We combine theory and numerical calculations to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To validate our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using 'continuous-flow lithography'. Contrary to what was reported in earlier work (Uspal et al. in Nat Commun 4:2666, 2013), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme.

中文翻译：

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计算Hele-Shaw通道中高度受限的任意形状粒子的运动。

我们结合理论和数值计算来准确预测各向异性颗粒在浅微流体通道中的运动，其中，颗粒在垂直方向上受到强烈约束。我们通过Brinkman方程对围绕颗粒的Stokes流进行了有效的准二维描述，可以在比三维问题快两个数量级的时间内解决该问题。计算速度的提高使我们能够计算通道中粒子的完整轨迹。为了验证我们的方案，我们使用“连续流光刻”研究在微流体通道中产生的哑铃形颗粒的运动。与早期工作中报道的情况相反（Uspal等人，Nat Commun，4：2666，2013），我们发现，哑铃颗粒在外流中的重新定向时间随其盘尺寸比的变化而显示出最小值。这一发现与新实验非常吻合，从而证实了我们方案的预测能力。