메뉴 건너뛰기




Volumn 15, Issue 1, 2004, Pages 1-37

Hele-Shaw flow with a point sink: Generic solution breakdown

Author keywords

[No Author keywords available]

Indexed keywords


EID: 2542567216     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S095679250400539X     Document Type: Article
Times cited : (10)

References (49)
  • 2
    • 33749006179 scopus 로고
    • Exact self-similar shapes in viscous fingering
    • BEN AMAR, M. (1991) Exact self-similar shapes in viscous fingering. Phys. Rev. A, 43(10), 5724-5727.
    • (1991) Phys. Rev. A , vol.43 , Issue.10 , pp. 5724-5727
    • Ben Amar, M.1
  • 3
    • 5844281477 scopus 로고
    • Viscous fingering in a wedge
    • BEN AMAR, M. (1991) Viscous fingering in a wedge. Phys. Rev. A, 44(6), 3673-3685.
    • (1991) Phys. Rev. A , vol.44 , Issue.6 , pp. 3673-3685
    • Ben Amar, M.1
  • 4
    • 11744348000 scopus 로고    scopus 로고
    • Finger behaviour of a shear thinning fluid in a Hele-Shaw cell
    • POIRE, E. C. & BEN AMAR, M. (1998) Finger behaviour of a shear thinning fluid in a Hele-Shaw cell. Phys. Rev. Lett. 81(10), 2048-2051.
    • (1998) Phys. Rev. Lett. , vol.81 , Issue.10 , pp. 2048-2051
    • Poire, E.C.1    Ben Amar, M.2
  • 5
    • 0001005698 scopus 로고    scopus 로고
    • Pushing a non-newtonian fluid in a Hele-Shaw cell: From fingers to needles
    • BEN AMAR, M. & POIRE, E. C. (1999) Pushing a non-Newtonian fluid in a Hele-Shaw cell: From fingers to needles. Phys Fluids, 11(7), 1757-1767.
    • (1999) Phys Fluids , vol.11 , Issue.7 , pp. 1757-1767
    • Ben Amar, M.1    Poire, E.C.2
  • 6
    • 84956246282 scopus 로고
    • Selection of the viscous finger in the 90° geometry
    • BRENER, E. A., KESSLER, D. A., LEVINE, H. & RAPPEL, W.-J. (1990) Selection of the viscous finger in the 90° geometry. Europhys. Lett. 13(2), 161-166.
    • (1990) Europhys. Lett. , vol.13 , Issue.2 , pp. 161-166
    • Brener, E.A.1    Kessler, D.A.2    Levine, H.3    Rappel, W.-J.4
  • 8
    • 0001165338 scopus 로고    scopus 로고
    • Numerical study of Hele-Shaw flow with suction
    • CENICEROS, H. D., HOU, T. Y. & SI, H. (1999) Numerical study of Hele-Shaw flow with suction. Phys. Fluids, 11(9), 2471-2486.
    • (1999) Phys. Fluids , vol.11 , Issue.9 , pp. 2471-2486
    • Ceniceros, H.D.1    Hou, T.Y.2    Si, H.3
  • 9
    • 0033263944 scopus 로고    scopus 로고
    • On the role of Stokes lines in the selection of Saffman-Taylor fingers with small surface tension
    • CHAPMAN, S. J. (1999) On the role of Stokes lines in the selection of Saffman-Taylor fingers with small surface tension. Euro. J. Appl. Math. 10, 513-534.
    • (1999) Euro. J. Appl. Math. , vol.10 , pp. 513-534
    • Chapman, S.J.1
  • 10
    • 0038668932 scopus 로고    scopus 로고
    • The selection of Saffman-Taylor fingers by kinetic undercooling
    • CHAPMAN, S. J. & KING, J. R. (2003) The selection of Saffman-Taylor fingers by kinetic undercooling. J. Eng. Math. 46(1), 1-32.
    • (2003) J. Eng. Math. , vol.46 , Issue.1 , pp. 1-32
    • Chapman, S.J.1    King, J.R.2
  • 12
  • 13
    • 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(4), 453-456.
    • (1991) Phys. Rev. Lett. , vol.67 , Issue.4 , pp. 453-456
    • Combescot, R.1    Ben Amar, M.2
  • 14
    • 0000636997 scopus 로고
    • Saffman-Taylor fingers in the sector geometry
