메뉴 건너뛰기




Volumn 770, Issue , 2015, Pages 458-498

The lamellar description of mixing in porous media

Author keywords

geophysical and geological flows; low Reynolds number flows; mixing and dispersion

Indexed keywords

COALESCENCE; DEFORMATION; DIFFERENTIAL EQUATIONS; DIFFUSION; FORECASTING; MIXING; MIXTURES; POROUS MATERIALS; REYNOLDS NUMBER;

EID: 84927591463     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2015.117     Document Type: Article
Times cited : (108)

References (61)
  • 2
    • 84903807365 scopus 로고    scopus 로고
    • The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows
    • DE ANNA, P., DENTZ, M., TARTAKOVSKY, A. & LE BORGNE, T. 2014a The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows. Geophys. Res. Lett. 41, 4586-4593.
    • (2014) Geophys. Res. Lett. , vol.41 , pp. 4586-4593
    • De Anna, P.1    Dentz, M.2    Tartakovsky, A.3    Le Borgne, T.4
  • 4
    • 84877767153 scopus 로고    scopus 로고
    • Flow intermittency, dispersion, and correlated continuous time random walks in porous media
    • DE ANNA, P., LE BORGNE, T., DENTZ, M., TARTAKOVSKY, A., BOLSTER, D. & DAVY, P. 2013 Flow intermittency, dispersion, and correlated continuous time random walks in porous media. Phys. Rev. Lett. 110, 184502.
    • (2013) Phys. Rev. Lett. , vol.110 , pp. 184502
    • De Anna, P.1    Le Borgne, T.2    Dentz, M.3    Tartakovsky, A.4    Bolster, D.5    Davy, P.6
  • 5
    • 0032655161 scopus 로고    scopus 로고
    • Temporal behavior of a solute cloud in a chemically heterogeneous porous medium
    • ATTINGER, S., DENTZ, M., KINZELBACH, H. & KINZELBACH, W. 1999 Temporal behavior of a solute cloud in a chemically heterogeneous porous medium. J. Fluid Mech. 386, 77-104.
    • (1999) J. Fluid Mech. , vol.386 , pp. 77-104
    • Attinger, S.1    Dentz, M.2    Kinzelbach, H.3    Kinzelbach, W.4
  • 6
    • 84955741400 scopus 로고
    • Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. General discussion and the case of small conductivity
    • BATCHELOR, G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113-133.
    • (1959) J. Fluid Mech. , vol.5 , pp. 113-133
    • Batchelor, G.K.1
  • 8
    • 34848820544 scopus 로고    scopus 로고
    • Probability density function of non-reactive solute concentration in heterogeneous porous formations
    • BELLIN, A. & TONINA, D. 2007 Probability density function of non-reactive solute concentration in heterogeneous porous formations. J. Contam. Hydrol. 94, 109-125.
    • (2007) J. Contam. Hydrol. , vol.94 , pp. 109-125
    • Bellin, A.1    Tonina, D.2
  • 9
    • 33845247896 scopus 로고    scopus 로고
    • Modeling non-Fickian transport in geological formations as a continuous time random walk
    • 2005RG000178
    • BERKOWITZ, B., CORTIS, A., DENTZ, M. & SCHER, H. 2006 Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44, 2005RG000178.
    • (2006) Rev. Geophys. , vol.44
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 11
    • 0001577913 scopus 로고
    • A simple model for hydrodynamic dispersion
    • BOUCHAUD, J. P. & GEORGES, A. 1988 A simple model for hydrodynamic dispersion. C. R. Acad. Sci. Paris II 307, 1431-1436.
    • (1988) C. R. Acad. Sci. Paris II , vol.307 , pp. 1431-1436
    • Bouchaud, J.P.1    Georges, A.2
  • 12
    • 0000591233 scopus 로고
    • Probability distribution of a stochastically advected scalar field
    • CHEN, H. D., CHEN, S. Y. & KRAICHNAN, R. H. 1989 Probability distribution of a stochastically advected scalar field. Phys. Rev. Lett. 63 (24), 2657-2660.
