the motion of bubbles in a Hele-Shaw cell and porous medium
    • TAYLOR, G. I. & SAFFMAN, P. G. 1959 A note on the motion of bubbles in a Hele-Shaw cell and porous medium. Q. J. Mech. Appl. Maths 12, 265.
    • (1959) Q. J. Mech. Appl. Maths , vol.12 , pp. 265
    • Taylor, G.I.1    Saffman, P.G.2
  • 102
    • 0000820856 scopus 로고
    • The Saffman-Taylor instability: From the linear to the circular geometry
    • THOME, H., RABAUD, M., HAKIM, V. & COUDER, Y. 1989 The Saffman-Taylor Instability: From the linear to the circular geometry. Phys. Fluids A 1, 224.
    • (1989) Phys. Fluids A , vol.1 , pp. 224
    • Thome, H.1    Rabaud, M.2    Hakim, V.3    Couder, Y.4
  • 103
    • 0000395122 scopus 로고
    • Fingers in a Hele-Shaw cell with surface tension
    • VANDEN-BROECK, J. M. 1983 Fingers in a Hele-Shaw cell with surface tension. Phys. Fluids 26, 2033.
    • (1983) Phys. Fluids , vol.26 , pp. 2033
    • Vanden-Broeck, J.M.1
  • 104
    • 84972017262 scopus 로고
    • A theoretical study of two phase flow through a narrow gap with a moving contact line: Viscous fingering in a Hele-Shaw cell
    • WEINSTEIN, S. J., DUSSAN V., E. B. & UNGAR, L. H. 1990 A theoretical study of two phase flow through a narrow gap with a moving contact line: viscous fingering in a Hele-Shaw cell. J. Fluid Mech. 221, 53.
    • (1990) J. Fluid Mech. , vol.221 , pp. 53
    • Weinstein, S.J.1    Dussan, V.E.B.2    Ungar, L.H.3
  • 106
    • 84972004495 scopus 로고
    • Globally unstable oscillatory modes in viscous fingering
    • Xu, J. J. 1991 Globally unstable oscillatory modes in viscous fingering. Eur. J. Appl. Maths 2, 105.
    • (1991) Eur. J. Appl. Maths , vol.2 , pp. 105
    • Xu, J.J.1
  • 107
    • 0005099975 scopus 로고
    • Finger narrowing under local perturbations in the Saffman-Taylor problem
    • ZOCCHI, G., SHAW, B., LIBCHABER, A. & KADANOFF, L. 1987 Finger narrowing under local perturbations in the Saffman-Taylor problem. Phys. Rev. A 36, 1894.
    • (1987) Phys. Rev. A , vol.36 , pp. 1894
    • Zocchi, G.1    Shaw, B.2    Libchaber, A.3    Kadanoff, L.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.