D. M. Anderson, G. B. Mcfadden, and A. A. Wheeler, DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.139-165, 1998.
DOI : 10.1146/annurev.fluid.30.1.139

C. Andrieu, D. A. Beyssens, V. S. Nykolaev, and Y. Pomeau, Coalescence of sessile drops, Journal of Fluid Mechanics, vol.453, pp.427-438, 2002.
DOI : 10.1017/S0022112001007121
URL : https://hal.archives-ouvertes.fr/hal-00710181

L. K. Antanovskii, Microscale theory of surface tension, Physical Review E, vol.54, issue.6, pp.6285-6290, 1996.
DOI : 10.1103/PhysRevE.54.6285

L. K. Antanovskii, A phase field model of capillarity, Physics of Fluids, vol.7, issue.4, pp.747-753, 1995.
DOI : 10.1063/1.868598

F. Auteri, N. Parolini, and L. Quartapelle, Numerical Investigation on the Stability of Singular Driven Cavity Flow, Journal of Computational Physics, vol.183, issue.1, pp.1-25, 2002.
DOI : 10.1006/jcph.2002.7145

F. Auteri, L. Quartapelle, and L. Vigevano, Accurate ??-?? Spectral Solution of the Singular Driven Cavity Problem, Journal of Computational Physics, vol.180, issue.2, pp.597-615, 2002.
DOI : 10.1006/jcph.2002.7108

F. Auteri and L. Quartapelle, Galerkin Spectral Method for the Vorticity and Stream Function Equations, Journal of Computational Physics, vol.149, issue.2, pp.306-322, 1999.
DOI : 10.1006/jcph.1998.6155

J. Barrat and L. Bocquet, Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface, Faraday Discussions, vol.112, issue.112, pp.121-129, 1999.
DOI : 10.1039/a809733j

A. Batoul, H. Khallouf, and G. Labrosse, «Une méthode de résolution directe (pseudospectrale ) du problème de Stokes 2D/3D instationnaire. Application à la cavité entraînée carrée», Série II), pp.319-1455, 1994.

D. Bedeaux and I. Oppenheim, Hydrodynamic response and free surface modes for two immiscible fluids, Physica A: Statistical Mechanics and its Applications, vol.90, issue.1, pp.39-57, 1978.
DOI : 10.1016/0378-4371(78)90043-2

D. Bedeaux, A. M. Albano, and P. Mazur, Boundary conditions and non-equilibrium thermodynamics, Physica A: Statistical Mechanics and its Applications, vol.82, issue.3, pp.438-462, 1976.
DOI : 10.1016/0378-4371(76)90017-0

T. D. Blake, M. Bracke, and Y. D. Shikhmurzaev, Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle, Physics of Fluids, vol.11, issue.8, pp.1995-2007, 1999.
DOI : 10.1063/1.870063

O. Botella and R. Peyret, Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method, International Journal for Numerical Methods in Fluids, vol.96, issue.2, pp.125-163, 2001.
DOI : 10.1002/fld.121

O. Botella and R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Computers & Fluids, vol.27, issue.4, pp.421-433, 1998.
DOI : 10.1016/S0045-7930(98)00002-4

O. Botella, Résolution numérique de problèmes de Navier-Stokes singuliers par une méthode de projection Tchebychev, Thèse de doctorat, 1998.

O. Bouizi, Instabilités 3D de convection thermocapillaire en zone-flottante, Thèse de doctorat, 2004.

M. J. Boussinesq, «Sur l'existence d'une viscosité superficielle dans la mince couche de transition séparant un liquide d'un autre fluide contigu», Ann. Chim. Phys, vol.29, pp.349-364, 1913.