    • (1989) Phys. Rev. Lett. , vol.63 , Issue.24 , pp. 2657-2660
    • Chen, H.D.1    Chen, S.Y.2    Kraichnan, R.H.3
  • 14
    • 43749089340 scopus 로고    scopus 로고
    • Concentration statistics for mixing-controlled reactive transport in random heterogeneous media
    • CIRPKA, O. A., SCHWEDE, R. L., LUO, J. & DENTZ, M. 2008 Concentration statistics for mixing-controlled reactive transport in random heterogeneous media. J. Contam. Hydrol. 98, 61-74.
    • (2008) J. Contam. Hydrol. , vol.98 , pp. 61-74
    • Cirpka, O.A.1    Schwede, R.L.2    Luo, J.3    Dentz, M.4
  • 15
    • 34247117269 scopus 로고    scopus 로고
    • Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state
    • CIRPKA, O. A. & VALOCCHI, A. J. 2007 Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state. Adv. Water Resour. 30, 1668-1679.
    • (2007) Adv. Water Resour. , vol.30 , pp. 1668-1679
    • Cirpka, O.A.1    Valocchi, A.J.2
  • 16
    • 21344481403 scopus 로고
    • Nonequilibrium statistical mechanics of preasymptotic dispersion
    • CUSHMAN, J. H., HU, X. & GINN, T. R. 1994 Nonequilibrium statistical mechanics of preasymptotic dispersion. J. Stat. Phys. 75, 859-878.
    • (1994) J. Stat. Phys. , vol.75 , pp. 859-878
    • Cushman, J.H.1    Hu, X.2    Ginn, T.R.3
  • 17
    • 0023249063 scopus 로고
    • Theory of solute transport by groundwater
    • DAGAN, G. 1987 Theory of solute transport by groundwater. Annu. Rev. Fluid Mech. 19, 183-215.
    • (1987) Annu. Rev. Fluid Mech. , vol.19 , pp. 183-215
    • Dagan, G.1
  • 18
    • 77956561350 scopus 로고
    • The definition and measurement of some characteristics of mixtures
    • DANCKWERTS, P. V. 1952 The definition and measurement of some characteristics of mixtures. Appl. Sci. Res. A 3, 279-296.
    • (1952) Appl. Sci. Res. A , vol.3 , pp. 279-296
    • Danckwerts, P.V.1
  • 19
    • 24444437044 scopus 로고
    • Continuous flow systems
    • DANCKWERTS, P. V. 1953 Continuous flow systems. Chem. Engng Sci. 2 (1), 1-13.
    • (1953) Chem. Engng Sci. , vol.2 , Issue.1 , pp. 1-13
    • Danckwerts, P.V.1
  • 20
    • 84861324324 scopus 로고    scopus 로고
    • Flow topology and scalar mixing in spatially heterogeneous flow fields
    • DE BARROS, F., DENTZ, M., KOCH, J. & NOWAK, W. 2012 Flow topology and scalar mixing in spatially heterogeneous flow fields. Geophys. Res. Lett. 39, L08404.
    • (2012) Geophys. Res. Lett. , vol.39 , pp. L08404
    • De Barros, F.1    Dentz, M.2    Koch, J.3    Nowak, W.4
  • 21
    • 0020968450 scopus 로고
    • Hydrodynamic dispersion in unsaturated porous media
    • DE GENNES, P. G. 1983 Hydrodynamic dispersion in unsaturated porous media. J. Fluid Mech. 136, 189-200.
    • (1983) J. Fluid Mech. , vol.136 , pp. 189-200
    • De Gennes, P.G.1
  • 22
    • 34548772493 scopus 로고    scopus 로고
    • Longitudinal and transverse dispersion in porous media
    • DELGADO, J. M. P. Q. 2007 Longitudinal and transverse dispersion in porous media. Chem. Engng Res. Des. 85 (A9), 1245-1252.
    • (2007) Chem. Engng Res. Des. , vol.85 , Issue.A9 , pp. 1245-1252
    • Delgado, J.M.P.Q.1
  • 23
    • 84855252978 scopus 로고    scopus 로고
    • Concentration statistics for transport in heterogeneous media due to stochastic fluctuations of the center of mass velocity
    • DENTZ, M. 2012 Concentration statistics for transport in heterogeneous media due to stochastic fluctuations of the center of mass velocity. Adv. Water Resour. 36, 11-22.
