A multipole-accelerated 3D boundary-integral algorithm is developed to model pressure-driven flow of a highly-concentrated emulsion of many deformable drops through a periodic channel with tight constrictions. The drops are monodisperse, free from surfactant, and the Reynolds number is small for Stokes equations to apply. The channel surface consists of four solid panels: front and back parallel to each other, and band-like top and bottom panels with an arbitrary profile. The algorithm is for arbitrary channel aspect ratios, but the results are obtained for extreme cases, when the channel depth (front-back distance) is the same as the minimum channel height and both can be much smaller than the non-deformed drop diameter, making the drops flow as a monolayer. Strong hydrodynamic interactions (especially, drop-wall) necessitate very high surface resolutions combined with novel desingularization tools for the boundary integrals. Multipole acceleration gives, at least, two orders of magnitude gain over direct summations and facilitates long-time simulations, with many drop rearrangements. Examples for homoviscous emulsions with 40-92 drops in two types of channels at 80-90% drop volume fractions and different capillary numbers demonstrate single-file drop motion intermittent with pairs or triplets of drops in the constriction. Such squeezing interactions can result in extreme drop elongations, but are still not sufficient to promote breakup for the channel geometries, capillary numbers and drop confinements considered. Integral properties (the entire drop-phase and constriction flow velocities) are also analyzed.

开发了一种多极加速3D边界积分算法，以模拟压力驱动的许多可变形液滴的高浓度乳液通过紧缩的周期性通道的流动。液滴是单分散的，不含表面活性剂，对于应用斯托克斯方程，雷诺数小。通道表面由四个实体面板组成：前面板和后面板彼此平行，以及具有任意轮廓的带状顶部和底部面板。该算法适用于任意通道长宽比，但是当通道深度（前后距离）与最小通道高度相同且两者都可能比未变形的墨滴直径小得多时，才可在极端情况下获得结果。使液滴像单层一样流动。强大的水动力相互作用（尤其是，墙）需要非常高的表面分辨率，并需要使用新颖的去奇化工具来处理边界积分。与直接求和相比，多极加速至少可提供两个数量级的增益，并且可以进行长时间的仿真，并且具有许多墨滴重排。在两种类型的通道中以80-90％的液滴体积分数和不同的毛细管数在40-92滴中滴落的高粘度乳液的实例表明，在缩窄处间歇性地以成对或三重液滴的形式进行单行滴注运动。这种挤压相互作用可导致极端的液滴伸长，但仍不足以促进考虑到的通道几何形状，毛细管数和液滴限制的破裂。还分析了整体性质（整个液滴相和收缩流速度）。