Yang Seung-Man, Leal L Gary, Kim Young-Seok
Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, Taejon, 305-701, Korea.
J Colloid Interface Sci. 2002 Jun 15;250(2):457-65. doi: 10.1006/jcis.2002.8376.
In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.
在本文中，我们考虑了处于渐近润滑状态下两个涂覆有薄可变形液体的不等径球体之间的流体动力学相互作用。这个问题是通过所谓的“薄膜排水”机制实现液滴聚并的一个原型模型，其中除了范德华相互作用力外，流体动力学贡献主要来自润滑区域。首先，针对两个非常靠近且发生对头碰撞的不等径涂覆球体，推导了一个通用公式。对得到的关于变形薄膜形状和应力分布的一组演化方程进行了数值求解。确定了薄膜形状和流体动力学相互作用力与分离距离、薄膜厚度、粘度比以及毛细管数的函数关系。结果表明，当两个球体相互靠近时，薄膜开始变平，最终在其前部区域形成负曲率（或一个宽凹坑），在该区域形成高润滑压力。随着毛细管数增加，凹坑形成得更早。对于大毛细管数，薄膜液体从其前部区域排出，并且在两个薄膜“接触”之前，涂覆的液体薄膜就会破裂。同时，对于小毛细管数，间隙液体首先排出，并且两个液体薄膜最终聚并。