M. Brillouin, Leçons sur la viscosité des liquides et des gaz, 1907.

O. R. Burggraf, Analytical and numerical studies of the structure of steady separated flows, Journal of Fluid Mechanics, vol.7, issue.01, pp.113-151, 1966.
DOI : 10.1143/JPSJ.16.2307

J. W. Cahn and J. E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics, vol.28, issue.2, pp.258-267, 1958.
DOI : 10.1063/1.1744102

D. Canright, Thermocapillary flow near a cold wall, Physics of Fluids, vol.6, issue.4, pp.1415-1424, 1994.
DOI : 10.1063/1.868256

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral methods in fluid Dynamics, p.1, 1988.
DOI : 10.1007/978-3-642-84108-8

P. Cardin, H. Nataf, and P. Dewost, Thermal coupling in layered convection: evidence for an interface viscosity control from mechanical experiments and marginal stability analysis, Journal de Physique II, vol.1, issue.6, pp.599-622, 1991.
DOI : 10.1051/jp2:1991193
URL : https://hal.archives-ouvertes.fr/jpa-00247544

A. Carré and P. Woehl, Hydrodynamic Behavior at the Triple Line of Spreading Liquids and the Divergence Problem, Langmuir, vol.18, issue.9, pp.3600-3603, 2002.
DOI : 10.1021/la0117202

I. Catton, Effect of Wall Conduction on the Stability of a Fluid in a Rectangular Region Heated from Below, Journal of Heat Transfer, vol.94, issue.4, pp.446-452, 1972.
DOI : 10.1115/1.3449966

P. Cerisier, S. Rahal, J. Cordonnier, and G. Lebon, Thermal influence of boundaries on the onset of Rayleigh-B??nard convection, International Journal of Heat and Mass Transfer, vol.41, issue.21, pp.3309-3320, 1998.
DOI : 10.1016/S0017-9310(97)00364-5

É. Chénier, C. Delcarte, G. Kasperski, and G. Labrosse, Thermocapillary flows and vorticity singularity, Lecture notes in Physics, pp.176-199, 2003.

É. Chénier, C. Delcarte, G. Kasperski, and G. Labrosse, Sensitivity of the liquid bridge hydrodynamics to local capillary contributions, Physics of Fluids, vol.14, issue.9, pp.3109-3117, 2002.
DOI : 10.1063/1.1490350

É. Chénier, Étude de la stabilité linéaire des écoulements thermocapillaires et thermogravitationnels en croissance cristalline, Thèse de doctorat, 1997.

N. V. Churaev, V. D. Sobolev, and A. N. Somov, Slippage of liquids over lyophobic solid surfaces, Journal of Colloid and Interface Science, vol.97, issue.2, pp.574-581, 1984.
DOI : 10.1016/0021-9797(84)90330-8

C. Cottin-bizonne, J. Barrat, L. Bocquet, and É. Charlaix, Low-friction flows of liquid at nanopatterned interfaces, Nature Materials, vol.2, issue.4, p.238, 2003.
DOI : 10.1038/nmat857

C. Cottin-bizonne, S. Jurine, J. Baudry, J. Crassous, F. Restagno et al., «Nanorhelogy : an investigation of the boundary condition at hydrophobic and hydrophilic interfaces», European Physical Journal E, vol.9, issue.1, pp.47-53, 2002.

R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, Journal of Fluid Mechanics, vol.81, issue.-1, pp.169-194, 1986.
DOI : 10.1021/ie50320a024

V. S. Craig, C. Neto, and D. R. Williams, Shear-Dependent Boundary Slip in an Aqueous Newtonian Liquid, Physical Review Letters, vol.87, issue.5, pp.54504-54505, 2001.
DOI : 10.1103/PhysRevLett.87.054504

H. Dang-vu and C. Delcarte, An Accurate Solution of the Poisson Equation by the Chebyshev Collocation Method, Journal of Computational Physics, vol.104, issue.1, pp.211-220, 2001.
DOI : 10.1006/jcph.1993.1021

S. H. Davis, Convection in a box: linear theory, Journal of Fluid Mechanics, vol.85, issue.03, pp.465-478, 1967.
DOI : 10.1007/BF00281334

W. Dean and P. Montagnon, On the steady motion of viscous liquid in a corner, Proc. Camb, p.389, 1949.
DOI : 10.1112/plms/s2-19.1.373

