Width distribution of contact lines on a disordered substrate

Sébastien Moulinet; Alberto Rosso; Werner Krauth; Etienne Rolley

doi:10.1103/PhysRevE.69.035103

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Width distribution of contact lines on a disordered substrate

Sébastien Moulinet^1,*, Alberto Rosso², Werner Krauth¹, and Etienne Rolley¹

¹CNRS-Laboratoire de Physique Statistique de l’Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France
²Université de Genève, DPMC, 24 Quai Ernest Ansermet, CH-1211 Genève 4, Switzerland

^*Now at LPMCN, Université Claude Bernard, 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

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Phys. Rev. E 69, 035103(R) – Published 31 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.035103

Abstract

We have studied the roughness of a contact line on a disordered substrate by measuring its width distribution, which characterizes the roughness completely. The measured distribution is in excellent agreement with the distribution calculated in previous works, extended here to the case of open boundary conditions. This type of analysis, which is performed here on experimental data, provides a strong confirmation that the Joanny–de Gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold.

References (33)

S. Lemerle, J. Ferré, C. Chappert, V. Mathet, T. Giamarchi, and P. Le Doussal, Phys. Rev. Lett. 80, 849 (1998).
T. Tybell, P. Paruch, T. Giamarchi, and J.M. Triscone, Phys. Rev. Lett. 89, 097601 (2002).
H. Gao and J.R. Rice, J. Appl. Mech. 56, 828 (1989).
J.F. Joanny and P.G. de Gennes, J. Chem. Phys. 81, 552 (1984).
Y. Pomeau and J. Vannimenus, J. Colloid Interface Sci. 104, 477 (1985).
J.F. Joanny and M.O. Robbins, J. Chem. Phys. 92, 3206 (1990).
D. Ertaş and M. Kardar, Phys. Rev. E 49, R2532 (1996).
A. Hazareesing and M. Mézard, Phys. Rev. E 60, 1269 (1999).
R. Golestanian and E. Raphaël, Europhys. Lett. 55, 228 (2001).
A. Prevost, E. Rolley, and C. Guthmann, Phys. Rev. B 65, 064517 (2002).
S. Moulinet, C. Guthmann, and E. Rolley, Eur. Phys. J. E 8, 437 (2002).
T. Nattermann, S. Stepanow, L.H. Tang, and H. Leschhorn, J. Phys. (Paris) 2, 1483 (1992).
O. Narayan and D. Fisher, Phys. Rev. B 48, 7030 (1993).
M.O. Robbins and J.F. Joanny, Europhys. Lett. 3, 729 (1987).
A. Tanguy, M. Gounelle, and S. Roux, Phys. Rev. E 58, 1577 (1998).
S. Ramanathan and D.S. Fisher, Phys. Rev. B 58, 6026 (1998).
P. Chauve, P. Le Doussal, and K.J. Wiese, Phys. Rev. Lett. 86, 1785 (2001).
A. Rosso and W. Krauth, Phys. Rev. E 65, 025101(R) (2002).
E.L. Decker and S. Garoff, Langmuir 13, 6321 (1997).
J.-M.D. Meglio, Europhys. Lett. 17, 607 (1991).
A. Paterson and M. Fermigier, Phys. Fluids 9, 2210 (1997).
G. Foltin, K. Oerding, Z. Rácz, R.L. Workman, and R.K.P. Zia, Phys. Rev. E 50, R639 (1994).
M. Plischke, Z. Rácz, and R.K.P. Zia, Phys. Rev. E 50, 3589 (1994).
Z. Rácz and M. Plischke, Phys. Rev. E 50, 3530 (1994).
S.T. Bramwell et al., Phys. Rev. Lett. 84, 3744 (2000).
A. Rosso, W. Krauth, P. Le Doussal, J. Vannimenus, and K.J. Wiese, Phys. Rev. E 68, 036128 (2003).
T. Antal, M. Droz, G. Györgyi, and Z. Rácz, Phys. Rev. E 65, 046140 (2001).
P. Le Doussal and K.J. Wiese, Phys. Rev. E 68, 046118 (2003).
J. Schmittbuhl and K.J. Måløy, Phys. Rev. Lett. 78, 3888 (1997).
A. Delaplace, J. Schmittbuhl, and K.J. Måløy, Phys. Rev. E 60, 1337 (1999).
E. Bouchaud, J.P. Bouchaud, D.S. Fisher, S. Ramanathan, and J.R. Rice, J. Mech. Phys. Solids 50, 1703 (2002).
A. Rosso and W. Krauth, Phys. Rev. Lett. 87, 187002 (2001).
Let us evaluate the number of independent configurations that can be obtained in our experiment. For the lower magnification the observed length of the line is 4.7 mm. During an experiment the total displacement is of the order of 15 mm. As the maximum width of the contact line is ∼30 μm, the number of independent configuration is 500. As an example, for a size $L = 500 μ m,$ φ is then determined from typically 5000 independent samples.

