论文标题
液滴运动在具有传质的化学异质底物上。 I.二维动力学
Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics
论文作者
论文摘要
我们考虑在滑动，传质和毛细血管的综合作用下移动的化学异质表面上的二维粘性液滴的动力学。液滴厚度所得的长波演化方程通过匹配的渐近扩张的方法进行分析处理，以缓慢的质量转移速率，准静态动力学和消失的小滑动长度的限制，以推断出两个移动前部的综合方程式的较低维度系统。我们证明，推导系统的预测与对分析适用性领域中许多代表性案例的完整模型的模拟非常吻合。具体而言，我们专注于滴滴的质量定期变化以突出动态的许多有趣特征，其中包括滑滑，类似滞后的效果，以及在恒定 - 拉迪乌斯和恒定角度之间交替的液滴的可能性，这些阶段以前在相关工作中已在相关工作中已经报道过。通过研究液滴质量变化，液滴平衡的分叉结构如何发展，进一步审查了动力学的这些特征。
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasi-static dynamics and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simulations of the full model for a number of representative cases within the domain of applicability of the analysis. Specifically, we focus on situations where the mass of the drop changes periodically to highlight a number of interesting features of the dynamics, which include stick-slip, hysteresis-like effects, as well as the possibility for the droplet to alternate between the constant-radius and constant-angle stages which have been previously reported in related works. These features of the dynamics are further scrutinized by investigating how the bifurcation structure of droplet equilibria evolves as the mass of the droplet varies.