M. M. Denn, «Extrusion instabilities and wall slip», Annu. Rev. Fluid Mech, vol.33, pp.267-287, 2001.
DOI : 10.1146/annurev.fluid.33.1.265

J. Désidéri, Modèles discrets et Schémas Itératifs (Hermes, Éditions Hermes, 8 quai du marché-Neuf, 75004 Paris, 1998), 1 re édition

P. A. Durbin, Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop, Journal of Fluid Mechanics, vol.34, issue.-1, pp.157-169, 1988.
DOI : 10.1016/0021-9797(67)90183-X

E. B. Dussan, The moving contact line: the slip boundary condition, Journal of Fluid Mechanics, vol.1, issue.04, pp.665-684, 1976.
DOI : 10.1016/0021-9797(67)90183-X

E. B. Dussan and S. H. Davis, On the motion of a fluid-fluid interface along a solid surface, Journal of Fluid Mechanics, vol.14, issue.01, pp.71-95, 1974.
DOI : 10.1016/0021-9797(71)90280-3

J. C. Earnshaw and J. C. Hughes, High-frequency capillary waves on the clean surface of water, Langmuir, vol.7, issue.11, pp.2419-2421, 1991.
DOI : 10.1021/la00059a002

D. A. Edwards, H. Brenner, and T. Wasan, Interfacial transport processes and rheology. Butterworth-Heinemann series in chemical engineering, p.1, 1991.

M. Fermigier, Dynamique d'une interface liquide dans un capillaire, Thèse de doctorat, 1989.

J. M. Floryan and L. Czechowski, On the Numerical Treatment of Corner Singularity in the Vorticity Field, Journal of Computational Physics, vol.118, issue.2, pp.222-228, 1995.
DOI : 10.1006/jcph.1995.1094

A. Fortin, M. Jardak, J. Gervais, and R. Pierre, Localization of Hopf bifurcations in fluid flow problems, International Journal for Numerical Methods in Fluids, vol.11, issue.11, pp.1185-1210, 1997.
DOI : 10.1002/(SICI)1097-0363(19970615)24:11<1185::AID-FLD535>3.0.CO;2-X

R. Gatignol and R. Prud-'homme, SECOND GRADIENT THEORY APPLIED TO INTERFACIAL MEDIUM, 2001.
DOI : 10.1142/9789812810625_0006

T. B. Gatski, C. E. Grosch, and M. E. Rose, A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables, Journal of Computational Physics, vol.48, issue.1, pp.1-22, 1982.
DOI : 10.1016/0021-9991(82)90032-8

P. G. De-gennes, On Fluid/Wall Slippage, Langmuir, vol.18, issue.9, pp.3413-3414, 2002.
DOI : 10.1021/la0116342

P. G. De-gennes, X. Hua, and P. Levinson, Dynamics of wetting: local contact angles, Journal of Fluid Mechanics, vol.288, issue.-1, pp.55-63, 1990.
DOI : 10.1103/RevModPhys.57.827

U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, vol.48, issue.3, pp.387-411, 1982.
DOI : 10.1016/0021-9991(82)90058-4

K. Goda, A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows, Journal of Computational Physics, vol.30, issue.1, pp.76-95, 1979.
DOI : 10.1016/0021-9991(79)90088-3

S. Goldstein, Note on the conditions at the surface of contact of a fluid with a solid, The Oxford engineering science series, pp.676-680, 1938.

A. Gomilko, V. Malyuga, and V. Meleshko, On steady Stokes flow in a trihedral rectangular corner, Journal of Fluid Mechanics, vol.476, pp.159-177, 2003.
DOI : 10.1017/S0022112002003026

F. C. Goodrich, The Theory of Capillary Excess Viscosities, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.374, issue.1758, pp.341-367, 1981.
DOI : 10.1098/rspa.1981.0026

H. Gouin, The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines, Continuum Mechanics and Thermodynamics, vol.15, issue.6, pp.581-596, 2003.
DOI : 10.1007/s00161-003-0136-2
URL : https://hal.archives-ouvertes.fr/hal-00203362

