Long-time emergent dynamics of liquid films undergoing thermocapillary instability

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Steven A. Kedda, Michael C. Dallaston, Scott W. McCue
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引用次数: 0

Abstract

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equations that model how the evolution of the film height is affected by different forces. We investigate a model of interaction between surface tension and the thermocapillary Marangoni effect, with a particular focus on the long-time limit. In this limit, the model predicts the creation of an infinite cascade of successively smaller satellite droplets near points where the film thickness vanishes. Motivated by recent progress on the analysis of discrete self-similarity in thin film equations, we compute solutions in a space- and time-rescaled coordinate system. Using this rescaled system we observe the dynamics much further in time than has previously been achieved. The observed behavior is close to, but distinct from, previous observations of discretely self-similar thin film flows, in that the rescaled system does not settle down to a periodic solution, but instead has aspects that continue to evolve monotonically in scaled time. This discovery suggests there are as-yet unexplored ways in which discrete self-similarity may be exhibited.

Abstract Image

经历热毛细管不稳定性的液体薄膜的长期突发动力学
对粘性薄膜流动的研究导致了高度非线性偏微分方程的发展,该方程模拟了薄膜高度的演变如何受到不同作用力的影响。我们研究了表面张力与热毛细管马兰戈尼效应之间的相互作用模型,尤其侧重于长时间极限。在这一极限中,该模型预测在薄膜厚度消失的点附近会产生由连续变小的卫星液滴组成的无限级联。受薄膜方程中离散自相似性分析最新进展的启发,我们计算了空间和时间比例坐标系中的解。利用这种重比例坐标系,我们可以观察到比以前更远的时间动态。观察到的行为接近于之前对离散自相似薄膜流的观察,但又有别于之前的观察,因为重标度系统不会稳定在一个周期性的解上,而是有一些方面会在标度时间内继续单调演化。这一发现表明,离散自相似性还有一些尚未探索的表现形式。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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