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Spatial degeneracy vs functional response
Analysis for wetting on rough surfaces by a three-dimensional phase field model
1. | The State Key Laboratory of Scientic and Engineering Computing, Institute of Computational Mathematics and Scientic/Engineering Computing, Chinese Academy of Sciences, Beijing 100190, China |
References:
[1] |
Y. Achdou, P. Le Tallec, F Valentin and O. Pironneau, Constructing wall laws with domain decomposition or asymptotic expansion techniques, Compt. Methods Appl. Mech. Engrg, 151 (1998), 215-232.
doi: 10.1016/S0045-7825(97)00118-7. |
[2] | |
[3] |
G. Alberti and A. DeSimone, Wetting of rough surfaces: A homogenization approach, Proc. R. Soc. A, 461 (2005), 79-97.
doi: 10.1098/rspa.2004.1364. |
[4] |
D. Bonn, J. Eggers, J. Indekeu, J. Meunier and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81 (2009), 739-805.
doi: 10.1103/RevModPhys.81.739. |
[5] |
D. Bonn and D. Ross, Wetting transitions, Rep. Prog. Phys. 64 (2001), 1085-1163. |
[6] |
A. Braids, $\Gamma$-convergence for Beginners, Oxford Lecture Series in Mathematics and its Applications, Vol. 22, Oxford University Press, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[7] |
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.
doi: 10.1007/BF00254827. |
[8] |
A. Cassie and S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc., 40 (1944), 546-551.
doi: 10.1039/tf9444000546. |
[9] |
J. Cahn, Critical point wetting, J. Chem. Phys., 66 (1977), 3667-3672. |
[10] |
W. Choi, A. Tuteja, J. M. Mabry, R. E. Cohen and G. H. McKinley, A modified Cassie-Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces, J. Colloid Interface Sci., 339 (2009), 208-216.
doi: 10.1016/j.jcis.2009.07.027. |
[11] |
G. Dal Maso, Introduction to $\Gamma$-convergence, Birkhauser, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[12] |
H. Y. Erbil, The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review, Surface Science Reports, 69 (2014), 325-365.
doi: 10.1016/j.surfrep.2014.09.001. |
[13] |
L. Gao and T. J. McCarthy, How Wenzel and Cassie were wrong, Langmuir, 23 (2007), 3762-3765.
doi: 10.1021/la062634a. |
[14] |
P. G. de Gennes, Wetting: Statics and dynamics, Rev. Modern Phy., 57 (1985), 827-863. |
[15] |
P. G. de Gennes, F. Brochard-Wyart and D. Quere, Capillarity and Wetting Phenomena, Springer, Berlin, 2004.
doi: 10.1007/978-0-387-21656-0. |
[16] |
E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2003.
doi: 10.1142/9789812795557. |
[17] |
A. L. Madureira and F. Valentin, Asymptotics of the Poisson problem in domains with curved rough boundaries, SIAM J. Math. Anal., 38 (2007), 1450-1473.
doi: 10.1137/050633895. |
[18] |
M. De Menech, Modeling of droplet breakup in a microfluidic t-shaped junction with a phase-field model, Phys. Rev. E, 73 (2006), 031505. |
[19] |
G. Mchale, Cassie and Wenzel: Were they really so wrong, Langmuir, 23 (2007), 8200-8205.
doi: 10.1021/la7011167. |
[20] |
A. Marmur and E. Bittoun, When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations, Langmuir, 25 (2009), 1277-1281.
doi: 10.1021/la802667b. |
[21] |
J. Nevard and J. B. Keller, Homogenization of rough boundaries and interfaces, SIAM J. Appl. Math. 57 (1997), 1660-1686.
doi: 10.1137/S0036139995291088. |
[22] |
M. V. Panchagnula and S. Vedantam, Comment on how wenzel and cassie were wrong by gao and McCarthy, Langmuir, 23 (2007), 13242-13242.
doi: 10.1021/la7022117. |
[23] |
N. A. Pantanka, On the modeling of hydrophyobic angles on rough surfaces, Langmuir, 19 (2003), 1249-1253. |
[24] |
D. Quere, Wetting and roughness, Annu. Rev. Mater. Res., 38 (2008), 71-99. |
[25] |
R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem., 28 (1936), 988-994.
doi: 10.1021/ie50320a024. |
[26] |
G. Whyman, E. Bormashenko and T. Stein, The rigorous derivative of Young, Cassie-Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon, Chem. Phy. Letters, 450 (2008), 355-359. |
[27] |
G. Wolansky and A. Marmur, Apparent contact angles on rough surfaces: The Wenzel equation revisited, Colloids and Surfaces A, 156 (1999), 381-388.
doi: 10.1016/S0927-7757(99)00098-9. |
[28] |
X. Xu and X.-P. Wang, Derivation of Wenzel's and Cassie's equations from a phase field model for two phase flow on rough surface, SIAM J. Appl. Math., 70 (2010), 2929-2941.
doi: 10.1137/090775828. |
[29] |
X. Xu and X.-P. Wang, A modified Cassie's equation and contact angle hysteresis, Colloid Polymer Sci., 291 (2013), 299-306.