S. R. De-groot and P. Mazur, Non-equilibrium thermodynamics, 1984.

M. M. Gupta, A comparison of numerical solutions of convective and divergence forms of the Navier-Stokes equations for the driven cavity problem, Journal of Computational Physics, vol.43, issue.2, pp.260-267, 1981.
DOI : 10.1016/0021-9991(81)90122-4

M. M. Gupta, R. P. Manohar, and B. Noble, Nature of viscous flows near sharp corners, Computers & Fluids, vol.9, issue.4, pp.379-388, 1981.
DOI : 10.1016/0045-7930(81)90009-8

D. H. Haidvogel and T. A. Zang, The accurate solution of poisson's equation by expansion in chebyshev polynomials, Journal of Computational Physics, vol.30, issue.2, pp.167-180, 1979.
DOI : 10.1016/0021-9991(79)90097-4

P. Haldenwang, G. Labrosse, S. Abboudi, and M. Deville, Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation, Journal of Computational Physics, vol.55, issue.1, pp.115-128, 1984.
DOI : 10.1016/0021-9991(84)90018-4

C. Hancock, E. Lewis, and H. K. Moffatt, Effects of inertia in forced corner flows, Journal of Fluid Mechanics, vol.12, issue.-1, pp.315-327, 1981.
DOI : 10.1017/S0022112077001785

E. B. Hansen and M. A. Kelmanson, An integral equation justification of the boundary conditions of the driven-cavity problem, Computers & Fluids, vol.23, issue.1, pp.225-240, 1994.
DOI : 10.1016/0045-7930(94)90036-1

C. P. Hills and H. K. Moffatt, Rotary honing: a variant of the Taylor paint-scraper problem, Journal of Fluid Mechanics, vol.418, pp.119-135, 2000.
DOI : 10.1017/S0022112000001075

L. M. Hocking, The wetting of a plane surface by a fluid, Physics of Fluids, vol.7, issue.6, pp.1214-1220, 1995.
DOI : 10.1063/1.868579

L. M. Hocking, The spreading of drops with intermolecular forces, Physics of Fluids, vol.6, issue.10, pp.3224-3228, 1994.
DOI : 10.1063/1.868054

L. M. Hocking, The influence of intermolecular forces on thin fluid layers, Physics of Fluids A: Fluid Dynamics, vol.5, issue.4, pp.793-799, 1993.
DOI : 10.1063/1.858627

L. M. Hocking and A. D. Rivers, The spreading of a drop by capillary action, Journal of Fluid Mechanics, vol.34, issue.-1, pp.425-442, 1982.
DOI : 10.1017/S0022112077000123

L. M. Hocking, A moving fluid interface. Part 2. The removal of the force singularity by a slip flow, Journal of Fluid Mechanics, vol.262, issue.02, pp.209-229, 1977.
DOI : 10.1016/0021-9797(71)90188-3

L. M. Hocking, A moving fluid interface on a rough surface, Journal of Fluid Mechanics, vol.262, issue.04, pp.801-817, 1976.
DOI : 10.1017/S0022112074001261

C. O. Horgan, «Recent developements concerning Saint-Venant's principle», Appl. Mech. Rev, vol.48, pp.101-111, 1996.

C. O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flows, Quarterly of Applied Mathematics, vol.47, issue.1, pp.147-157, 1989.
DOI : 10.1090/qam/987903

R. G. Horn, O. I. Vinogradova, M. E. Mackay, and N. , Hydrodynamic slippage inferred from thin film drainage measurements in a solution of nonadsorbing polymer, The Journal of Chemical Physics, vol.112, issue.14, pp.6424-6443, 2000.
DOI : 10.1063/1.481274

C. Huh and S. G. Mason, The steady movement of a liquid meniscus in a capillary tube, Journal of Fluid Mechanics, vol.85, issue.03, pp.401-419, 1977.
DOI : 10.1103/PhysRev.17.273

C. Huh and L. E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, Journal of Colloid and Interface Science, vol.35, issue.1, pp.85-101, 1971.
DOI : 10.1016/0021-9797(71)90188-3

