润滑介导液滴运动速度标度中由倾角诱导的交叉现象
Inclination-Induced Crossover in the Velocity Scaling of Lubrication-Mediated Droplet Motion
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中文总结 AI 辅助
该研究通过实验揭示了润滑介导液滴运动的速度标度存在由倾角诱导的连续交叉，其主导耗散机制的变化未直接反映在液滴全局形态中，确定倾角为关键控制参数。
中文摘要 AI 辅助
我们实验研究了浸没在粘性油中的倾斜表面上滑动的水滴的蠕变运动，在宽范围的液滴尺寸和倾角下测量了液滴的速度、宽度和高度。速度随液滴半径呈幂律增长，但对应的指数强烈依赖于倾角：小倾角下指数接近3/2，大倾角下则逐渐趋近于9/4。因此，结果揭示了润滑介导液滴运动的速度-尺寸标度中存在由倾角诱导的连续交叉现象。基于Landau-Levich-Derjaguin膜形成和动态弯月面中粘性耗散的标度分析重现了这些极限行为，分别对应准球形和薄饼状标度 regime。值得注意的是，速度标度的演化比宏观液滴形状的相应演化显著得多：尽管速度数据在大倾角下逐渐趋近于薄饼状标度律，但全局液滴尺寸的演化比简单薄饼形状图像的预期更为复杂，特别是，即使测量的液滴尺寸仍远偏离相应的薄饼极限几何，也会出现向薄饼状速度标度的趋近。这些观察结果表明，液滴下方主导的润滑耗散机制发生了交叉，而这并未直接反映在全局液滴形态中。结果确定了倾角是控制润滑介导液滴运动的关键参数，并强调了液-液系统中全局形状演化与局部耗散动力学之间的区别。
英文摘要
We experimentally investigate the creeping motion of water droplets sliding along an inclined surface immersed in a viscous oil. The droplet velocity, width, and height are measured over a broad range of droplet sizes and inclination angles. The velocity increases with droplet radius according to a power law, but the corresponding exponent depends strongly on the inclination angle. At small inclinations, the exponent is close to 3/2, whereas at larger inclinations it progressively approaches 9/4. The results therefore reveal a continuous inclination-induced crossover in the velocity-size scaling of lubrication-mediated droplet motion. A scaling analysis based on Landau-Levich-Derjaguin film formation and viscous dissipation in the dynamic meniscus reproduces these limiting behaviors, which correspond to the quasi-spherical and pancake scaling regimes, respectively. Remarkably, the evolution of the velocity scaling is substantially more pronounced than the corresponding evolution of the macroscopic droplet shape. While the velocity data progressively approach the pancake scaling law at large inclinations, the global droplet dimensions evolve in a more complex manner than expected from a simple pancake-shape picture. In particular, the approach to pancake-like velocity scaling occurs even when the measured droplet dimensions remain far from the corresponding pancake-limit geometry. These observations suggest a crossover in the dominant lubrication-dissipation mechanism beneath the droplet that is not directly reflected in the global droplet morphology. The results identify inclination angle as a key control parameter governing lubrication-mediated droplet motion and highlight the distinction between global shape evolution and local dissipation dynamics in liquid-liquid systems.
