메뉴 건너뛰기




Volumn 68, Issue 3, 2007, Pages 760-783

Shock solutions for particle-laden thin films

Author keywords

Contact lines; Riemann problem; Sedimentation; Singular shocks; Suspension flow; Systems of conservation laws; Thin liquid films

Indexed keywords

APPLIED MATHEMATICS; CONSERVATION LAWS; CONSTANT FLUX; CONTACT LINES; CONTINUUM MODELING; HEAVY PARTICLES; LENGTH SCALING; MIXTURE VISCOSITY; ONE-DIMENSION; PARTICLE CONCENTRATIONS; PARTICLE SETTLING; PARTICLE SETTLING VELOCITY; PARTICLE VOLUME FRACTIONS; RIEMANN PROBLEMS; THIN FILM FLOWS; VISCOUS FLUIDS;

EID: 47149101615     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/060677811     Document Type: Article
Times cited : (48)

References (60)
  • 1
    • 0000345144 scopus 로고
    • Existence and role of the precursor film in the spreading of polymer liquids
    • D. AUSSERRÉ, A. M. PICARD, AND L. LÉGER, Existence and role of the precursor film in the spreading of polymer liquids, Phys. Rev. Lett., 57 (1986), pp. 2671-2674.
    • (1986) Phys. Rev. Lett , vol.57 , pp. 2671-2674
    • AUSSERRÉ, D.1    PICARD, A.M.2    LÉGER, L.3
  • 3
    • 0031103749 scopus 로고    scopus 로고
    • Linear stability and transient growth in driven contact lines
    • A. L. BERTOZZI AND M. P. BRENNER, Linear stability and transient growth in driven contact lines, Phys. Fluids, 9 (1997), pp. 530-539.
    • (1997) Phys. Fluids , vol.9 , pp. 530-539
    • BERTOZZI, A.L.1    BRENNER, M.P.2
  • 4
    • 0038919593 scopus 로고    scopus 로고
    • Undercompressive shocks in thin film flows
    • A. L. BERTOZZI, A. MUNCH, AND M. SHEARER, Undercompressive shocks in thin film flows, Phys. D, 134 (1999), pp. 431-464.
    • (1999) Phys. D , vol.134 , pp. 431-464
    • BERTOZZI, A.L.1    MUNCH, A.2    SHEARER, M.3
  • 5
    • 0035252639 scopus 로고    scopus 로고
    • That sinking feeling
    • M. P. BRENNER AND P. J. MUCHA, That sinking feeling, Nature, 409 (2001), pp. 568-570.
    • (2001) Nature , vol.409 , pp. 568-570
    • BRENNER, M.P.1    MUCHA, P.J.2
  • 6
    • 84972262906 scopus 로고
    • Nonlinear stability of evaporating/ condensing liquid films
    • J. P. BURELBACH, S. G. BANKOFF, AND S. H. DAVIS, Nonlinear stability of evaporating/ condensing liquid films, J. Fluid Mech., 195 (1988), pp. 463-494.
    • (1988) J. Fluid Mech , vol.195 , pp. 463-494
    • BURELBACH, J.P.1    BANKOFF, S.G.2    DAVIS, S.H.3
  • 8
    • 0022269123 scopus 로고
    • Variance in the sedimentation speed of a suspension
    • R. E. CAFLISCH AND J. H. C. LUKE, Variance in the sedimentation speed of a suspension, Phys. Fluids, 28 (1985), pp. 759-760.
    • (1985) Phys. Fluids , vol.28 , pp. 759-760
    • CAFLISCH, R.E.1    LUKE, J.H.C.2
  • 9
    • 0037059091 scopus 로고    scopus 로고
    • Gravitational instability in suspension flow
    • I. C. CARPEN AND J. F. BRADY, Gravitational instability in suspension flow, J. Fluid Mech., 472 (2002), pp. 201-210.
    • (2002) J. Fluid Mech , vol.472 , pp. 201-210
    • CARPEN, I.C.1    BRADY, J.F.2
  • 11
    • 0022182635 scopus 로고
    • Sedimentation of noncolloidal particles at low Reynolds numbers
    • R. H. DAVIS AND A. ACRIVOS, Sedimentation of noncolloidal particles at low Reynolds numbers, Annu. Rev. Fluid Mech. 17 (1985), pp. 91-118.
    • (1985) Annu. Rev. Fluid Mech , vol.17 , pp. 91-118
    • DAVIS, R.H.1    ACRIVOS, A.2
  • 12
    • 0001756612 scopus 로고
    • Growth of fingers at a driven three-phase contact line
    • J. R. DE BRUYN, Growth of fingers at a driven three-phase contact line, Phys. Rev. A, 46 (1992), pp. R4500-R4503.
