Abstract The motion of small droplets through microfluidic channels, membrane pores, and other confined geometries presents considerable computational challenge due to drop deformation, small clearances, and complex geometries. This paper addresses the challenge by developing a moving-frame boundary-integral method and demonstrating its utility with simulations of a three-dimensional, freely-suspended deformable drop moving through a T-shaped microchannel at small Reynolds number. The drop size is comparable to the channel height, which is much smaller than the channel depth. The drop is fed into a straight channel or arm of the T-junction, with prescribed flow ratio through the other two branches. This setup typically results in strong drop interaction with the furthest corner of the junction. For computational efficiency, the base flow in the channel without the drop is first determined. Then, a “moving-frame” or computational cell around the drop is dynamically generated, using the first solution to provide the fluid velocity on the cell boundary. This method is used to map the outcomes (movement into one branch or the other, or breakup and partitioning between the branches) as a function of the flow ratio between the two branches and the drop capillary number, size relative to the channel height, and viscosity ratio with the carrier fluid. A critical capillary number or size ratio is observed, below which the drop does not break. Above the critical value, the range of flow ratios over which impending breakup is predicted increases with increasing capillary number and size ratio. The volume partitioning in the range where breakup occurs is essentially unity for equal flow rates between the two branches, even though the geometry is asymmetric, and then the volume partition of the daughter drops favors the branch with higher flow rate and with a stronger dependence on the flow ratio for the smaller drop sizes and capillary numbers. The viscosity ratio has a small but noticeable effect, with drops of similar viscosity to the carrier fluid breaking most easily.

中文翻译：

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T形微通道中自由悬浮液滴的边界积分研究

摘要 由于液滴变形、小间隙和复杂的几何形状，小液滴通过微流体通道、膜孔和其他受限几何形状的运动提出了相当大的计算挑战。本文通过开发一种移动框架边界积分方法并通过模拟以小雷诺数移动通过 T 形微通道的三维、自由悬浮的可变形液滴来展示其效用来解决这一挑战。液滴尺寸与通道高度相当，通道高度远小于通道深度。液滴被送入 T 型接头的直通道或臂，通过其他两个分支具有规定的流量比。这种设置通常会导致与结点最远角的强烈液滴相互作用。为了计算效率，首先确定没有液滴的通道中的基流。然后，动态生成围绕液滴的“移动框架”或计算单元，使用第一个解决方案提供单元边界上的流体速度。该方法用于将结果（移动到一个分支或另一个分支，或分支之间的分裂和分割）映射为两个分支之间的流量比和毛细管数量、尺寸相对于通道高度的函数，以及与载液的粘度比。观察到临界毛细管数或尺寸比，低于该值时液滴不会破裂。在临界值之上，预测即将破裂的流量比范围随着毛细管数量和尺寸比的增加而增加。发生破裂的范围内的体积分配对于两个分支之间的相等流速基本上是统一的，即使几何形状是不对称的，然后子体的体积分配下降有利于具有更高流速和更强依赖性的分支较小液滴尺寸和毛细管数的流量比。粘度比的影响很小但很明显，与载液粘度相似的液滴最容易破裂。