Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm
Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm
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DOI：
10.1017/s0022112099005285
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发表时间：
1999-07-25
影响因子：
3.7
通讯作者：
Davis, RH
中科院分区：
文献类型：
--
作者：
Zinchenko, AZ;Rother, MA;Davis, RH
开发了一种用于斯托克斯流中相互作用的可变形液滴的三维边界积分算法。该算法适用于非常大的变形和极端情况，包括尖角界面和接近破裂的液滴。使用了一种新的无曲率边界积分公式，仅包含法向量，法向量通常比曲率对离散化误差不太敏感。适当的正则化使该方法适用于小表面间距和任意 lambda，其中 lambda 是液滴和介质的粘度之比。无曲率形式消除了二维尖点固有的集中毛细管力的困难，并允许模拟具有点和线奇点的三维液滴/气泡运动，而传统形式只能处理点奇点。无曲率形式与自适应网格稳定的特殊被动技术相结合，可以对接近破裂的高纵横比液滴进行三维模拟。使用具有固定拓扑的高度拉伸三角剖分。该代码用于研究两个气泡或液滴在重力作用下的相对运动，当尖端和破裂是典型情况时，键数 B 适中。计算了变形引起的气泡和低粘度液滴的捕获效率，发现其与 Manga & Stone (1993, 1995b) 的现有实验相当一致。还考虑了由于 lambda = O(1) 与较大液滴相互作用而导致较小液滴的三维破碎，并且该算法通过外推法准确模拟了中等超临界条件的初级破碎时刻和体积分配。破碎效率的计算表明，在 lambda = O(1) 且 B 大于或等于 5-10 且尺寸分布窄的沉降乳液中，由于相互作用而导致的破碎是显着的。在模拟中还观察到了一种结合的捕获和破碎现象，即较小的液滴开始破裂而没有从较大的液滴上形成的凹坑中释放出来。对 lambda = O(1) 的两滴相互作用的可能模式进行了一般分类。
A three-dimensional boundary-integral algorithm for interacting deformable drops in Stokes flow is developed. The algorithm is applicable to very large deformations and extreme cases, including cusped interfaces and drops closely approaching breakup. A new, curvatureless boundary-integral formulation is used, containing only the normal vectors, which are usually much less sensitive than is the curvature to discretization errors. A proper regularization makes the method applicable to small surface separations and arbitrary lambda, where lambda is the ratio of the viscosities of the drop and medium. The curvatureless form eliminates the difficulty with the concentrated capillary force inherent in two-dimensional cusps and allows simulation of three-dimensional drop/bubble motions with point and line singularities, while the conventional form can only handle point singularities. A combination of the curvatureless form and a special, passive technique for adaptive mesh stabilization allows three-dimensional simulations for high aspect ratio drops closely approaching breakup. using highly stretched triangulations with fixed topology. The code is applied to study relative motion of two bubbles or drops under gravity for moderately high Bond numbers B, when cusping and breakup are typical. The deformation-induced capture efficiency of bubbles and low-viscosity drops is calculated and found to be in reasonable agreement with available experiments of Manga & Stone (1993, 1995b). Three-dimensional breakup of the smaller drop due to the interaction with a larger one for lambda = O(1) is also considered, and the algorithm is shown to accurately simulate both the primary breakup moment and the volume partition by extrapolation for moderately supercritical conditions. Calculations of the breakup efficiency suggest that breakup due to interactions is significant in a sedimenting emulsion with narrow size distribution at lambda = O(1) and B greater than or equal to 5-10. A combined capture and breakup phenomenon, when the smaller drop starts breaking without being released from the dimple formed on the larger one, is also observed in the simulations. A general classification of possible modes of two-drop interactions for lambda = O(1) is made.