Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (8): 1039-1046.doi: https://doi.org/10.1007/s10483-011-1479-9
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E. M. TIAN, T. P. SVOBODNY, J. D. PHILLIPS
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Abstract: The development of stationary patterns on a thin polymer surface subject to an electric field is studied by means of the hexagonal-planform weakly nonlinear stability analysis and numerical simulations. The time evolution of the interface between the air and the polymer film on the unbounded spatial domain is described by a thin film equation, incorporating the electric driving force and the surface diffusion. The nonlinear interfacial growth includes the amplitude equations and superposition 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.
2010 MSC Number:
35B36
65P40
76A20
76E17
E. M. TIAN;T. P. SVOBODNY;J. D. PHILLIPS. Thin liquid film morphology driven by electro-static field. Applied Mathematics and Mechanics (English Edition), 2011, 32(8): 1039-1046.
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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-011-1479-9
https://www.amm.shu.edu.cn/EN/Y2011/V32/I8/1039