Bandyopadhyay Dipankar, Sharma Ashutosh
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India.
J Colloid Interface Sci. 2007 Jul 15;311(2):595-608. doi: 10.1016/j.jcis.2007.02.089. Epub 2007 Mar 7.
A long wave nonlinear theory and simulations on the electric field induced instability of a thin (<1000 nm thick) viscous bilayer resting on a solid substrate are presented. The instabilities in these systems are initiated by one of the two basic short time modes of deformation at the twin interfaces-in-phase bending or out of phase squeezing. Linear stability analysis (LSA) is carried out to identify the conditions for these modes. It is shown that these modes can be switched and the relative amplitudes of deformation at the interfaces can be profoundly altered by varying the thicknesses, viscosities, interfacial tensions and dielectric constants of the films. Nonlinear simulations are presented to support the results obtained from the LSA. In addition, simulations show a number of interesting interfacial morphologies including: (a) embedded upper layer in the array of lower layer columns, (b) columns of the upper layer grown towards the substrate and sheathed by the lower layer liquid, (c) lower layer columns sheathed by the upper layer liquid leading to concentric core-shell columns, (d) droplets of upper liquid on the largely undisturbed lower layer, (e) symmetry breaking traveling waves at the interfaces, and (f) evolution of two different wavelengths at the two interfaces of a bilayer. The effects of viscous and the capillary resistances on the evolution of instability and morphology are also discussed.
本文提出了一种长波非线性理论，并对置于固体基底上的薄（<1000 nm厚）粘性双层膜在电场诱导下的不稳定性进行了模拟。这些系统中的不稳定性由双界面处两种基本的短时间变形模式之一引发，即同相弯曲或异相挤压。进行了线性稳定性分析（LSA）以确定这些模式的条件。结果表明，通过改变薄膜的厚度、粘度、界面张力和介电常数，可以切换这些模式，并显著改变界面处的相对变形幅度。给出了非线性模拟以支持从LSA获得的结果。此外，模拟还展示了许多有趣的界面形态，包括：（a）上层嵌入下层柱状阵列中；（b）上层柱体朝着基底生长并被下层液体包裹；（c）下层柱体被上层液体包裹形成同心核壳柱体；（d）上层液体的液滴位于基本未受干扰的下层之上；（e）界面处的对称破缺行波；（f）双层膜两个界面处出现两种不同波长的演化。还讨论了粘性和毛细管阻力对不稳定性演化和形态的影响。