D. Jacqmin, Contact-line dynamics of a diffuse fluid interface, Journal of Fluid Mechanics, vol.402, issue.402, pp.57-88, 2000.
DOI : 10.1017/S0022112099006874

D. Jacqmin, Calculation of Two-Phase Navier???Stokes Flows Using Phase-Field Modeling, Journal of Computational Physics, vol.155, issue.1, pp.96-127, 1999.
DOI : 10.1006/jcph.1999.6332

D. Jamet, D. Torres, and J. U. Brackbill, On the Theory and Computation of Surface Tension: The Elimination of Parasitic Currents through Energy Conservation in the Second-Gradient Method, Journal of Computational Physics, vol.182, issue.1, pp.262-276, 2002.
DOI : 10.1006/jcph.2002.7165

D. Jamet, O. Lebaigue, N. Coutris, and J. M. Delhaye, The Second Gradient Method for the Direct Numerical Simulation of Liquid???Vapor Flows with Phase Change, Journal of Computational Physics, vol.169, issue.2, pp.624-651, 2001.
DOI : 10.1006/jcph.2000.6692

K. M. Jansons, Moving contact lines at non-zero capillary number, Journal of Fluid Mechanics, vol.70, issue.-1, pp.393-407, 1986.
DOI : 10.1017/S0022112076002838

D. Jasnow and J. Viñals, Coarse???grained description of thermo???capillary flow, Physics of Fluids, vol.8, issue.3, pp.660-669, 1995.
DOI : 10.1063/1.868851

G. E. Karniadakis, M. Israeli, and S. A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol.97, issue.2, pp.414-443, 1991.
DOI : 10.1016/0021-9991(91)90007-8

B. Karp, Dynamic version of Saint-Venant's principle???historical account and recent results, Article en cours de publication), 2005.
DOI : 10.1016/j.na.2005.01.035

G. Kasperski and G. Labrosse, On the numerical treatment of viscous singularities in wall-confined thermocapillary convection, Physics of Fluids, vol.12, issue.11, pp.2695-2697, 2000.
DOI : 10.1063/1.1287513

G. Kasperski, Convection thermocapillaire bidimensionnelle en pont liquide chauffé latéralement, Thèse de doctorat, 1999.

J. Kim and C. Kim, «Nanostructured surfaces for dramatic reduction of flow resistance in droplet-based microfluids», IEEE conference MEMS, 2002.

J. K. Knowles, «On Saint-Venant's principle in linear theory of elasticity», Arch. Rational Mech. Anal, vol.21, issue.1, pp.1-21, 1966.

J. Koplik and J. R. Banavar, Reentrant corner flows of Newtonian and non-Newtonian fluids, Journal of Rheology, vol.41, issue.3, pp.787-805, 1997.
DOI : 10.1122/1.550832

J. Koplik and J. R. Banavar, Corner flow in the sliding plate problem, Physics of Fluids, vol.7, issue.12, pp.3118-3125, 1995.
DOI : 10.1063/1.868619

J. Koplik and J. R. Banavar, Continuum Deductions from Molecular Hydrodynamics, Annual Review of Fluid Mechanics, vol.27, issue.1, pp.257-292, 1995.
DOI : 10.1146/annurev.fl.27.010195.001353

J. Koplik, J. R. Banavar, and J. F. Willemsen, «Molecular dynamics of fluid flow at solid surfaces», Phys. Fluids A, vol.5, issue.1, pp.781-794, 1989.

J. Koplik, J. R. Banavar, and J. F. Willemsen, Molecular dynamics of Poiseuille flow and moving contact lines, Physical Review Letters, vol.60, issue.13, pp.1282-1285, 1988.
DOI : 10.1103/PhysRevLett.60.1282

D. Langevin, Viscolelasticity of monolayers, pp.5584-5599, 2002.

P. and L. Quéré, Étude de la transition à l'instationnarité des écoulements de la convection naturelle en cavité verticale différentiellement chauffée par méthodes spectrales Tchebycheff : application à la convection naturelle, Thèse de doctorat d'état, 1987.

