Emmanuelle, Rio (2005) Gouttes, Flaques et Arches Sèches: des lignes de contact en présence d'un écoulement. PhD thesis physique, ESPCI.

Full text available as: - main.pdf ( 75392 Kb )

Licence: Copyright

Abstract

L'interaction entre des lignes de contact et un écoulement hydrodynamique intervient dans de nombreuses situations industrielles ou fondamentales. Nous étudions la dynamique de gouttes ruisselantes, tout d'abord le long de leur axe de symétrie (Partie I) puis à trois dimensions (Partie II) en mesurant la distribution d'angle de contact autour de cette goutte par réfraction d'une nappe laser et le champ de vitesse à la surface. Nous montrons que la situation est localement à deux dimensions, dans la direction perpendiculaire à la ligne de contact. L'angle de contact ne dépend que de la vitesse de la ligne de contact mesurée perpendiculairement à elle-même, vitesse qui coïncide avec la vitesse locale du liquide, dont la composante tangentielle s'annule à la ligne de contact. Dans le cas de lignes singulières (en coin), ou deux normales coexistent en un point, nous montrons que le champ de vitesse est autosimilaire à l'approche de ce point, Nous abordons également (Partie III) la question des lignes de contact statiques dans un écoulement à travers l'étude de la stabilité et de la forme de zones sèches dans un film liquide en écoulement. Nous montrons en particulier l'influence du mouillage sur ces objets et nous mesurons l'angle de contact tout autour de ces zones sèches. Nous montrons que la distribution d'angle de contact est, suivant l'histoire de la zone sèche, uniforme et bloquée à l'angle d'avancée (ce qui permet de construire des modèles simples) ou au contraire relativement désordonnée, Enfin nous mettons en évidence un phénomène encore non reconnu de stick-slip de la ligne de contact lorsqu'une goutte de suspension colloïdale en cours de séchage avance (interaction entre dépôt et hydrodynamique).