    • (2012) Adv. Water Resour. , vol.36 , pp. 11-22
    • Dentz, M.1
  • 24
    • 0034502679 scopus 로고    scopus 로고
    • Temporal behavior of a solute cloud in a heterogeneous porous medium. Part 1. Point-like injection
    • DENTZ, M., KINZELBACH, H., ATTINGER, S. & KINZELBACH, W. 2000 Temporal behavior of a solute cloud in a heterogeneous porous medium. Part 1. Point-like injection. Water Resour. Res. 36, 3591-3604.
    • (2000) Water Resour. Res. , vol.36 , pp. 3591-3604
    • Dentz, M.1    Kinzelbach, H.2    Attinger, S.3    Kinzelbach, W.4
  • 25
    • 79251624632 scopus 로고    scopus 로고
    • Mixing, spreading and reaction in heterogeneous media: A brief review
    • DENTZ, M., LE BORGNE, T., ENGLERT, A. & BIJELJIC, B. 2011 Mixing, spreading and reaction in heterogeneous media: a brief review. J. Contam. Hydrol. 120-121, 1-17.
    • (2011) J. Contam. Hydrol. , vol.120-121 , pp. 1-17
    • Dentz, M.1    Le Borgne, T.2    Englert, A.3    Bijeljic, B.4
  • 26
    • 79251523178 scopus 로고    scopus 로고
    • Probability density functions for passive scalars dispersed in random velocity fields
    • DENTZ, M. & TARTAKOVSKY, D. M. 2010 Probability density functions for passive scalars dispersed in random velocity fields. Geophys. Res. Lett. 37, L24406.
    • (2010) Geophys. Res. Lett. , vol.37 , pp. L24406
    • Dentz, M.1    Tartakovsky, D.M.2
  • 27
    • 77953464045 scopus 로고    scopus 로고
    • A nonsequential turbulent mixing process
    • DUPLAT, J., INNOCENTI, C. & VILLERMAUX, E. 2010 A nonsequential turbulent mixing process. Phys. Fluids 22, 035104.
    • (2010) Phys. Fluids , vol.22 , pp. 035104
    • Duplat, J.1    Innocenti, C.2    Villermaux, E.3
  • 28
    • 57049099249 scopus 로고    scopus 로고
    • Mixing by random stirring in confined mixtures
    • DUPLAT, J. & VILLERMAUX, E. 2008 Mixing by random stirring in confined mixtures. J. Fluid Mech. 617, 51-86.
    • (2008) J. Fluid Mech. , vol.617 , pp. 51-86
    • Duplat, J.1    Villermaux, E.2
  • 29
    • 41349087490 scopus 로고    scopus 로고
    • Stochastic mixing model with power law decay of variance
    • FEDOTOV, S., IHME, M. & PITSCH, H. 2005 Stochastic mixing model with power law decay of variance. Phys. Rev. E 71 (1), 016310.
    • (2005) Phys. Rev. E , vol.71 , Issue.1 , pp. 016310
    • Fedotov, S.1    Ihme, M.2    Pitsch, H.3
  • 30
    • 0035703347 scopus 로고    scopus 로고
    • The Lagrangian concentration approach for determining dilution in aquifer transport: Theoretical analysis and comparison with field experiments
    • FIORI, A. 2001 The Lagrangian concentration approach for determining dilution in aquifer transport: theoretical analysis and comparison with field experiments. Water Resour. Res. 37, 3105-3114.
    • (2001) Water Resour. Res. , vol.37 , pp. 3105-3114
    • Fiori, A.1
  • 31
    • 0032950902 scopus 로고    scopus 로고
    • Concentration fluctuations in transport by groundwater: Comparison between theory and field experiments
    • FIORI, A. & DAGAN, G. 1999 Concentration fluctuations in transport by groundwater: comparison between theory and field experiments. Water Resour. Res. 35, 105-112.
    • (1999) Water Resour. Res. , vol.35 , pp. 105-112
    • Fiori, A.1    Dagan, G.2
  • 32
    • 0033844573 scopus 로고    scopus 로고
    • Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications
    • FIORI, A. & DAGAN, G. 2000 Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J. Contam. Hydrol. 45 (1-2), 139-163.
    • (2000) J. Contam. Hydrol. , vol.45 , Issue.1-2 , pp. 139-163
    • Fiori, A.1    Dagan, G.2
  • 33
    • 0036722540 scopus 로고    scopus 로고
    • Concentration statistics in heterogeneous aquifers for finite Péclet values
    • FIOROTTO, V. & CARONI, E. 2002 Concentration statistics in heterogeneous aquifers for finite Péclet values. Trans. Porous Med. 48, 331-351.
