论文标题
扩散式接口方法，用于粘性流与捏合动力学扩散之间的竞争
Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics
论文作者
论文摘要
已经通过数值模拟和理论分析研究了液态的捏合动力学。出现在小长度尺度上，捏合动力学接受可以分类为Stokes制度和扩散为主导的方案的相似性解决方案，而后者最近在水溶液两相系统中进行了实验观察到[Phys。莱特牧师。 123，134501（2019）]。 Cahn-Hilliard-Navier-Stokes模型通过应用Onsager的变分原理得出，该模型被用作最小模型，能够描述不仅由对流又扩散驱动的界面运动。通过分析模型中的自由能耗散机制，引入了特征长度尺度，以测量界面运动中扩散和粘性流之间的竞争。该长度比例通常是远离临界点的系统的纳米尺度，但可以接近靠近临界点的水性两相系统的微米尺度。 Cahn-Hilliard-Navier-Stokes模型是通过在具有轴对称性的圆柱形结构域中使用准确有效的光谱方法来求解的。提出了足够的数值示例，以显示Stokes制度和扩散为主的制度中的捏合过程。特别是，在数值和分析上研究了这两个方案之间的交叉，以揭示相似性解决方案的缩放行为如何在定性上发生变化，因为界面的缝制颈部不可避免地可以访问特征长度尺度。还提供了针对长长液体细丝的分解的数值示例的讨论，并在不同的缩放制度中显示出质量不同的现象。
The pinch-off dynamics of a liquid thread has been studied through numerical simulations and theoretical analysis. Occurring at small length scales, the pinch-off dynamics admits similarity solutions that can be classified into the Stokes regime and the diffusion-dominated regime, with the latter being recently experimentally observed in aqueous two-phase systems [Phys. Rev. Lett. 123, 134501 (2019)]. Derived by applying Onsager's variational principle, the Cahn-Hilliard-Navier-Stokes model is employed as a minimal model capable of describing the interfacial motion driven by not only advection but also diffusion. By analyzing the free energy dissipation mechanisms in the model, a characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. This length scale is typically of nanometer scale for systems far from the critical point, but can approach micrometer scale for aqueous two-phase systems close to the critical point. The Cahn-Hilliard-Navier-Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry. Ample numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively. In particular, the crossover between these two regimes is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is inevitably accessed by the pinching neck of the interface. Discussions are also provided for numerical examples that are performed for the breakup of long liquid filaments and show qualitatively different phenomena in different scaling regimes.