References

[1] P-G de Gennes, F. Brochard-Wyart, and D. Quere. Gouttes, bulles, perles et ondes, Belin, 2002.
[2] F. Brochart-Wyart. La juste argile: introduction à la matière molle. Chapitre 1: Histoires de gouttes: capillarité et mouillage. Les Editions de Physique, 1995.
[3] S.F. Kistler and P.M. Schweizer. Liquid Film coating - Scientific principles and their technological implications. Chapman & Hall, 1997.
[4] T. Podgorski. Ruissellement en conditions de mouillage partiel. PhD thesis, Université Paris 6, 2000.
[5] N. Le Grand, A. Daerr, and L. Limat. Shape and motion of drops sliding down an inclined plane. accepted to J. Fluid Mech.
[6] L. Limat and H. A. Stone. Three dimensional lubrication model of a contact line corner singularity. Europhys. Lett., 65(3) :365{371, 2004.
[7] E.B. Dussan. On the spreading of liquids on solid surfaces: static and dynamic contact liines. Ann. Rev. Fluid Mech., 11 :371{400, 1979.
[8] P-G. de Gennes. wetting: statics and dynamics. Rev Mod. Phys., 57 :827{, 1985.
[9] T.D. Blake and K.J. Ruschak. Wetting: static and dynamic contact lines. Chapman
& Hall, 1997.
[10] J-F. Joanny and P.G de Gennes. Model for contact angle hysteresis. J. Chem Phys.,
81 (1) :552{562, 1990.
[11] J-F. Joanny and M.O. Robbins. Motion of a contact line on a heterogenous surface.
J. Chem Phys., 92(5) :3206{3212, 1990.
[12] E.B. Dussan. On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. part 2. small drops or bubbles having contact angles of arbitrary size. J.
Fluid Mech., 151 :1{20, 1985.
[13] C. Huh and L.E. Scriven. Hydrodynamic model of steady movement of a solid/liquid contact line. J. Coll. Int. Sc., 35(1) :85{101, 1971.
[14] E.B. Dussan. The moving contact line: the slip boundary condition. J. Fluid Mech.,77(4) :665{684, 1976.
[15] R.G. Cox. The dynamics of the spreading of liquids on a solid surface. J. Fluid.Mech., 168 :169{220, 1986.
[16] O.V. Voinov. Hydrodynamics of wetting. Fluid Dynamics, 11 :714{, 1976.
[17] P-G. de Gennes, X. Hua, and P. Levinson. Dynamics of wetting: local contact angles.J. Fluid. Mech., 212 :55{63, 1990.
[18] Y. Shikhmurzaev. Moving contact lines in Liquid/liquid/solid systems. J. Fluid Mech.,334 :211{249, 1997.
[19] Y. Pomeau. Representation de la ligne de contact mobile dans les equations de la mecanique des Fluides. C. R. Acad. Sc., 11 :411{, 2000.
[20] T.D. Blake, J. De Coninck, and U. d'Ortona. Models of wetting: immiscible lattice boltzmann automata versus molecular kinetic theory. Langmuir, 11 :4588{4592, 1995.
[21] T.Podgorski, J-M Flesselles, and L. Limat. Corners, cusps and pearls in running drops. Phys. Rev. Lett., 87(3) :036102, 2001.
[22] J. Buehrle, S. Herminghaus, and F. Mugele. Interface profiles near three-phase contact lines in electric fields. Phys. Rev. Lett., 91(8) :086101, 2003.
[23] C.G. Ngan and E.B. Dussan V. On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech., 118 :27{, 1982.
[24] H.P.Kavehpour, B.Ovryn, and G.H.McKinley. Microscopic and macroscopic structure of the precursor layer in spreading viscous drops. Phys. Rev. Lett., 91 :196104,
2003.[25] R.L. Hoffman. A study of the advancing interface shape in liquide gassystems. J. Coll. Int Sc., 50 :228{241, 1975.
[26] L. Tanner. On the spreading of liquids on solid surfaces: static and dynamic contact lines. J. Phys. D, 12 :1473{, 1979.
[27] M. Fermigier and P. Jenffer. an experimental investigation of the dynamic contact angle in liquid/liquid systems. J. Coll. Int. Sc., 146 :226{, 1991.
[28] E.B. Gutoff and C.E. Kendrick. dynamic contact angles. AIChE Journal, 28(3) :459{466, 1982.
[29] E. Rio, A. Daerr, and L. Limat. Probing with a laser sheet the contact angle distribution along a contact line. J. Coll. Int. Sc., 269 :164, 2003.
[30] A.W. Adamson and A.P. Gast. Physical Chemistry of surfaces, volume Ch. X. Wiley
& Sons, 1997.
[31] C. Allain, D. Aussere, and F. Rondelez. A new method for contact angle measurements of sessile drops. J. Coll. Int. Sc., 107(1) :5{13, 1985.
[32] A-M. Cazabat, F. Heslot, S. M. Troian, and P. Carles. Fingering instability of thin spreading Films driven by temperature gradients. Nature, 346 :824{826, 1999.
[33] H.S. Khesgi and L.E. Scriven. Measurement of liquid film profiles by moire topography.
Chem. Eng. Sci., 38 :525{, 1983.
[34] C. Andrieu, C. Sykes, and F. Brochard-Wyart. Dynamics of fast dewetting on model solid substrates. J. Adhesion, 58 :15, 1996.
[35] M.F.G Johnson, R.A. Schutler, and S.G. Bankoff. Fluorescent imaging system for global measurement of liquid film thickness and dynamic contact angle in free surface flows. Rev. Sci. Instrum., 68(11) :4097{4102, 1997.
[36] R.T. Godwin. An Investigation of a Viscous Coating Flow. PhD thesis, Stanford University, 1991.
[37] A. Buguin, L. Vovelle, and F. Brochard-Wyart. Shocks in inertial dewetting. Phys.Rev. Lett., 83 :1183{1186, 1999.
[38] A.G. Gonzales, J. Diez, J. Gomba, and R. Gratton. Spreading of a thin twodimensional strip of uid on a vertical plane: experiments and modeling. Phys.Rev. E, 70 :026309, 2004.
[39] V.R. Roy. Modelisation and slimuation of film, drops and rivulet flows. private communication, 2003.
[40] R. Burley and B.S. Kennedy. An experimental study of air entrainment at a solid/liquid/gas interface. Chem. Engineering Sc., 31 :901{911, 1976.
