In this paper, we describe the unification and extension of multiple kinematic theories on the advection of colloidal particles through periodic obstacle lattices of arbitrary geometry and infinitesimally small obstacle size. We focus specifically on the particle displacement lateral to the flow direction (termed “deterministic lateral displacement”) and the particle-obstacle interaction frequency, and develop methods for describing these as a function of particle size and lattice parameters for arbitrary lattice geometries. We then demonstrate design algorithms for microfluidic devices consisting of chained obstacle lattices of this type that approximate any lateral displacement function of size to arbitrary accuracy with respect to multiple optimization metrics, prove their validity mathematically, and compare the generated results favorably to designs in the literature with respect to metrics such as accuracy, device size, and complexity.

中文翻译：

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基于对称诱导的循环动力学的基于尺寸的颗粒分选微设备的合理设计协议

在本文中，我们描述了多种运动学理论关于胶体粒子对流的统一和扩展，它们通过任意几何形状和无限小的障碍物尺寸的周期性障碍物格构成。我们特别关注流向横向的粒子位移（称为“确定性横向位移”）和粒子与障碍物的相互作用频率，并开发了将其描述为任意晶格几何形状的粒度和晶格参数的函数的方法。然后，我们演示了由这种类型的链式障碍晶格组成的微流控设备的设计算法，该算法可以将任意大小的横向位移函数近似于多个优化指标的任意精度，并通过数学方式证明其有效性，