É. Leriche, E. Perchat, G. Labrosse, and M. O. Deville, Numerical Evaluation of the Accuracy and Stability Properties of High-order Direct Stokes Solvers with or without Temporal Splitting, Journal of Scientific Computing, vol.1, issue.1, 2004.
DOI : 10.1007/s10915-004-4798-0

É. Leriche and G. Labrosse, High-Order Direct Stokes Solvers with or Without Temporal Splitting: Numerical Investigations of Their Comparative Properties, SIAM Journal on Scientific Computing, vol.22, issue.4, pp.1386-1410, 2000.
DOI : 10.1137/S1064827598349641

M. Linthon and K. L. Sutherland, «Dynamic surface forces, drop circulation, and liquidliquid mass transfer», Proc. 2nd Int. Congr. Surface Activity, pp.494-502, 1957.

R. J. Mannheimer and R. S. Schechter, An improved apparatus and analysis for surface rheological measurements, Journal of Colloid and Interface Science, vol.32, issue.2, pp.195-211, 1970.
DOI : 10.1016/0021-9797(70)90044-5

L. , M. Witkowski, and J. S. Walker, «Solutocapillary instabilities in liquid bridges», Phys. Fluids, vol.14, issue.8, pp.2647-2656, 2002.

B. Mathieu, Études physique, expérimentale et numérique des mécanismes de base intervenant dans les écoulement diphasiques, Thèse de doctorat, 2003.

E. Millour, G. Labrosse, and É. Tric, Sensitivity of binary liquid thermal convection to confinement, Physics of Fluids, vol.15, issue.10, pp.2791-2802, 2003.
DOI : 10.1063/1.1600439
URL : https://hal.archives-ouvertes.fr/hal-00407037

H. K. Moffatt, Viscous and resistive eddies near a sharp corner, Journal of Fluid Mechanics, vol.6, issue.01, pp.1-18, 1964.
DOI : 10.1017/S0022112064000015

J. Monnier and P. Witomski, Analysis of a Local Hydrodynamic Model with Marangoni Effect, Journal of Scientific Computing, vol.334, issue.4, pp.369-403, 2004.
DOI : 10.1007/s10915-004-4095-y

C. G. Ngan and E. B. Dussan, On the nature of the dynamic contact angle: an experimental study, Journal of Fluid Mechanics, vol.1, issue.-1, pp.27-40, 1982.
DOI : 10.1017/S0022112077002134

S. Nguyen and C. Delcarte, A spectral collocation method to solve Helmholtz problems with boundary conditions involving mixed tangential and normal derivatives, Journal of Computational Physics, vol.200, issue.1, pp.34-49, 2004.
DOI : 10.1016/j.jcp.2004.03.004

X. Nie, S. Chen, and M. O. Robbins, Hybrid continuum-atomistic simulation of singular corner flow, Physics of Fluids, vol.16, issue.10, pp.3579-3591, 2004.
DOI : 10.1063/1.1779531

J. G. Oldroyd, The Effect of Interfacial Stabilizing Films on the Elastic and Viscous Properties of Emulsions, Proc. R. Soc. London, pp.567-577, 1955.
DOI : 10.1098/rspa.1955.0240

S. A. Orszag, M. Israeli, and M. O. Deville, Boundary conditions for incompressible flows, Journal of Scientific Computing, vol.96, issue.1, pp.75-111, 1986.
DOI : 10.1007/BF01061454

L. M. Pismen and B. Y. Rubinstein, Kinetic Slip Condition, van der Waals Forces, and Dynamic Contact Angle, Langmuir, vol.17, issue.17, pp.5265-5270, 2001.
DOI : 10.1021/la001452s

L. M. Pismen, B. Y. Rubinstein, and I. Bazhlekov, Spreading of a wetting film under the action of van der Waals forces, Physics of Fluids, vol.12, issue.3, pp.480-483, 2000.
DOI : 10.1063/1.870253