    • (1992) Phys. Rev. A , vol.46
    • DE BRUYN, J.R.1
  • 13
    • 1842695585 scopus 로고
    • Wetting: Statics and dynamics
    • P. G. DE GENNES, Wetting: Statics and dynamics, Rev. Modern Phys., 57 (1985), pp. 827-863.
    • (1985) Rev. Modern Phys , vol.57 , pp. 827-863
    • DE GENNES, P.G.1
  • 14
    • 0016091290 scopus 로고    scopus 로고
    • E. B. DUSSAN V. AND S. H. DAVIS, On the motion of fluid-fluid interface along a solid surface, J. Fluid Mech., 65 (1974), pp. 71-95.
    • E. B. DUSSAN V. AND S. H. DAVIS, On the motion of fluid-fluid interface along a solid surface, J. Fluid Mech., 65 (1974), pp. 71-95.
  • 16
    • 0000454176 scopus 로고
    • Viscous flow down a slope in the vicinity of a contact line
    • R. GOODWIN AND G. M. HOMSY, Viscous flow down a slope in the vicinity of a contact line, Phys. Fluids A, 3 (1991), pp. 515-528.
    • (1991) Phys. Fluids A , vol.3 , pp. 515-528
    • GOODWIN, R.1    HOMSY, G.M.2
  • 17
    • 0017926990 scopus 로고
    • On the motion of a small viscous droplet that wets a surface
    • H. P. GREENSPAN, On the motion of a small viscous droplet that wets a surface, J. Fluid Mech., 84 (1978), pp. 125-143.
    • (1978) J. Fluid Mech , vol.84 , pp. 125-143
    • GREENSPAN, H.P.1
  • 19
    • 0025382895 scopus 로고
    • Spreading and instability of a viscous fluid sheet
    • L. M. HOCKING, Spreading and instability of a viscous fluid sheet, J. Fluid Mech., 211 (1990), pp. 373-392.
    • (1990) J. Fluid Mech , vol.211 , pp. 373-392
    • HOCKING, L.M.1
  • 20
    • 0014995788 scopus 로고
    • Hydrodynamic model of steady movement of a solid/liquid/fluid contact line
    • C. HUH AND L. E. SCRIVEN, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci., 35 (1971), pp. 85-101.
    • (1971) J. Colloid Interface Sci , vol.35 , pp. 85-101
    • HUH, C.1    SCRIVEN, L.E.2
  • 21
    • 34247465115 scopus 로고
    • Flow and instability of a viscous current down a slope
    • H. E. HUPPERT, Flow and instability of a viscous current down a slope, Nature, 300 (1982), pp. 427-429.
    • (1982) Nature , vol.300 , pp. 427-429
    • HUPPERT, H.E.1
  • 22
    • 0032048569 scopus 로고    scopus 로고
    • The dynamics of thin films I: General theory
    • M. P. IDA AND M. J. MIKSIS, The dynamics of thin films I: General theory, SIAM J. Appl. Math., 58 (1998), pp. 456-473.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 456-473
    • IDA, M.P.1    MIKSIS, M.J.2
  • 23
    • 0032181920 scopus 로고    scopus 로고
    • Front dynamics and fingering of a driven contact, line
    • A. INDEKINA, I. VERETENNIKOV. AND H.-C. CHANG, Front dynamics and fingering of a driven contact, line. J. Fluid Mech., 373 (1998), pp. 81-110.
    • (1998) J. Fluid Mech , vol.373 , pp. 81-110
    • INDEKINA, A.1    VERETENNIKOV, I.2    CHANG, H.-C.3
  • 24
    • 0026807201 scopus 로고
    • Fingering instability of a gravitationally driven contact line
    • J. M. JERRETT AND J. R. DE BRUYN, Fingering instability of a gravitationally driven contact line, Phys. Fluids A. 4 (1992), pp. 234-242.
    • (1992) Phys. Fluids A , vol.4 , pp. 234-242
    • JERRETT, J.M.1    DE BRUYN, J.R.2
  • 25
    • 0000635775 scopus 로고    scopus 로고
    • Experimental study of rivulet formation on an inclined plate by fluorescent imaging
    • M. F. G. JOHNSON. R. A. SCHLÜTER, M. J. MIKSIS, AND S. G. BANKOFF, Experimental study of rivulet formation on an inclined plate by fluorescent imaging, J. Fluid Mech., 394 (1999), pp. 339-354.
    • (1999) J. Fluid Mech , vol.394 , pp. 339-354
    • JOHNSON, M.F.G.1    SCHLÜTER, R.A.2    MIKSIS, M.J.3    BANKOFF, S.G.4