doi: 10.1007/s00396-012-2748-1. |
[30] |
X. Xu, Modified Wenzel and Cassie equations for wetting on rough surfaces, preprint, 2015. |
[31] |
T. Young, An essay on the cohesion of fluids, Philos. Trans. R. Soc. London, 95 (1805), 65-87. |
show all references
References:
[1] |
Y. Achdou, P. Le Tallec, F Valentin and O. Pironneau, Constructing wall laws with domain decomposition or asymptotic expansion techniques, Compt. Methods Appl. Mech. Engrg, 151 (1998), 215-232.
doi: 10.1016/S0045-7825(97)00118-7. |
[2] | |
[3] |
G. Alberti and A. DeSimone, Wetting of rough surfaces: A homogenization approach, Proc. R. Soc. A, 461 (2005), 79-97.
doi: 10.1098/rspa.2004.1364. |
[4] |
D. Bonn, J. Eggers, J. Indekeu, J. Meunier and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81 (2009), 739-805.
doi: 10.1103/RevModPhys.81.739. |
[5] |
D. Bonn and D. Ross, Wetting transitions, Rep. Prog. Phys. 64 (2001), 1085-1163. |
[6] |
A. Braids, $\Gamma$-convergence for Beginners, Oxford Lecture Series in Mathematics and its Applications, Vol. 22, Oxford University Press, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[7] |
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.
doi: 10.1007/BF00254827. |
[8] |
A. Cassie and S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc., 40 (1944), 546-551.
doi: 10.1039/tf9444000546. |
[9] |
J. Cahn, Critical point wetting, J. Chem. Phys., 66 (1977), 3667-3672. |
[10] |
W. Choi, A. Tuteja, J. M. Mabry, R. E. Cohen and G. H. McKinley, A modified Cassie-Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces, J. Colloid Interface Sci., 339 (2009), 208-216.
doi: 10.1016/j.jcis.2009.07.027. |
[11] |
G. Dal Maso, Introduction to $\Gamma$-convergence, Birkhauser, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[12] |
H. Y. Erbil, The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review, Surface Science Reports, 69 (2014), 325-365.
doi: 10.1016/j.surfrep.2014.09.001. |
[13] |
L. Gao and T. J. McCarthy, How Wenzel and Cassie were wrong, Langmuir, 23 (2007), 3762-3765.
doi: 10.1021/la062634a. |
[14] |
P. G. de Gennes, Wetting: Statics and dynamics, Rev. Modern Phy., 57 (1985), 827-863. |
[15] |
P. G. de Gennes, F. Brochard-Wyart and D. Quere, Capillarity and Wetting Phenomena, Springer, Berlin, 2004.
doi: 10.1007/978-0-387-21656-0. |
[16] |
E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2003.
doi: 10.1142/9789812795557. |
[17] |
A. L. Madureira and F. Valentin, Asymptotics of the Poisson problem in domains with curved rough boundaries, SIAM J. Math. Anal., 38 (2007), 1450-1473.
doi: 10.1137/050633895. |
[18] |
M. De Menech, Modeling of droplet breakup in a microfluidic t-shaped junction with a phase-field model, Phys. Rev. E, 73 (2006), 031505. |
[19] |
G. Mchale, Cassie and Wenzel: Were they really so wrong, Langmuir, 23 (2007), 8200-8205.
doi: 10.1021/la7011167. |
[20] |
A. Marmur and E. Bittoun, When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations, Langmuir, 25 (2009), 1277-1281.
doi: 10.1021/la802667b. |
[21] |
J. Nevard and J. B. Keller, Homogenization of rough boundaries and interfaces, SIAM J. Appl. Math. 57 (1997), 1660-1686.
doi: 10.1137/S0036139995291088. |
[22] |
M. V. Panchagnula and S. Vedantam, Comment on how wenzel and cassie were wrong by gao and McCarthy, Langmuir, 23 (2007), 13242-13242.
doi: 10.1021/la7022117. |
[23] |
N. A. Pantanka, On the modeling of hydrophyobic angles on rough surfaces, Langmuir, 19 (2003), 1249-1253. |
[24] |
D. Quere, Wetting and roughness, Annu. Rev. Mater. Res., 38 (2008), 71-99. |
[25] |
R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem., 28 (1936), 988-994.
doi: 10.1021/ie50320a024. |
[26] |
G. Whyman, E. Bormashenko and T. Stein, The rigorous derivative of Young, Cassie-Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon, Chem. Phy. Letters, 450 (2008), 355-359. |
[27] |
G. Wolansky and A. Marmur, Apparent contact angles on rough surfaces: The Wenzel equation revisited, Colloids and Surfaces A, 156 (1999), 381-388.
doi: 10.1016/S0927-7757(99)00098-9. |
[28] |
X. Xu and X.-P. Wang, Derivation of Wenzel's and Cassie's equations from a phase field model for two phase flow on rough surface, SIAM J. Appl. Math., 70 (2010), 2929-2941.
doi: 10.1137/090775828. |
[29] |
X. Xu and X.-P. Wang, A modified Cassie's equation and contact angle hysteresis, Colloid Polymer Sci., 291 (2013), 299-306.
doi: 10.1007/s00396-012-2748-1. |
[30] |
X. Xu, Modified Wenzel and Cassie equations for wetting on rough surfaces, preprint, 2015. |
[31] |
T. Young, An essay on the cohesion of fluids, Philos. Trans. R. Soc. London, 95 (1805), 65-87. |
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