L. M. Pismen and Y. Pomeau, Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics, Physical Review E, vol.62, issue.2, pp.2480-2492, 2000.
DOI : 10.1103/PhysRevE.62.2480

L. M. Pismen and A. Nir, Motion of a contact line, Physics of Fluids, vol.25, issue.1, pp.3-7, 1982.
DOI : 10.1063/1.863626

R. Pit, H. H. Et, and L. Liliane, Direct Experimental Evidence of Slip in Hexadecane: Solid Interfaces, Physical Review Letters, vol.85, issue.5, pp.980-983, 2001.
DOI : 10.1103/PhysRevLett.85.980

R. Pit, Mesure locale de la vitesse à l'interface solide-liquide simple : glissement et rôle des interactions, Thèse de doctorat, 1999.

Y. Pomeau, Repr??sentation de la ligne de contact mobile dans les ??quations de la m??canique des fluides, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics, vol.328, issue.5, pp.411-416, 2000.
DOI : 10.1016/S1620-7742(00)00043-X

T. Qian and X. Wang, Driven Cavity Flow: From Molecular Dynamics to Continuum Hydrodynamics, Multiscale Modeling & Simulation, vol.3, issue.4, 2004.
DOI : 10.1137/040604868

V. C. Regnier, P. M. Parmentier, G. Lebon, and J. K. Platten, Numerical simulations of interface viscosity effects on thermoconvective motion in two-dimensional rectangular boxes, International Journal of Heat and Mass Transfer, vol.38, issue.14, pp.2539-2548, 1995.
DOI : 10.1016/0017-9310(95)00016-3

S. Richardson, On the no-slip boundary condition, Journal of Fluid Mechanics, vol.3, issue.04, pp.707-719, 1973.
DOI : 10.1017/S0022112073001801

J. S. Rowlinson and B. Widom, Molecular theory of capillarity, 1982.

E. Ruckenstein, The Moving Contact Line of a Droplet on a Smooth Solid, Journal of Colloid and Interface Science, vol.170, issue.1, pp.284-286, 1995.
DOI : 10.1006/jcis.1995.1099

E. Schnell, Slippage of Water over Nonwettable Surfaces, Journal of Applied Physics, vol.27, issue.10, pp.1149-1152, 1956.
DOI : 10.1063/1.1722220

W. W. Schultz, N. Lee, and J. P. Boyd, Chebyshev pseudospectral method of viscous flows with corner singularities, Journal of Scientific Computing, vol.53, issue.1, pp.1-24, 1989.
DOI : 10.1007/BF01061264

L. E. Scriven, Dynamics of a fluid interface Equation of motion for Newtonian surface fluids, Chemical Engineering Science, vol.12, issue.2, pp.98-108, 1960.
DOI : 10.1016/0009-2509(60)87003-0

P. Seppecher, Moving contact lines in the Cahn-Hilliard theory, International Journal of Engineering Science, vol.34, issue.9, pp.977-992, 1996.
DOI : 10.1016/0020-7225(95)00141-7
URL : https://hal.archives-ouvertes.fr/hal-00527283

P. Seppecher, Étude d'une modélisation des zones capillaires fluides : interfaces et lignes de contact, Thèse de doctorat, 1987.

P. N. Shankar and M. D. Deshpande, Fluid Mechanics in the Driven Cavity, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.93-136, 2000.
DOI : 10.1146/annurev.fluid.32.1.93

J. Shen, Hopf bifurcation of the unsteady regularized driven cavity flow, Journal of Computational Physics, vol.95, issue.1, pp.228-245, 1991.
DOI : 10.1016/0021-9991(91)90261-I

J. Shen, «Numerical simulation of the regularized driven cavity flows at high Reynolds numbers». Dans Spectral and high order methods for partial differential equations, pp.273-280, 1989.