  • 26
    • 33744986031 scopus 로고    scopus 로고
    • A constitutive law for dense granular flows
    • P. JOP, Y. FORTERRE. AND O. POULIQUEN, A constitutive law for dense granular flows, Nature, 441 (2006), pp. 727-730.
    • (2006) Nature , vol.441 , pp. 727-730
    • JOP, P.1    FORTERRE, Y.2    POULIQUEN, O.3
  • 27
    • 0001556426 scopus 로고
    • Spaces of weighted measures for conservation laws with singular shock solutions
    • B. L. KEYFITZ AND H. C. KRANZER, Spaces of weighted measures for conservation laws with singular shock solutions, J. Differential Equations, 118 (1995), pp. 420-451.
    • (1995) J. Differential Equations , vol.118 , pp. 420-451
    • KEYFITZ, B.L.1    KRANZER, H.C.2
  • 28
    • 0035504841 scopus 로고    scopus 로고
    • Pattern formation in the flow of thin films down an incline: Constant flux configuration
    • L. KONDIC AND J. DIEZ, Pattern formation in the flow of thin films down an incline: Constant flux configuration, Phys. Fluids, 13 (2001), pp. 3168-3184.
    • (2001) Phys. Fluids , vol.13 , pp. 3168-3184
    • KONDIC, L.1    DIEZ, J.2
  • 29
    • 47149092512 scopus 로고    scopus 로고
    • H. C. KRANZER AND B. L. KEYFITZ, A strictly hyperbolic system of conservation laws admitting singular shocks, in Nonlinear Evolution Equations That Change Type, IMA Math. Appl. 27, Springer, New York, 1990, pp. 107-125.
    • H. C. KRANZER AND B. L. KEYFITZ, A strictly hyperbolic system of conservation laws admitting singular shocks, in Nonlinear Evolution Equations That Change Type, IMA Vol. Math. Appl. 27, Springer, New York, 1990, pp. 107-125.
  • 30
    • 49649141957 scopus 로고
    • Rheology of monodisperse latices
    • I. M. KRIEGER, Rheology of monodisperse latices, Adv. Colloid Interface Sci., 3 (1972), pp. 111-136.
    • (1972) Adv. Colloid Interface Sci , vol.3 , pp. 111-136
    • KRIEGER, I.M.1
  • 31
    • 0010086308 scopus 로고
    • A theory of sedimentation
    • G. J. KYNCH, A theory of sedimentation, Trans. Faraday Soc., 48 (1952), pp. 166-176.
    • (1952) Trans. Faraday Soc , vol.48 , pp. 166-176
    • KYNCH, G.J.1
  • 32
    • 0003261490 scopus 로고
    • Hyperbolic Systems of Conservation Laws and Mathematical Theory of Shock Waves
    • SIAM, Philadelphia
    • P. D. LAX, Hyperbolic Systems of Conservation Laws and Mathematical Theory of Shock Waves, CBMS-NSF Regional Conf. Ser. in Appl. Math. 11, SIAM, Philadelphia, 1973.
    • (1973) CBMS-NSF Regional Conf. Ser. in Appl. Math , vol.11
    • LAX, P.D.1
  • 34
    • 0023482733 scopus 로고
    • The shear-induced migration of particles in concentrated suspensions
    • D. LEIGHTON AND A. ACRIVOS, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech., 181 (1987), pp. 415-439.
    • (1987) J. Fluid Mech , vol.181 , pp. 415-439
    • LEIGHTON, D.1    ACRIVOS, A.2
  • 35
    • 33750161072 scopus 로고    scopus 로고
    • The motion of a thin liquid film driven by surfactant and gravity
    • R. LEVY AND M. SHEARER, The motion of a thin liquid film driven by surfactant and gravity, SIAM J. Appl. Math., 66 (2006), pp. 1588-1609.
    • (2006) SIAM J. Appl. Math , vol.66 , pp. 1588-1609
    • LEVY, R.1    SHEARER, M.2
  • 36
    • 84968497544 scopus 로고
    • The Riemann problem for general 2× 2 conservation laws
    • T.-P. LIU, The Riemann problem for general 2× 2 conservation laws, Trans. Amer. Math. Soc., 199 (1974), pp. 89-112.
    • (1974) Trans. Amer. Math. Soc , vol.199 , pp. 89-112
    • LIU, T.-P.1
  • 37
    • 0001513936 scopus 로고
    • Riemann problem for general systems of conservation laws