    • COMBESCOT, R. (1992) Saffman-Taylor fingers in the sector geometry. Phys. Rev. A, 45(2), 873-884.
    • (1992) Phys. Rev. A , vol.45 , Issue.2 , pp. 873-884
    • Combescot, R.1
  • 16
    • 0028166588 scopus 로고
    • Two related free boundary problems
    • CRASTER, R. V. (1994) Two related free boundary problems. IMA Jl. Appl. Math. 52, 253-270.
    • (1994) IMA Jl. Appl. Math. , vol.52 , pp. 253-270
    • Craster, R.V.1
  • 17
    • 0000973660 scopus 로고    scopus 로고
    • The solution of a class of free boundary problems
    • CRASTER, R. V. (1997) The solution of a class of free boundary problems. Proc. R. Soc. Lond. A, 453, 607-630.
    • (1997) Proc. R. Soc. Lond. A , vol.453 , pp. 607-630
    • Craster, R.V.1
  • 18
    • 0000108670 scopus 로고    scopus 로고
    • Applications of Fuchsian differential equations to free boundary problems
    • CRASTER, R. V. & HOANG, V. H. (1998) Applications of Fuchsian differential equations to free boundary problems. Proc. R. Soc. Lond. A, 454, 1241-1252.
    • (1998) Proc. R. Soc. Lond. A , vol.454 , pp. 1241-1252
    • Craster, R.V.1    Hoang, V.H.2
  • 19
    • 0033276268 scopus 로고    scopus 로고
    • Flow around a wedge of arbitrary angle in a Hele-Shaw cell
    • CUMMINGS, L. J. (2000) Flow around a wedge of arbitrary angle in a Hele-Shaw cell. Euro. J. Appl. Math. 10, 547-560.
    • (2000) Euro. J. Appl. Math. , vol.10 , pp. 547-560
    • Cummings, L.J.1
  • 20
    • 84971155357 scopus 로고
    • A variational inequality approach to Hele-Shaw flow with a moving boundary
    • ELLIOTT, C. M. & JANOVSKY, V. (1981) A variational inequality approach to Hele-Shaw flow with a moving boundary. Proc. Roy. Soc. Edin. A88, 93-107.
    • (1981) Proc. Roy. Soc. Edin. , vol.A88 , pp. 93-107
    • Elliott, C.M.1    Janovsky, V.2
  • 21
    • 0000280217 scopus 로고
    • Unsteady filtration with a free surface
    • (in Russian)
    • GALIN, L. A. (1945) Unsteady filtration with a free surface Dokl. Akad. Nauk. S.S.S.R. 47, 246-249 (in Russian).
    • (1945) Dokl. Akad. Nauk. S.S.S.R. , vol.47 , pp. 246-249
    • Galin, L.A.1
  • 23
    • 0032043370 scopus 로고    scopus 로고
    • Pseudo-steady-state solutions for solidification in a wedge
    • HOANG, HA V., HILL, J. M. & DEWYNNE, J. N. (1998) Pseudo-steady-state solutions for solidification in a wedge. IMA J. Appl. Math. 60, 109-121.
    • (1998) IMA J. Appl. Math. , vol.60 , pp. 109-121
    • Hoang, Ha.V.1    Hill, J.M.2    Dewynne, J.N.3
  • 24
    • 0036895549 scopus 로고    scopus 로고
    • Wedge solidification with differing types of boundary conditions
    • HOANG, V. H. & CRASTER, R. V. (1998) Wedge solidification with differing types of boundary conditions. IMA J. Appl. Math. 67, 509-524.
    • (1998) IMA J. Appl. Math. , vol.67 , pp. 509-524
    • Hoang, V.H.1    Craster, R.V.2
  • 25
    • 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, 2032-2035.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 2032-2035
    • Hong, D.C.1    Langer, J.S.2
  • 26
    • 0024902049 scopus 로고
    • Explicit solutions to six free-boundary problems in fluid flow and diffusion
    • HOWISON, S. D. & KING, J. R. (1989) Explicit solutions to six free-boundary problems in fluid flow and diffusion. IMA J. Appl. Math. 42, 155-175.