Y. D. Shikhmurzaev, Moving contact lines in liquid/liquid/solid systems, Journal of Fluid Mechanics, vol.334, pp.211-249, 1997.
DOI : 10.1017/S0022112096004569

Y. D. Shikhmurzaev, «Mathematical modeling of wetting hydrodynamics». Fluid Dynamics Research, pp.45-64, 1994.

Y. D. Shikhmurzaev, The moving contact line on a smooth solid surface, International Journal of Multiphase Flow, vol.19, issue.4, pp.589-610, 1993.
DOI : 10.1016/0301-9322(93)90090-H

Y. D. Shikhmurzaev, A two-layer model of an interface between immiscible fluids, Physica A: Statistical Mechanics and its Applications, vol.192, issue.1-2, pp.47-62, 1993.
DOI : 10.1016/0378-4371(93)90143-R

L. Solomon, Principe de Saint-Venant, chapitre 4, pp.117-119, 1968.

C. V. Sternling and L. E. Scriven, Interfacial turbulence: Hydrodynamic instability and the marangoni effect, AIChE Journal, vol.5, issue.4, pp.514-523, 1959.
DOI : 10.1002/aic.690050421

T. Störtkuhl, C. Zenger, and S. Zimmer, An asymptotic solution for the singularity at the angular point of the lid driven cavity, International Journal of Numerical Methods for Heat & Fluid Flow, vol.4, issue.1, pp.47-59, 1994.
DOI : 10.1108/EUM0000000004030

G. I. Taylor, The scientific papers of sir Geoffrey Ingram Taylor, tome IV, article «On scraping viscous fluid from a plane surface», pp.410-413, 1962.

P. A. Thompson and S. M. Troian, «A general boundary condition for liquid flow at solid surfaces», Nature, vol.389, pp.360-362, 1997.

P. A. Thompson and M. O. Robbins, Shear flow near solids: Epitaxial order and flow boundary conditions, Physical Review A, vol.41, issue.12, pp.41-6830, 1990.
DOI : 10.1103/PhysRevA.41.6830

P. A. Thompson and M. O. Robbins, Simulations of contact-line motion: Slip and the dynamic contact angle, Physical Review Letters, vol.63, issue.7, pp.766-769, 1989.
DOI : 10.1103/PhysRevLett.63.766

D. M. Tolstoi, «Molecular theory of the slip of liquids on solid surfaces», Dokl. Akad. Nauk S.S.S.R, vol.85, pp.1089-1092, 1952.

D. C. Tretheway and C. D. Meinhart, Apparent fluid slip at hydrophobic microchannel walls, Physics of Fluids, vol.14, issue.3, pp.9-12, 2002.
DOI : 10.1063/1.1432696

M. A. Vila, V. A. Kuz, and A. E. Rodríguez, Surface viscosity of pure liquids, Journal of Colloid and Interface Science, vol.107, issue.2, pp.314-321, 1985.
DOI : 10.1016/0021-9797(85)90183-3

O. Vinogradova, N. F. Bunkin, N. V. Churaev, O. A. Kiseleva, A. V. Lobeyev et al., Submicrocavity Structure of Water between Hydrophobic and Hydrophilic Walls as Revealed by Optical Cavitation, Journal of Colloid and Interface Science, vol.173, issue.2, pp.443-447, 1995.
DOI : 10.1006/jcis.1995.1345

J. D. Van-der-waals, «The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation of density», J. Stat. Phys, vol.20, p.197, 1893.

K. Watanabe, Y. Udagawa, and H. Udagawa, Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall, Journal of Fluid Mechanics, vol.381, pp.225-238, 1999.
DOI : 10.1017/S0022112098003747

D. E. Weidner and L. W. Schwartz, Contact???line motion of shear???thinning liquids, Physics of Fluids, vol.6, issue.11, pp.3535-3538, 1994.
DOI : 10.1063/1.868412

A. Zebib, G. H. Homsy, and E. Meiburg, High Marangoni number convection in a square cavity, Physics of Fluids, vol.28, issue.12, pp.3467-3476, 1985.
DOI : 10.1063/1.865300

Y. Zhu and S. Grannick, Limits of the Hydrodynamic No-Slip Boundary Condition, Physical Review Letters, vol.88, issue.10, pp.106102-106103, 2002.
DOI : 10.1103/PhysRevLett.88.106102