    • (2002) Trans. Porous Med. , vol.48 , pp. 331-351
    • Fiorotto, V.1    Caroni, E.2
  • 36
    • 0020971569 scopus 로고
    • Three-dimensional stochastic analysis of macrodispersion in aquifers
    • GELHAR, L. W. & AXNESS, C. L. 1983 Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19 (1), 161-180.
    • (1983) Water Resour. Res. , vol.19 , Issue.1 , pp. 161-180
    • Gelhar, L.W.1    Axness, C.L.2
  • 37
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • GRASSBERGER, P. & PROCACCIA, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50, 346-349.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Procaccia, I.2
  • 38
    • 19244387358 scopus 로고    scopus 로고
    • Simple model of intermittent passive scalar turbulence
    • KALDA, J. 2000 Simple model of intermittent passive scalar turbulence. Phys. Rev. Lett. 84, 471-474.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 471-474
    • Kalda, J.1
  • 39
    • 0028667835 scopus 로고
    • The concept of the dilution index
    • KITANIDIS, P. K. 1994 The concept of the dilution index. Water Resour. Res. 30, 2011-2026.
    • (1994) Water Resour. Res. , vol.30 , pp. 2011-2026
    • Kitanidis, P.K.1
  • 40
    • 0024629229 scopus 로고
    • The effect of order on dispersion in porous media
    • KOCH, D. L., COX, R. G., BRENNER, H. & BRADY, J. F. 1989 The effect of order on dispersion in porous media. J. Fluid Mech. 200, 173-188.
    • (1989) J. Fluid Mech. , vol.200 , pp. 173-188
    • Koch, D.L.1    Cox, R.G.2    Brenner, H.3    Brady, J.F.4
  • 41
    • 78649633350 scopus 로고    scopus 로고
    • Non-Fickian mixing: Temporal evolution of the scalar dissipation rate in heterogeneous porous media
    • LE BORGNE, T., DENTZ, M., BOLSTER, D., CARRERA, J., DE DREUZY, J. R. & DAVY, P. 2010 Non-Fickian mixing: temporal evolution of the scalar dissipation rate in heterogeneous porous media. Adv. Water Resour. 33, 1468-1475.
    • (2010) Adv. Water Resour. , vol.33 , pp. 1468-1475
    • Le Borgne, T.1    Dentz, M.2    Bolster, D.3    Carrera, J.4    De Dreuzy, J.R.5    Davy, P.6
  • 42
    • 51349167211 scopus 로고    scopus 로고
    • Lagrangian statistical model for transport in highly heterogeneous velocity fields
    • LE BORGNE, T., DENTZ, M. & CARRERA, J. 2008 Lagrangian statistical model for transport in highly heterogeneous velocity fields. Phys. Rev. Lett. 101 (9), 090601.
    • (2008) Phys. Rev. Lett. , vol.101 , Issue.9 , pp. 090601
    • Le Borgne, T.1    Dentz, M.2    Carrera, J.3
  • 44
    • 84877823659 scopus 로고    scopus 로고
    • Stretching, coalescence and mixing in porous media
    • LE BORGNE, T., DENTZ, M. & VILLERMAUX, E. 2013 Stretching, coalescence and mixing in porous media. Phys. Rev. Lett. 110, 204501.
    • (2013) Phys. Rev. Lett. , vol.110 , pp. 204501
    • Le Borgne, T.1    Dentz, M.2    Villermaux, E.3
  • 45
    • 84863474162 scopus 로고    scopus 로고
    • Plume spreading in groundwater by stretching and folding
    • MAYS, D. & NEUPAUER, M. 2012 Plume spreading in groundwater by stretching and folding. Water Resour. Res. 48, W07501.
    • (2012) Water Resour. Res. , vol.48 , pp. W07501
    • Mays, D.1    Neupauer, M.2
  • 47
    • 78649964366 scopus 로고    scopus 로고
    • The diffusive strip method for scalar mixing in two dimensions
    • MEUNIER, P. & VILLERMAUX, E. 2010 The diffusive strip method for scalar mixing in two dimensions. J. Fluid Mech. 662, 134-172.
