静电场驱动下液体薄膜的几何形状

E·M·田; T·P·斯沃博德内; J·D·菲利普斯

doi:10.3879/j.issn.1000-0887.2011.08.008

静电场驱动下液体薄膜的几何形状

doi: 10.3879/j.issn.1000-0887.2011.08.008

莱特州立大学数学与统计学院,代顿,俄亥俄州 45435,美国

详细信息

中图分类号: O357.1
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- 被引次数: 0
出版历程
- 收稿日期: 2011-01-17
- 修回日期: 2011-05-24
- 刊出日期: 2011-08-15

Thin Liquid Film Morphology Driven by Electro-Static Field

Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA

摘要

摘要: 利用六边形-俯视图的弱非线性稳定性分析和数值仿真，在电场作用下，研究高分子薄膜表面静态模式的发展过程．在无限空间域上，空间和高分子薄膜之间的界面，由薄膜方程给出其随时间的演变，综合考虑了电力的驱动和表面张力的传播．非线性界面的增长包括：波幅方程的增长，以及在准对规律方向上，一维结构的叠合．模式的选择由亚临界不稳定性机理确定，高分子薄膜的相对厚度在其中起着决定性的作用．
- 薄膜 /
- 模式的形成 /
- 电流体动力学不稳定性
Abstract: The development of stationary patterns on a thin polymer surface subject to an electric field was studied by means of a hexagonal-planform weakly nonlinear stability analysis and numerical simulations.The time evolution of the interface between air and polymer film on the unbounded spatial domain was described by the thin film equation,incorporating the electric driving force and the surface diffusion.The nonlinear interfacial growth includes the amplitude equations and superpo sition of one-dimensional structures at regular orientations.The pattern selection is driven by the subcritical instability mechanism in which the relative thickness of the polymer film plays a critical role.
- thin film /
- pattern formation /
- electrohydrodynamic instability

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参考文献(28)

[1]	Chou S Y, Zhuang L. Lithographically induced self-assembly of periodic polymer micropillar arrays[J]. J Vac Sci Technol B, 1999, 17(6): 3197-3202.
[2]	Schffer E, Thurn-Albrecht T, Russell T P, Stelner U. Electrically induced structure formation and pattern transfer[J]. Nature, 2000, 403: 874-877. doi: 10.1038/35002540
[3]	Wu N, Russel W B. Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution[J]. Langmuir, 2005, 21(26):12290-12302. doi: 10.1021/la052099z
[4]	Kim D, Lu W. Interface instability and nanostructure patterning[J]. Computational Materials Science, 2006, 38(2): 418-425. doi: 10.1016/j.commatsci.2006.03.015
[5]	Lin Z Q, Kerle T, Baker S M, Hoagland D A. Electric field induced instabilities at liquid/liquid interfaces[J]. Journal of Chemical Physics, 2001, 114(5): 2377-2381. doi: 10.1063/1.1338125
[6]	Pease L F III, Russel W B. Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: a generalized linear stability analysis[J]. Journal of Chemical Physics, 2003, 118(8): 3790-3803. doi: 10.1063/1.1529686
[7]	Pease L F III, Russel W B. Limitations on length scales for electrostatically induced submicrometer pillars and holes[J]. Langmuir, 2004, 20(3): 795-804. doi: 10.1021/la035022o
[8]	Schffer E, Thurn-Albrecht T, Russell T P, Stelner U. Electrohydrodynamic instabilities in polymer films[J]. Europhysics Letters, 2001, 53(4), 518-524.
[9]	Tian E M. Pattern formation induced by an electric field in thin liquid films[J]. Journal of Mathematics, Statistics, and Allied Fields, 2007, 1(1):1-6.
[10]	Wu N, Russel W B. Micro- and nano-patterns created via electrohydrodynamic instabilities[J]. Nano Today, 2009, 4(2): 180-192. doi: 10.1016/j.nantod.2009.02.002
[11]	Yeoh H K, Xu Q, Basaran O A. Equilibrium shapes and stability of a liquid film subjected to a nonuniform electric field[J]. Physics of Fluids, 2007, 19(11):114111. doi: 10.1063/1.2798806
[12]	Pease L F III, Russel W B. Linear stability analysis of thin leaky dielectric films subjected to electric fields[J]. Journal of Non-Newtonian Fluid Mechanics, 2002, 102(2): 233-250. doi: 10.1016/S0377-0257(01)00180-X
[13]	Shanker V, Sharma A. Instability of the interface between thin fluid films subjected to electric fields[J]. Journal of Colloid and Interface Science, 2004, 274(1): 294-308. doi: 10.1016/j.jcis.2003.12.024
[14]	Verma R, Sharma A, Kargupta K, Bhaumik J. Electric field induced instability and pattern formation in thin liquid films[J]. Langmuir, 2005, 21(8): 3710-3721. doi: 10.1021/la0472100
[15]	Scanlon J W, Segel L A. Finite amplitude cellular convection induced by surface tension[J]. J Fluid Mech, 1967, 30(1): 149-162. doi: 10.1017/S002211206700134X
[16]	Segel L A, Stuart J T. On the question of the preferred mode in cellular thermal convection[J]. J Fluid Mech, 1962, 13(2): 289-306. doi: 10.1017/S0022112062000683
[17]	Segel L A. The nonlinear interaction of a finite number of disturbances to a layer of fluid heated from below[J]. J Fluid Mech, 1965, 21(2): 359-384. doi: 10.1017/S002211206500023X
[18]	Busse F H. The stability of finite amplitude cellular convection and its relation to an extremum principle[J]. J Fluid Mech, 1967, 30(4): 625-649. doi: 10.1017/S0022112067001661
[19]	Palm E. Nonlinear thermal convection[J]. Ann Rev Fluid Mech, 1975, 7: 39-61. doi: 10.1146/annurev.fl.07.010175.000351
[20]	Tian E M, Wollkind D J. Nonlinear stability analyses of pattern formation in thin liquid films[J]. Interfaces and Free Boundaries, 2003, 5: 1-25.
[21]	Wollkind D J, Sriranganathan R, Oulton D B. Interfacial patterns during plane front alloy solidification[J]. Physica D, 1984, 12(1/3):215-240. doi: 10.1016/0167-2789(84)90526-8
[22]	Wollkind D J, Stephenson L E. Chemical turing pattern formation analyses: comparison of theory with experiment[J]. SIAM J Appl Math, 2000, 61(2): 387-431. doi: 10.1137/S0036139997326211
[23]	Chang H C. Wave evolution on a falling film[J]. Annu Rev Fluid Mech, 1994, 26: 103-36. doi: 10.1146/annurev.fl.26.010194.000535
[24]	Oron A, Davis S H, Bankoff S G. Long-scale evolution of thin liquid films[J]. Reviews of Modern Physics, 1997, 69(3): 931-980. doi: 10.1103/RevModPhys.69.931
[25]	Landau L D, Lifshitz E M. Electrodynamics of Continuous Media[M]. New York: Pergamon Press, 1960.
[26]	Saville D A. Electrohydrodynamics: the Taylor-Melcher leaky dielectric model[J]. Annu Rev Fluid Mech, 1997, 29: 27-64. doi: 10.1146/annurev.fluid.29.1.27
[27]	Zaks M A, Auer M, Busse F H. Undulating rolls and their instabilities in a Rayleigh-Benard layer[J]. Physical Review E, 1996, 53(5): 4807-4819. doi: 10.1103/PhysRevE.53.4807
[28]	Davis S H. Thermocapillary instabilities[J]. Ann Rev Fluid Mech, 1987, 19: 403-435. doi: 10.1146/annurev.fl.19.010187.002155