[41] M. Yamamura, H. Miura, T. Kajiwara, and K. Adachi. Postponed air entrainment in particle dispersion: air film splitting. In proceedings of the 5th European Coating
Symposium, ISBN 3-033-00139-4, 2003.
[42] H.Benkreira, R. Pael, I. Khan M. Zandi, and O. Cohu. Substrate characteristics and their effects in air entrainment in dip and curtain coating. In proceedings of the 5th European Coating Symposium, ISBN 3-033-00139-4, 2003.
[43] T.D. Blake and K.J. Ruschak. A maximum speed of dewetting. Nature, 282 :489{492,1979.
[44] E. Lorenceau, F. Restagno, and D. Quere. Fracture of a viscous liquid. Phys. rev.Lett., 90(18) :184501, 2003.
[45] M. Legendre, T. Maxworthy, P. Pettjeans, and P. Kurowski. Cusp obtenu par l'action de cylindres contrarotatifs. In 8eme Journees de la Matieres Condensee, Actes, 412, page 074501, minicolloque 17, Marseille, 27-30 ao^ut 2002.
[46] I. Cohen and S.R. Nagel. Scaling at the selective withdrawal transition through a tube suspended above the uid surface. Phys. rev. Lett., 88(7) :074501, 2002.
[47] J. Snoeijer, E. Rio, N. Le Grand, and L. Limat. Self-similar flow and contact line geometry at the rear of cornered drops. Phys. of Fluids, 17 :072101, 2005.
[48] H.A. Stone, L. Limat, S.K. Wilson, J-M. Flesselles, and T. Podgorski. Singularite anguleuse d'une ligne de contact en mouvement sur un substrat solide. C. R. Acad.Sci. Paris, t.2(Serie IV) :1{8, 2001.
[49] L. M. Hocking. Meniscus drax-up and draining. Eur. J. Appl. Math, 12 :195, 2001.
[50] G.I. Taylor and D.H. Michael. On making holes in a sheet of fluid. J. Fluid. Mech,58(4) :625{639, 1973.
[51] C.Redon, F. Brochard-Wyart, and F. Rondelez. Dynamics of dewetting. Phys. Rev.Lett., 66 :715{718, 1991.
[52] D.E. Hartley and W. Murgatroyd. Criteria for the break-up of thin liquid layers flowing isothermally over solid surfaces. Int. J. Heat Mass Transfer, 7 :1003{1015,
1964.[53] W. Murgatroyd. The role of shear and form forces in the stability of a dry patch in two-phase film flow. Int. J. Heat Mass Transfer, 8 :297{301, 1965.
[54] A.B. Ponter, G.A. Davies, T.K. Ross, and P.G. Thornley. The influence of mass transfer on liquid film breakdown. Int. J. Heat Mass Transfer, 10 :349{359, 1967.
[55] S.G. Bankoff. Minimum thickness of a draining liquid film. Int. J. Heat Mass Transfer, 14 :2143{2146, 1971.
[56] S.G. Bankoff. Problems in interfacial instability. Annals N.Y. Acad. Sc., pages 405{419, 1983.
[57] S.D.R Wilson. The stability of a dry patch on a wetted wall. Int. J. Heat Mass Transfer, 17 :1607{1615, 1974.
[58] T.Podgorski, J-M Flesselles, and L. Limat. Courbure de la frontiere d'une zone seche dans un film en ecoulement. C. R. Acad. Sci. Paris, t.2(Serie IV) :1361{1367, 2001.
[59] T.Podgorski, J-M Flesselles, and L. Limat. Dry arches within flowing films. Phys.Fluids, 11(4) :845{852, 1999.
[60] E. Adachi, A. S. Dimitrov, and K. Nagayama. Stripe patterns on a glass surface during droplet evaporation. Langmuir, 11 :1057{1060, 1995.
[61] L. Shmuylovich, A. Q. Shen, and H. A. Stone. Surface morphology of drying latex films: multiple ring formation. Langmuir, 18 :3441{3445, 2002.
[62] M. Abkarian, J. Nunes, and H. A. Stone. Colloidal crystallization and banding in a cylindrical geometry. J. Am. Chem. Soc., 126 :5978{5979, 2004.
[63] N.D. Denkov, O.D. Velev, P.A. Kralchevsky, I.B. Ivanov, H. Yoshimura, and K. Nagayama.Mechanism of formation of two-dimensional crystals from latex particles on substrates. Langmuir, 8 :3183{3190, 1992.
[64] A. S. Dimitrov and K. Nagayama. Continuous convective assembling of ne particules into two-dimensional arrays on solid surfaces. Langmuir, 12 :1303{1311, 1996.
[65] P. Pieranski, L. Strzelecki, and B.Pansu. Thin colloidal crystals. Phys. Rev. Lett.,50(12) :900{903, 1983.
[66] F. Parisse and C. Allain. Drying of colloidal suspension droplets: experimental study and profile renormalization. Langmuir, 13 :3598{3602, 1997.
[67] R.D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten. Capillary flow as the cause of ring stains from dried liquid drops. Nature, 389 :827{828, 1997.
[68] R.D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten. Contact line deposits in an evaorating drop. Phys. Rev E, 62(1) :756{765, 1999.
[69] C. Poulard, O. Benichou, and A-M. Cazabat. Freely receding evaporating droplets Langmuir, 19 :8828{8834, 2003.
[70] M. Cachile, C. Poulard, O. Benichou, and A-M. Cazabat. Evaporating droplets. Langmuir, 18 :8070{8078, 2002.

Table of content

Table des matières
I Angles de contact dynamiques: paradoxes, méthodes et questionnement 15
1 Introduction 17
2 Mesure d'angles de contact dynamiques 31
3 Exploration du prol d'une goutte 55
II Ruissellement de gouttes 67
1 Introduction: des gouttes pointues - 69
2 Tourner autour d'une goutte 73
3 Champ de vitesse dans une goutte arrondie 81
III Arches seches, archi sèches 97
1 Introduction 99
2 Dispositif expérimental 107
3 Evolution de l'arche avec le débit 115
4 Distribution de l'angle de contact 123
5 Débits critiques: stabilité de la zone sèche 133
IV Gouttes de suspension colloïdale 143
1 Introduction 145
2 Gouttes gonflées 155
3 Gouttes poussées 161
4 Que dépose-t-on réellement ? 171
5 Une tentative de modélisation 177

Statistiques de consultation

Repository Staff Only: edit this item