Risbud Sumedh R, Drazer German
Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jul;90(1):012302. doi: 10.1103/PhysRevE.90.012302. Epub 2014 Jul 3.
We analyze the trajectory of suspended spherical particles moving through a square array of obstacles, in the deterministic limit and at zero Reynolds number. We show that in the dilute approximation of widely separated obstacles, the average motion of the particles is equivalent to the trajectory followed by a point particle moving through an array of obstacles with an effective radius. The effective radius accounts for the hydrodynamic as well as short-range repulsive nonhydrodynamic interactions between the suspended particles and the obstacles, and is equal to the critical offset at which particle trajectories become irreversible. Using this equivalent system we demonstrate the presence of directional locking in the trajectory of the particles and derive an inequality that accurately describes the "devil's staircase" type of structure observed in the migration angle as a function of the forcing direction. We use these results to determine the optimum resolution in the fractionation of binary mixtures using deterministic lateral-displacement microfluidic separation systems as well as to comment on the collision frequencies when the arrays of posts are utilized as immunocapture devices.
我们分析了在确定性极限和零雷诺数条件下，悬浮球形颗粒通过方形障碍物阵列时的轨迹。我们表明，在障碍物间距很大的稀溶液近似情况下，颗粒的平均运动等同于一个点粒子通过具有有效半径的障碍物阵列时所遵循的轨迹。有效半径考虑了悬浮颗粒与障碍物之间的流体动力学以及短程排斥非流体动力学相互作用，并且等于颗粒轨迹变得不可逆时的临界偏移量。利用这个等效系统，我们证明了颗粒轨迹中存在方向锁定现象，并推导出一个不等式，该不等式准确描述了作为强迫方向函数的迁移角中观察到的“魔鬼阶梯”型结构。我们利用这些结果来确定使用确定性横向位移微流体分离系统对二元混合物进行分馏时的最佳分辨率，并对将柱阵列用作免疫捕获装置时的碰撞频率进行评论。
