Surfaces with nonuniform wettability have attracted much attention recently due to their academic significance and applications in droplet lateral motion. In this study, numerical simulations and theoretical analyses are conducted to investigate the dynamic behaviors of a droplet impacting on a wettability-patterned surface, in which the superhydrophobic substrate is decorated with a hydrophilic pattern. An improved diffuse interface method coupled with the adaptive mesh-refinement technique and Kistler dynamic contact angle model is adopted to capture the interfacial evolution. After the validation of the numerical method, the dynamic mechanisms of impacting droplets are explored by analyzing the variation of the contact line and velocity profile. Then, systematic simulations are conducted using hydrophilic patterns with different geometric parameters. And the parameter of effective retraction area S is introduced to quantify the wettability patterns. On this basis, the general rules between the patterns and droplet lateral motion are established, and the design principles of hydrophilic patterns are obtained. The numerical results indicate that arc-shape hydrophilic patterns are more appropriate for realizing the droplet lateral motion, which can produce a larger lateral velocity and less residual liquid. In addition, the relevant motion parameters of the droplet are predicted more accurately by using the previous theoretical method. And the mechanism of energy transformation and dissipation is further revealed. Moreover, a simple and practical model is proposed to predict the lateral velocity using the effective retraction area.

中文翻译：

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液滴在可湿性图案表面上的横向运动：数值和理论研究

由于其学术意义和在液滴横向运动中的应用，具有不均匀润湿性的表面最近引起了很多关注。在这项研究中，进行了数值模拟和理论分析，以研究液滴在润湿性图案表面上的动力学行为，其中超疏水性基材装饰有亲水性图案。采用改进的扩散界面方法结合自适应网格细化技术和奇石乐动态接触角模型来捕获界面演化。在数值方法验证之后，通过分析接触线和速度分布的变化来探索冲击液滴的动力学机理。然后，使用具有不同几何参数的亲水图案进行系统的模拟。以及有效回缩面积的参数引入S来量化润湿性模式。在此基础上，建立了图案与液滴横向运动之间的一般规律，得到了亲水图案的设计原理。数值结果表明，圆弧形亲水图案更适合于实现液滴的横向运动，可以产生更大的横向速度和更少的残留液体。另外，通过使用先前的理论方法，可以更准确地预测液滴的相关运动参数。进一步揭示了能量转化和耗散的机理。此外，提出了一个简单实用的模型来使用有效缩回面积预测横向速度。