Geoscientific Centre, University of Göttingen, D-37077 Göttingen, Germany.
Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
Phys Rev E. 2017 Sep;96(3-1):033115. doi: 10.1103/PhysRevE.96.033115. Epub 2017 Sep 28.
We employ a pairwise force smoothed particle hydrodynamics (PF-SPH) model to simulate sessile and transient droplets on rough hydrophobic and hydrophilic surfaces. PF-SPH allows modeling of free-surface flows without discretizing the air phase, which is achieved by imposing the surface tension and dynamic contact angles with pairwise interaction forces. We use the PF-SPH model to study the effect of surface roughness and microscopic contact angle on the effective contact angle and droplet dynamics. In the first part of this work, we investigate static contact angles of sessile droplets on different types of rough surfaces. We find that the effective static contact angles of Cassie and Wenzel droplets on a rough surface are greater than the corresponding microscale static contact angles. As a result, microscale hydrophobic rough surfaces also show effective hydrophobic behavior. On the other hand, microscale hydrophilic surfaces may be macroscopically hydrophilic or hydrophobic, depending on the type of roughness. We study the dependence of the transition between Cassie and Wenzel states on roughness and droplet size, which can be linked to the critical pressure for the given fluid-substrate combination. We observe good agreement between simulations and theoretical predictions. Finally, we study the impact of the roughness orientation (i.e., an anisotropic roughness) and surface inclination on droplet flow velocities. Simulations show that droplet flow velocities are lower if the surface roughness is oriented perpendicular to the flow direction. If the predominant elements of surface roughness are in alignment with the flow direction, the flow velocities increase compared to smooth surfaces, which can be attributed to the decrease in fluid-solid contact area similar to the lotus effect. We demonstrate that classical linear scaling relationships between Bond and capillary numbers for droplet flow on flat surfaces also hold for flow on rough surfaces.
我们采用了一种基于粒子的光滑质点流体动力学（PF-SPH）模型来模拟固着和瞬态液滴在粗糙疏水和亲水表面上的行为。PF-SPH 允许在不离散气相的情况下模拟自由表面流，这是通过施加表面张力和动态接触角的对力实现的。我们使用 PF-SPH 模型来研究表面粗糙度和微观接触角对有效接触角和液滴动力学的影响。在这项工作的第一部分，我们研究了固着液滴在不同类型粗糙表面上的静态接触角。我们发现Cassie 和 Wenzel 液滴在粗糙表面上的有效静态接触角大于相应的微观静态接触角。因此，微观疏水粗糙表面也表现出有效的疏水行为。另一方面，微观亲水表面在宏观上可能是亲水的或疏水的，这取决于粗糙度的类型。我们研究了 Cassie 和 Wenzel 状态之间的转变对粗糙度和液滴大小的依赖性，这可以与给定流体-基底组合的临界压力联系起来。我们观察到模拟结果与理论预测之间的良好一致性。最后，我们研究了粗糙度取向（即各向异性粗糙度）和表面倾斜对液滴流速的影响。模拟结果表明，如果表面粗糙度垂直于流动方向，则液滴流速较低。如果表面粗糙度的主要元素与流动方向一致，则与光滑表面相比，流速会增加，这可以归因于类似于莲花效应的流体-固体接触面积减小。我们证明了经典的线性标度关系，即用于平坦表面上液滴流动的 Bond 和毛细数之间的关系，也适用于粗糙表面上的流动。
