Ajaev Vladimir S, Tsekov Roumen, Vinogradova Olga I
Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Sep;78(3 Pt 1):031602. doi: 10.1103/PhysRevE.78.031602. Epub 2008 Sep 12.
We carry out a theoretical investigation of the evolution of a wetting film formed by pressing a bubble against a solid substrate. Our model incorporates the effects of capillarity and Derjaguin-Landau-Verwey-Overbeek (DLVO) (van der Waals and electrostatic) components of the disjoining pressure. Rapid changes in the relative position of the bubble and the substrate are shown to result in surprisingly rich dynamics of wetting film deformations. Even for stable films, we find transient rippled deformations with several points of local maximum of wetting film thickness and discuss how their evolution depends on changes in the meniscus position relative to the substrate and the disjoining pressure parameters. A connection is made to the recently reported experimental observations of one such rippled deformation, the so-called wimple, characterized by a local minimum of the thickness in the center, surrounded by a ring of greater film thickness and bounded at the outer edge by the barrier rim. Guidelines are provided for experimental detection of more complex rippled deformations in stable wetting films. Development of instability is studied in a situation when the electrostatic component of disjoining pressure is destabilizing, with particular emphasis on the nonlinear evolution and rupture of the film. Potential applications of our findings to small-scale mixing and deposition of nanoparticles are discussed.
我们对通过将气泡压向固体基板形成的润湿膜的演变进行了理论研究。我们的模型纳入了毛细作用以及分离压力的德亚金-朗道-韦弗-奥弗贝克(DLVO)(范德华力和静电力)分量的影响。气泡与基板相对位置的快速变化会导致润湿膜变形出现惊人丰富的动力学现象。即使对于稳定的膜,我们也发现了具有多个润湿膜厚度局部最大值点的瞬态波纹变形,并讨论了它们的演变如何取决于弯月面相对于基板的位置变化以及分离压力参数。我们将其与最近报道的一种此类波纹变形(即所谓的涟漪,其特征是中心厚度局部最小,周围是较厚膜的环,在外边缘由阻挡边缘界定)的实验观察结果建立了联系。为在稳定的润湿膜中实验检测更复杂的波纹变形提供了指导原则。当分离压力的静电分量起不稳定作用时,研究了不稳定性的发展,特别强调了膜的非线性演变和破裂。我们讨论了我们的研究结果在纳米颗粒的小规模混合和沉积方面的潜在应用。