[c1] S. Lemerle, J. Ferré, C. Chappert, V. Mathet, T. Giamarchi, and P. Le Doussal, Phys. Rev. Lett. 80, 849 (1998).

[c2] T. Tybell, P. Paruch, T. Giamarchi, and J.M. Triscone, Phys. Rev. Lett. 89, 097601 (2002).

[c3] H. Gao and J.R. Rice, J. Appl. Mech. 56, 828 (1989).

[c4] J.F. Joanny and P.G. de Gennes, J. Chem. Phys. 81, 552 (1984).

[c5] Y. Pomeau and J. Vannimenus, J. Colloid Interface Sci. 104, 477 (1985).

[c6] J.F. Joanny and M.O. Robbins, J. Chem. Phys. 92, 3206 (1990).

[c7] D. Ertaş and M. Kardar, Phys. Rev. E 49, R2532 (1996).

[c8] A. Hazareesing and M. Mézard, Phys. Rev. E 60, 1269 (1999).

[c9] R. Golestanian and E. Raphaël, Europhys. Lett. 55, 228 (2001).

[c10] A. Prevost, E. Rolley, and C. Guthmann, Phys. Rev. B 65, 064517 (2002).

[c11] S. Moulinet, C. Guthmann, and E. Rolley, Eur. Phys. J. E 8, 437 (2002).

[c12] T. Nattermann, S. Stepanow, L.H. Tang, and H. Leschhorn, J. Phys. (Paris) 2, 1483 (1992).

[c13] O. Narayan and D. Fisher, Phys. Rev. B 48, 7030 (1993).

[c14] M.O. Robbins and J.F. Joanny, Europhys. Lett. 3, 729 (1987).

[c15] A. Tanguy, M. Gounelle, and S. Roux, Phys. Rev. E 58, 1577 (1998).

[c16] S. Ramanathan and D.S. Fisher, Phys. Rev. B 58, 6026 (1998).

[c17] P. Chauve, P. Le Doussal, and K.J. Wiese, Phys. Rev. Lett. 86, 1785 (2001).

[c18] A. Rosso and W. Krauth, Phys. Rev. E 65, 025101(R) (2002).

[c19] E.L. Decker and S. Garoff, Langmuir 13, 6321 (1997).

[c20] J.-M.D. Meglio, Europhys. Lett. 17, 607 (1991).

[c21] A. Paterson and M. Fermigier, Phys. Fluids 9, 2210 (1997).

[c22] G. Foltin, K. Oerding, Z. Rácz, R.L. Workman, and R.K.P. Zia, Phys. Rev. E 50, R639 (1994).

[c23] M. Plischke, Z. Rácz, and R.K.P. Zia, Phys. Rev. E 50, 3589 (1994).

[c24] Z. Rácz and M. Plischke, Phys. Rev. E 50, 3530 (1994).

[c25] S.T. Bramwell et al., Phys. Rev. Lett. 84, 3744 (2000).

[c26] A. Rosso, W. Krauth, P. Le Doussal, J. Vannimenus, and K.J. Wiese, Phys. Rev. E 68, 036128 (2003).

[c27] T. Antal, M. Droz, G. Györgyi, and Z. Rácz, Phys. Rev. E 65, 046140 (2001).

[c28] P. Le Doussal and K.J. Wiese, Phys. Rev. E 68, 046118 (2003).

[c29] J. Schmittbuhl and K.J. Måløy, Phys. Rev. Lett. 78, 3888 (1997).

[c30] A. Delaplace, J. Schmittbuhl, and K.J. Måløy, Phys. Rev. E 60, 1337 (1999).

[c31] E. Bouchaud, J.P. Bouchaud, D.S. Fisher, S. Ramanathan, and J.R. Rice, J. Mech. Phys. Solids 50, 1703 (2002).

[c32] A. Rosso and W. Krauth, Phys. Rev. Lett. 87, 187002 (2001).

[c33] Let us evaluate the number of independent configurations that can be obtained in our experiment. For the lower magnification the observed length of the line is 4.7 mm. During an experiment the total displacement is of the order of 15 mm. As the maximum width of the contact line is ∼30 μm, the number of independent configuration is 500. As an example, for a size $L = 500 μ m,$ φ is then determined from typically 5000 independent samples.

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Width distribution of contact lines on a disordered substrate

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References (33)

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