Department of Chemical Engineering, Indian Institute of Technology, Delhi 110016, India.
Langmuir. 2010 Jun 1;26(11):8464-73. doi: 10.1021/la9049007.
A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short- to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (gamma/mu h) are uncovered, where gamma is the surface energy, mu is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength lambda approximately = 2.96 h is obtained for gamma/mu h < 0.1, whereas long waves that depend nonlinearly on the field strength and surface energy are obtained for gamma/mu h > 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.
本文提出了一种普遍的统一理论，用于描述范德华（van der Waals）、电场等场致薄黏弹性膜表面不稳定性，该理论考虑了失稳场以及弹性应变和表面能的稳定作用。该理论无缝涵盖了从弹性到粘性、从附着（受限）到润湿（自由表面）以及从短波长到长波长不稳定性的不同膜的不稳定性及其不同模式。发现失稳的临界条件强烈依赖于弹性特性，如膜的剪切模量，但主要波长与膜流变性显著无关。基于无量纲参数（γ/μ h）揭示了不同的模式，其中γ是表面能，μ是弹性剪切模量，h 是膜厚度。对于γ/μ h < 0.1，会得到具有波长λ≈2.96 h 的短波长、弹性响应，而对于γ/μ h > 1，则会得到与场强和表面能呈非线性关系的长波。由于其临界厚度较小，由分子间力失稳的润湿膜无论其粘弹性如何，总是表现出长波不稳定性。此外，我们基于不稳定润湿弹性膜的能量最小化的数值模拟表明，对于超薄膜会形成岛状结构，而对于相对较厚的膜则会出现嵌入膜中的孔状形态转变。然而，与粘性膜不同的是，不稳定的弹性膜不会显示出独特的主导波长，而是具有波长的双峰分布。