    • T.-P. Liu, Riemann problem for general systems of conservation laws, J. Differential Equations, 18 (1975), pp. 218-234.
    • (1975) J. Differential Equations , vol.18 , pp. 218-234
    • Liu, T.-P.1
  • 38
    • 0015126796 scopus 로고
    • The dynamics of thin liquid films in the presence of surface-tension gradients
    • V. LUDVIKSSON AND E. N. LIGHTFOOT, The dynamics of thin liquid films in the presence of surface-tension gradients, Am. Inst. Chem. Engrs. J., 17 (1971), pp. 1166-1173.
    • (1971) Am. Inst. Chem. Engrs. J , vol.17 , pp. 1166-1173
    • LUDVIKSSON, V.1    LIGHTFOOT, E.N.2
  • 39
    • 0000096914 scopus 로고
    • Dynamic considerations in the closing and opening of holes in thin liquid films
    • J. A. MORIARTY AND L. W. SCHWARTZ, Dynamic considerations in the closing and opening of holes in thin liquid films, J. Colloid Interface Sci., 161 (1993), pp. 335-342.
    • (1993) J. Colloid Interface Sci , vol.161 , pp. 335-342
    • MORIARTY, J.A.1    SCHWARTZ, L.W.2
  • 41
    • 0032007242 scopus 로고    scopus 로고
    • J. Multiphase Flow, 24 (1998), pp. 105-130.
    • (1998) J. Multiphase Flow , vol.24 , pp. 105-130
  • 42
    • 0033462786 scopus 로고    scopus 로고
    • Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination
    • A. MUNCH AND B. WAGNER, Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination, European J. Appl. Math., 10 (1999), pp. 297-318.
    • (1999) European J. Appl. Math , vol.10 , pp. 297-318
    • MUNCH, A.1    WAGNER, B.2
  • 43
    • 0028501577 scopus 로고
    • Pressure-driven flow of suspensions: Simulation and theory
    • P. R. NOTT AND J. F. BRADY, Pressure-driven flow of suspensions: Simulation and theory, J. Fluid Mech., 275 (1994), pp. 157-199.
    • (1994) J. Fluid Mech , vol.275 , pp. 157-199
    • NOTT, P.R.1    BRADY, J.F.2
  • 44
    • 0002717472 scopus 로고
    • Discontinuous solutions of nonlinear differential equations
    • O. A. OLEINIK, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl., 26 (1963), pp. 95-172.
    • (1963) Amer. Math. Soc. Transl , vol.26 , pp. 95-172
    • OLEINIK, O.A.1
  • 45
    • 0031480080 scopus 로고    scopus 로고
    • Long-scale evolution of thin liquid films
    • A. ORON, S. H. DAVIS, AND S. G. BANKOFF, Long-scale evolution of thin liquid films, Rev. Modern Phys., 69 (1997), pp. 931-980.
    • (1997) Rev. Modern Phys , vol.69 , pp. 931-980
    • ORON, A.1    DAVIS, S.H.2    BANKOFF, S.G.3
  • 46
    • 36449004475 scopus 로고
    • A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration
    • R. J. PHILLIPS, R. C. ARMSTRONG, R. A. BROWN, A. L. GRAHAM, AND J. R. ABBOTT, A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration, Phys. Fluids A, 4 (1992), pp. 30-40.
    • (1992) Phys. Fluids A , vol.4 , pp. 30-40
    • PHILLIPS, R.J.1    ARMSTRONG, R.C.2    BROWN, R.A.3    GRAHAM, A.L.4    ABBOTT, J.R.5
  • 47
    • 0002901837 scopus 로고
    • Sedimentation and fluidization: Part I
    • J. F. RICHARDSON AND W. N. ZAKI, Sedimentation and fluidization: Part I, Trans. Inst. Chem. Eng., 32 (1954), pp. 35-53.
    • (1954) Trans. Inst. Chem. Eng , vol.32 , pp. 35-53
    • RICHARDSON, J.F.1    ZAKI, W.N.2
  • 48
    • 0025458963 scopus 로고
    • Viscous resuspension of a sediment within a laminar and stratified flow
    • U. SCHAFLINGER, A. ACRIVOS, AND K. ZHANG, Viscous resuspension of a sediment within a laminar and stratified flow, Int. J. Multiphase Flow, 16 (1990), pp. 567-578.
    • (1990) Int. J. Multiphase Flow , vol.16 , pp. 567-578
    • SCHAFLINGER, U.1    ACRIVOS, A.2    ZHANG, K.3
  • 49
    • 44949251519 scopus 로고    scopus 로고
