We numerically investigate the curvature effect on the self-propelled capability of coalesced drops. The numerical method is based on a well validated multiphase flow solver that solves the three-dimensional Navier–Stokes equations. The liquid–air interface is captured using the moment of fluid method, and a direction splitting method is applied to advect the interface. Afterward, an approximate projection method is used to decouple the calculation of velocity and pressure. Different cases were validated by comparing the experimental results with the simulation results. The coalescence-induced jumping behavior on a flat surface is carefully captured using this numerical method. To investigate the effect of curvature of a curvy substrate on the self-jumping behavior, a case with a single drop impinging on a convex surface and a case with two drops’ coalescence on a fiber are also studied and compared with the experimental results. The asymmetric bouncing of a single drop on the convex surface leads to 40% reduction in contact time, as found in our study. Our study also reveals that due to the curvature of the wedge, the drop forms a lobe shaped region on the symmetric sides of the wedge. The lobed region forces the drop to convert more surface energy into kinetic energy in the upward direction. The jumping capability is improved by increasing the surface curvature. Our study also shows that at lower angles of contact, the drops can easily get attached to the substrate and, at the same time, have difficulty detaching from the substrate.

中文翻译：

---

表面曲率对聚结液滴自推进能力影响的数值研究

我们数值研究了凝聚液滴的自推进能力的曲率影响。数值方法基于经过充分验证的多相流求解器，可以求解三维Navier–Stokes方程。液-气界面是使用流体矩法来捕获的，方向分离法是用来平顺界面的。然后，使用近似投影方法来解耦速度和压力的计算。通过将实验结果与仿真结果进行比较来验证不同情况。使用此数值方法可以仔细捕获在平面上聚结引起的跳跃行为。要研究弯曲基材的曲率对自跳跃行为的影响，还研究了单滴撞击在凸面上的情况和两滴聚结在纤维上的情况，并与实验结果进行了比较。在我们的研究中发现，凸面上单滴的不对称弹跳导致接触时间减少40％。我们的研究还表明，由于楔形的曲率，液滴在楔形的对称侧面上形成了一个凸角形状的区域。突出的区域迫使液滴将更多的表面能沿向上的方向转换为动能。通过增加表面曲率来改善跳跃能力。我们的研究还表明，在较低的接触角下，液滴很容易附着在基材上，同时很难从基材上脱落。