    • (2010) J. Fluid Mech. , vol.662 , pp. 134-172
    • Meunier, P.1    Villermaux, E.2
  • 48
    • 64849090484 scopus 로고    scopus 로고
    • Perspective on theories of anomalous transport in heterogeneous media
    • NEUMAN, S. P. & TARTAKOVSKY, D. M. 2009 Perspective on theories of anomalous transport in heterogeneous media. Adv. Water Resour. 32, 670-680.
    • (2009) Adv. Water Resour. , vol.32 , pp. 670-680
    • Neuman, S.P.1    Tartakovsky, D.M.2
  • 50
    • 0003987999 scopus 로고    scopus 로고
    • Cambridge University Press
    • POPE, S. B. 2000 Turbulent Flows. Cambridge University Press.
    • (2000) Turbulent Flows
    • Pope, S.B.1
  • 52
    • 71849092994 scopus 로고    scopus 로고
    • Enhancement of dilution and transverse reactive mixing in porous media: Experiments and model-based interpretation
    • ROLLE, M., EBERHARDT, C., CHIOGNA, G., CIRPKA, O. A. & GRATHWOHL, P. 2009 Enhancement of dilution and transverse reactive mixing in porous media: experiments and model-based interpretation. J. Contam. Hydrol. 110, 130-142.
    • (2009) J. Contam. Hydrol. , vol.110 , pp. 130-142
    • Rolle, M.1    Eberhardt, C.2    Chiogna, G.3    Cirpka, O.A.4    Grathwohl, P.5
  • 53
    • 84872936628 scopus 로고    scopus 로고
    • Assessment and management of risk in subsurface hydrology: A review and perspective
    • TARTAKOVSKY, D. M. 2013 Assessment and management of risk in subsurface hydrology: a review and perspective. Adv. Water Resour. 51, 247-260.
    • (2013) Adv. Water Resour. , vol.51 , pp. 247-260
    • Tartakovsky, D.M.1
  • 55
    • 37049037335 scopus 로고    scopus 로고
    • Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations
    • TONINA, D. & BELLIN, A. 2008 Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations. Adv. Water Resour. 31, 339-354.
    • (2008) Adv. Water Resour. , vol.31 , pp. 339-354
    • Tonina, D.1    Bellin, A.2
  • 56
    • 0000747193 scopus 로고
    • A binomial Langevin model for turbulent mixing
    • VALIÑO, L. & DOPAZO, C. 1991 A binomial Langevin model for turbulent mixing. Phys. Fluids 3, 3034-3037.
    • (1991) Phys. Fluids , vol.3 , pp. 3034-3037
    • Valiño, L.1    Dopazo, C.2
  • 57
    • 84872373856 scopus 로고    scopus 로고
    • Mixing by porous media
    • VILLERMAUX, E. 2012 Mixing by porous media. C. R. Mécanique 340, 933-943.
    • (2012) C. R. Mécanique , vol.340 , pp. 933-943
    • Villermaux, E.1
  • 58
    • 0348220996 scopus 로고    scopus 로고
    • Mixing as an aggregation process
    • VILLERMAUX, E. & DUPLAT, J. 2003 Mixing as an aggregation process. Phys. Rev. Lett. 91, 184501.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 184501
    • Villermaux, E.1    Duplat, J.2
  • 59
    • 33749464040 scopus 로고    scopus 로고
    • Coarse grained scale of turbulent mixtures
    • VILLERMAUX, E. & DUPLAT, J. 2006 Coarse grained scale of turbulent mixtures. Phys. Rev. Lett. 97, 144506.
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 144506
    • Villermaux, E.1    Duplat, J.2
  • 60
    • 0000322002 scopus 로고    scopus 로고
    • On the geometry of turbulent mixing
    • VILLERMAUX, E. & INNOCENTI, C. 1999 On the geometry of turbulent mixing. J. Fluid Mech. 393, 123-145.
    • (1999) J. Fluid Mech. , vol.393 , pp. 123-145
    • Villermaux, E.1    Innocenti, C.2
  • 61
    • 0007866645 scopus 로고
    • The asymptotic law of heat transfer at small velocities in the finite domain problem
    • ZELDOVICH, Y. B. 1937 The asymptotic law of heat transfer at small velocities in the finite domain problem. Zh. Eksp. Teor. Fiz. 7 (12), 1466-1468.
    • (1937) Zh. Eksp. Teor. Fiz. , vol.7 , Issue.12 , pp. 1466-1468
    • Zeldovich, Y.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.