    • (1989) IMA J. Appl. Math. , vol.42 , pp. 155-175
    • Howison, S.D.1    King, J.R.2
  • 27
    • 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. Euro. J. Appl. Math. 3, 209-224.
    • (1992) Euro. J. Appl. Math. , vol.3 , pp. 209-224
    • Howison, S.D.1
  • 28
    • 0031320751 scopus 로고    scopus 로고
    • Numerical simulations of sink flow in the hele-shaw cell with small surface tension
    • KELLY, E. D. & HINCH, E. J. (1997) Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension. Euro. J. Appl. Math. 8, 533-550.
    • (1997) Euro. J. Appl. Math. , vol.8 , pp. 533-550
    • Kelly, E.D.1    Hinch, E.J.2
  • 29
    • 84974510185 scopus 로고
    • Persistence of corners in free boundaries in Hele-Shaw flow
    • KING, J. R., LACEY, A. A. & VAZQUEZ, J. L. (1995) Persistence of corners in free boundaries in Hele-Shaw flow. Euro. J. Appl. Math. 6, 455-490.
    • (1995) Euro. J. Appl. Math. , vol.6 , pp. 455-490
    • King, J.R.1    Lacey, A.A.2    Vazquez, J.L.3
  • 30
    • 84974489302 scopus 로고
    • Development of singularities in some moving boundary problems
    • KING, J. R. (1995) Development of singularities in some moving boundary problems. Euro. J. Appl. Math. 6, 491-507.
    • (1995) Euro. J. Appl. Math. , vol.6 , pp. 491-507
    • King, J.R.1
  • 31
    • 0013091915 scopus 로고
    • Moving boundary problems in the flow of liquid through porous media
    • LACEY, A. A. (1982) Moving boundary problems in the flow of liquid through porous media. J. Austral. Math. Soc. B24, 171-193.
    • (1982) J. Austral. Math. Soc. , vol.B24 , pp. 171-193
    • Lacey, A.A.1
  • 32
    • 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, 445-469.
    • (1981) J. Fluid Mech. , vol.102 , pp. 445-469
    • McLean, J.W.1    Saffman, P.G.2
  • 33
    • 0032000710 scopus 로고    scopus 로고
    • Singularities in Hele-Shaw flows
    • NIE, Q. & TIAN, F. R. (1998) Singularities in Hele-Shaw flows. S.I.A.M. J. Appl. Math. 58(1), 34-54.
    • (1998) S.I.A.M. J. Appl. Math. , vol.58 , Issue.1 , pp. 34-54
    • Nie, Q.1    Tian, F.R.2
  • 34
    • 0036252822 scopus 로고    scopus 로고
    • Singularities in Hele-Shaw flows driven by a multipole
    • NIE, Q. & TIAN, F. R. (2001) Singularities in Hele-Shaw flows driven by a multipole. S.I.A.M. J. Appl. Math. 62(2), 385-406.
    • (2001) S.I.A.M. J. Appl. Math. , vol.62 , Issue.2 , pp. 385-406
    • Nie, Q.1    Tian, F.R.2
  • 35
    • 0036642646 scopus 로고    scopus 로고
    • Hele-Shaw flows with nonlinear kinetic undercooling regularisation
    • PLESHCHINSKII, N. B. & REISSIG, M. (2002) Hele-Shaw flows with nonlinear kinetic undercooling regularisation. Nonlinear Anal. 50, 191-203.
    • (2002) Nonlinear Anal. , vol.50 , pp. 191-203
    • Pleshchinskii, N.B.1    Reissig, M.2
  • 38
    • 0347031071 scopus 로고    scopus 로고
    • Analytical and numerical treatment of a complex model for Hele-Shaw moving boundary problems with kinetic undercooling regularization
    • REISSIG, M., ROGOSIN, S. V. & HÜBNER, F. (1999) Analytical and numerical treatment of a complex model for Hele-Shaw moving boundary problems with kinetic undercooling regularization. Euro. J. Appl. Math. 10, 561-579.
    • (1999) Euro. J. Appl. Math. , vol.10 , pp. 561-579
    • Reissig, M.1    Rogosin, S.V.2    Hübner, F.3
  • 39
    • 0015491441 scopus 로고
    • Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
    • RICHARDSON, S. (1972) Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel. J. Fluid Mech. 56, 609-618.
    • (1972) J. Fluid Mech. , vol.56 , pp. 609-618
    • Richardson, S.1
  • 40
    • 0035567567 scopus 로고    scopus 로고
    • Hele-Shaw flows with free boundaries in a corner or around a wedge Part I: Liquid at the vertex
    • RICHARDSON, S. (2001) Hele-Shaw flows with free boundaries in a corner or around a wedge Part I: Liquid at the vertex. Euro. J. Appl. Math. 12(6), 665-676.
    • (2001) Euro. J. Appl. Math. , vol.12 , Issue.6 , pp. 665-676
    • Richardson, S.1
  • 41
    • 0035562105 scopus 로고    scopus 로고
    • Hele-Shaw flows with free boundaries in a corner or around a wedge Part II: Air at the vertex
    • RICHARDSON, S. (2001) Hele-Shaw flows with free boundaries in a corner or around a wedge Part II: Air at the vertex. Euro. J. Appl. Math. 12(6), 677-688.
    • (2001) Euro. J. Appl. Math. , vol.12 , Issue.6 , pp. 677-688
    • Richardson, S.1
  • 42
    • 0001383598 scopus 로고
    • The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
    • SAFFMAN, P. G. & TAYLOR, G. I. (1958) The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy, Soc. Lond. A, 245, 312-329.
    • (1958) Proc. Roy, Soc. Lond. A , vol.245 , pp. 312-329
    • Saffman, P.G.1    Taylor, G.I.2
  • 43
    • 35949017843 scopus 로고
    • Velocity selection and the Saffman-Taylor problem
    • SHRAIMAN, B. I. (1986) Velocity selection and the Saffman-Taylor problem. Phys. Rev. Lett. 56, 2028-2031.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 2028-2031
    • Shraiman, B.I.1
  • 44
    • 4244168693 scopus 로고    scopus 로고
    • Singular perturbation of smoothly evolving Hele-Shaw solutions
    • SIEGEL, M. & TANVEER, S. (1996) Singular perturbation of smoothly evolving Hele-Shaw solutions. Phys. Rev. Lett. 76(3).
    • (1996) Phys. Rev. Lett. , vol.76 , Issue.3
    • Siegel, M.1    Tanveer, S.2
  • 45
    • 0030239360 scopus 로고    scopus 로고
    • Singular effects of surface tension in Hele-Shaw cells
    • SIEGEL, M., TANVEER, S. & DAI, W.-S. (1996) Singular effects of surface tension in Hele-Shaw cells. J. Fluid Mech. 323, 201-236.
    • (1996) J. Fluid Mech. , vol.323 , pp. 201-236
    • Siegel, M.1    Tanveer, S.2    Dai, W.-S.3
  • 46
    • 0033927876 scopus 로고    scopus 로고
    • Surprises in viscous fingering
    • TANVEER, S. (2000) Surprises in viscous fingering. J. Fluid Mech. 409, 273-308.
    • (2000) J. Fluid Mech. , vol.409 , pp. 273-308
    • Tanveer, S.1
  • 47
    • 0000820856 scopus 로고
    • The Saffman-Taylor instability: From the linear to the circular geometry
    • THOMÉ, H., RABAUD, M., HAKIM, V. & COUDER, Y. (1989) The Saffman-Taylor instability: From the linear to the circular geometry. Phys. Fluids A, 1, 224-240.
    • (1989) Phys. Fluids A , vol.1 , pp. 224-240
    • Thomé, H.1    Rabaud, M.2    Hakim, V.3    Couder, Y.4
  • 48
    • 0001623951 scopus 로고
    • Saffman-Taylor problem in sector geometry: Solution and selection
    • Tu, Y. (1991) Saffman-Taylor problem in sector geometry: Solution and selection. Phys. Rev. A, 44(2), 1203-1210.
    • (1991) Phys. Rev. A , vol.44 , Issue.2 , pp. 1203-1210
    • Tu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.