Transient and self-similar dynamics in thin film coarsening
Transient and self-similar dynamics in thin film coarsening
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DOI：
10.1016/j.physd.2009.09.015
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发表时间：
2009-12-01
影响因子：
4
通讯作者：
Witelski, Thomas P.
中科院分区：
文献类型：
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作者：
Gratton, Michael B.;Witelski, Thomas P.
我们研究疏水基底上粘性流体一维薄膜简化模型的粗化。润滑理论表明，此类薄膜不稳定且反湿，形成液滴，然后在长时间尺度内聚集。液滴的质量和位置可以通过由 ODE 和删除规则组成的粗化动力系统 (CDS) 来描述。我们开发了离散和连续平均场模型，可以重现众所周知的 N(t) = O(t(-2/5)) 滴数长期统计幂律。 Lifshitz-Slyozov-Wagner 型 (LSW) 连续模型可预测与 CD 模拟和离散平均场模型生成的直方图相匹配的液滴质量的自相似分布。我们还描述了均质与异质去湿后的液滴分布，并将其用作 CD 模拟的初始条件，从而产生特征“阶梯”瞬态。瞬态还可以包括质量分布中反复出现的尖峰形成行为。对于理想化的初始条件，我们表明瞬态动力学可以跨越整个粗化过程，完全绕过幂律制度。 (C) 2009 Elsevier B.V. 保留所有权利。
We study coarsening in a simplified model of one-dimensional thin films of viscous fluids on hydrophobic substrates. Lubrication theory shows that such films are unstable and dewet to form droplets that then aggregate over long timescales. The masses and positions of the droplets can be described by a coarsening dynamical system (CDS) consisting of ODEs and deletion rules. We develop discrete and continuous mean-field models that reproduce the well-known N(t) = O(t(-2/5)) long-time statistical power law for the number of drops. A Lifshitz-Slyozov-Wagner-type (LSW) continuous model predicts the self-similar distribution of drop masses matching with histograms produced by CDs simulations and the discrete mean-field model. We also describe the distribution of drops following homogeneous versus heterogeneous dewetting and use these as initial conditions for the CDs simulations that yield characteristic "staircasing" transients. Transients can also include recurring spike formation behavior in the mass distribution. For idealized initial conditions, we show that the transient dynamics can span the full coarsening process, bypassing the power law regime entirely. (C) 2009 Elsevier B.V. All rights reserved.