D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Reviews of Modern Physics, vol.81, issue.2, pp.739-805, 2009.
DOI : 10.1103/RevModPhys.81.739

J. B. Bostwick, Spreading and bistability of droplets on differentially heated substrates, Journal of Fluid Mechanics, vol.9, pp.566-587
DOI : 10.1093/qjmam/36.1.55

J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2, pp.335-354, 1992.
DOI : 10.1016/0021-9991(92)90240-Y

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
DOI : 10.1021/ie50320a024

R. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Reviews of Modern Physics, vol.81, issue.3, pp.1131-1198, 2009.
DOI : 10.1103/RevModPhys.81.1131

S. H. Davis, In: Perspectives in Fluid Dynamics, Interfacial Fluid Dynamics, 2000.

G. J. Dunn, S. K. Wilson, B. R. Duffy, S. David, and K. Sefiane, The strong influence of substrate conductivity on droplet evaporation, Journal of Fluid Mechanics, vol.71, pp.329-351, 2009.
DOI : 10.1103/PhysRevLett.99.234502

P. Ehrhard and S. H. Davis, Non-isothermal spreading of liquid drops on horizontal plates, Journal of Fluid Mechanics, vol.36, issue.-1, pp.365-388, 1991.
DOI : 10.1017/S0022112080002066

P. Ehrhard, Experiments on isothermal and non-isothermal spreading, Journal of Fluid Mechanics, vol.229, issue.-1, pp.463-483, 1993.
DOI : 10.1016/0021-9797(67)90183-X

H. P. Greenspan, On the motion of a small viscous droplet that wets a surface, Journal of Fluid Mechanics, vol.77, issue.01, pp.125-143, 1977.
DOI : 10.1016/0021-9797(75)90149-6

P. De-gennes, F. Brochard-wyart, and D. Quéré, Capillarity and wetting phenomena: drops, bubbles, pearls, waves, 2004.
DOI : 10.1007/978-0-387-21656-0

M. Herrmann, J. M. Lopez, P. Brady, and M. Raessi, Thermocapillary motion of deformable drops and bubbles, Proceedings of the Summer Program, pp.155-170, 2008.

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, THE SPREADING OF A THIN DROP BY GRAVITY AND CAPILLARITY, The Quarterly Journal of Mechanics and Applied Mathematics, vol.36, issue.1, pp.55-69, 1983.
DOI : 10.1093/qjmam/36.1.55

L. M. Hocking, Rival contact-angle models and the spreading of drops, Journal of Fluid Mechanics, vol.223, issue.-1, pp.671-681, 1992.
DOI : 10.1017/S0022112078000075

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

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

W. Ren, E. , and W. , Boundary conditions for the moving contact line problem, Physics of Fluids, vol.19, issue.2, p.16306, 2007.
DOI : 10.1063/1.2646754

D. N. Sibley, A. Nold, N. Savva, and S. Kalliadasis, 2015a A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading, J. Engng Math

D. N. Sibley, A. Nold, and S. Kalliadasis, The asymptotics of the moving contact line: cracking an old nut, Journal of Fluid Mechanics, vol.23, pp.445-462
DOI : 10.1146/annurev.fluid.30.1.139

J. H. Snoeijer and B. Andreotti, Moving Contact Lines: Scales, Regimes, and Dynamical Transitions, Annual Review of Fluid Mechanics, vol.45, issue.1, pp.269-292, 2013.
DOI : 10.1146/annurev-fluid-011212-140734

Y. Sui, Moving towards the cold region or the hot region? Thermocapillary migration of a droplet attached on a horizontal substrate, Physics of Fluids, vol.26, issue.9, p.92102, 2014.
DOI : 10.1063/1.4894077

Y. Sui and P. D. Spelt, Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation, Journal of Fluid Mechanics, vol.146, pp.283-313
DOI : 10.1017/S0022112086000332

. Sui and P. D. Spelt, An efficient computational model for macroscale simulations of moving contact lines, Journal of Computational Physics, vol.242, pp.37-52
DOI : 10.1016/j.jcp.2013.02.005

URL : https://hal.archives-ouvertes.fr/hal-00788635

Y. Sui, H. Ding, and P. D. Spelt, Numerical Simulations of Flows with Moving Contact Lines, Annual Review of Fluid Mechanics, vol.46, issue.1, pp.97-119
DOI : 10.1146/annurev-fluid-010313-141338

URL : https://hal.archives-ouvertes.fr/hal-01296873

M. Sussman, G. S. Almgren, G. B. Bell, P. Colella, L. H. Howell et al., An Adaptive Level Set Approach for Incompressible Two-Phase Flows, Journal of Computational Physics, vol.148, issue.1, pp.81-124, 1999.
DOI : 10.1006/jcph.1998.6106

L. H. Tanner, The spreading of silicone oil drops on horizontal surfaces, Journal of Physics D: Applied Physics, vol.12, issue.9, pp.1473-1483, 1979.
DOI : 10.1088/0022-3727/12/9/009

N. O. Young, J. S. Goldstein, and M. J. Block, The motion of bubbles in a vertical temperature gradient, Journal of Fluid Mechanics, vol.178, issue.03, p.350356, 1959.
DOI : 10.1103/PhysRev.23.710