    • Distribution solutions of nonlinear systems of conservation laws
    • M. SEVER, Distribution solutions of nonlinear systems of conservation laws, Mem. Amer. Math. Soc., 889 (2007).
    • (2007) Mem. Amer. Math. Soc , vol.889
    • SEVER, M.1
  • 50
    • 0036732502 scopus 로고    scopus 로고
    • Rheology and microstructure in concentrated noncolloidal suspensions
    • A. SIEROU AND J. F. BRADY, Rheology and microstructure in concentrated noncolloidal suspensions, J. Rheology, 46 (2002), pp. 1031-1056.
    • (2002) J. Rheology , vol.46 , pp. 1031-1056
    • SIEROU, A.1    BRADY, J.F.2
  • 51
    • 0021892296 scopus 로고    scopus 로고
    • N. SILVI AND E. B. DUSSAN V., On the rewetting of an inclined solid surface by a liquid, Phys. Fluids, 28 (1985), pp. 5-7.
    • N. SILVI AND E. B. DUSSAN V., On the rewetting of an inclined solid surface by a liquid, Phys. Fluids, 28 (1985), pp. 5-7.
  • 52
    • 0028992597 scopus 로고
    • Stability of Newtonian and viscoelastic dynamic contact lines
    • M. A. SPAID AND G. M. HOMSY, Stability of Newtonian and viscoelastic dynamic contact lines, Phys. Fluids, 8 (1995), pp. 460-478.
    • (1995) Phys. Fluids , vol.8 , pp. 460-478
    • SPAID, M.A.1    HOMSY, G.M.2
  • 53
    • 14544306929 scopus 로고    scopus 로고
    • Fluid mechanics and rheology of dense suspensions
    • J. J. STICKEL AND R. L. POWELL, Fluid mechanics and rheology of dense suspensions, Annu. Rev. Fluid Mech., 37 (2005), pp. 129-149.
    • (2005) Annu. Rev. Fluid Mech , vol.37 , pp. 129-149
    • STICKEL, J.J.1    POWELL, R.L.2
  • 54
    • 0034274622 scopus 로고    scopus 로고
    • Stability considerations associated with the meniscoid particle band at advancing interfaces in Hele-Shaw suspension flows
    • H. TANG, W. GRIVAS, D. HOMENTCOVSCHI, J. GEER, AND T. SINGLER, Stability considerations associated with the meniscoid particle band at advancing interfaces in Hele-Shaw suspension flows, Phys. Rev. Lett., 85 (2000), pp. 2112-2115.
    • (2000) Phys. Rev. Lett , vol.85 , pp. 2112-2115
    • TANG, H.1    GRIVAS, W.2    HOMENTCOVSCHI, D.3    GEER, J.4    SINGLER, T.5
  • 55
    • 24944488751 scopus 로고    scopus 로고
    • Particle migration and free-surface topography in inclined plane flow of a suspension
    • B. D. TIMBERLAKE AND J. F. MORRIS, Particle migration and free-surface topography in inclined plane flow of a suspension, J. Fluid Mech., 538 (2005), pp. 309-341.
    • (2005) J. Fluid Mech , vol.538 , pp. 309-341
    • TIMBERLAKE, B.D.1    MORRIS, J.F.2
  • 57
    • 47149088919 scopus 로고
    • Physico-mathematical formulation
    • Springer-Verlag, New York
    • M. UNGARISH, Physico-mathematical formulation, in Hydrodynamics of Suspensions, Springer-Verlag, New York, 1993, pp. 7-36.
    • (1993) Hydrodynamics of Suspensions , pp. 7-36
    • UNGARISH, M.1
  • 58
    • 0034517240 scopus 로고    scopus 로고
    • Dynamics of three-dimensional thin film rupture
    • T. P. WITELSKI AND A. J. BERNOFF, Dynamics of three-dimensional thin film rupture, Phys. D, 147 (2000), pp. 155-176.
    • (2000) Phys. D , vol.147 , pp. 155-176
    • WITELSKI, T.P.1    BERNOFF, A.J.2
  • 59
    • 0141976802 scopus 로고    scopus 로고
    • L. XIANFAN AND C. POZRIKIDIS, Film flow of a suspension down an inclined plane, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 361 (2003), pp. 847-869
    • L. XIANFAN AND C. POZRIKIDIS, Film flow of a suspension down an inclined plane, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 361 (2003), pp. 847-869


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.