Pototsky Andrey, Bestehorn Michael, Merkt Domnic, Thiele Uwe
Lehrstuhl für Theoretische Physik II, Brandenburgische Technische Universität Cottbus, Erich-Weinert-Strasse 1, Cottbus D-03046, Germany.
J Chem Phys. 2005 Jun 8;122(22):224711. doi: 10.1063/1.1927512.
We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.
我们考虑在固体水平（加热）基底上由两层不混溶液体组成的薄膜。对于厚度小于100纳米的超薄层，由于有效的分子相互作用，或者在加热情况下由于温度梯度引起的马兰戈尼流，这种双层液体薄膜的自由液 - 液界面和液 - 气界面都可能不稳定。使用长波近似，我们推导了在基底允许滑移的一般非等温情况下界面轮廓的耦合演化方程。对于等温超薄层，考虑到破坏稳定性的长程和稳定的短程分子相互作用，对薄膜演化的短期和长期进行了线性和非线性分析。结果表明，初始不稳定性可以是静脉曲张型、之字形或混合型。然而，在演化的非线性阶段，模式类型以及图案形态可以通过在两个不同的稳态解分支之间切换或通过沿单个分支粗化来改变。
