Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
Soft Matter. 2023 Mar 29;19(13):2385-2396. doi: 10.1039/d3sm00066d.
Semiflexible filaments deform into a variety of configurations that dictate different phenomena manifesting at low Reynolds number. Harnessing the elasticity of these filaments to perform transport-related processes at the microfluidic scale requires structures that can be directly manipulated to attain controllable geometric features during their deformation. The configuration of semiflexible chains assembled from paramagnetic colloids can be readily controlled upon the application of external time-varying magnetic fields. In circularly rotating magnetic fields, these chains undergo coiling dynamics in which their ends close into loops that wrap inward, analogous to the curling of long nylon filaments under shear. The coiling is promising for the precise loading and targeted transport of small materials, however effective implementation requires an understanding of the role that field parameters and chain properties play on the coiling features. Here, we investigate the formation of coils in semiflexible paramagnetic chains using numerical simulations. We demonstrate that the size and shape of the initial coils are governed by the Mason and elastoviscous numbers, related to the field parameters and the chain bending stiffness. The size of the initial coil follows a nonmonotonic behavior with Mason number from which two regions are identified: (1) an elasticity-dependent nonlinear regime in which the coil size decreases with increasing field strength and for which loop shape tends to be circular, and (2) an elasticity-independent linear regime where the size increases with field strength and the shape become more elliptical. From the time scales associated to these regimes, we identify distinct coiling mechanisms for each case that relate the coiling dynamics to two other configurational dynamics of paramagnetic chains: wagging and folding behaviors.
半刚性纤维可以变形为多种形态，这些形态决定了在低雷诺数下表现出的不同现象。利用这些纤维的弹性在微流控尺度上执行与传输相关的过程，需要能够直接操纵的结构，以在其变形过程中获得可控的几何特征。在外加时变磁场的作用下，可轻易控制由顺磁性胶体组装而成的半刚性链的形态。在圆形旋转磁场中，这些链经历了卷曲动力学，其两端闭合成向内包裹的环，类似于在剪切下长尼龙纤维的卷曲。这种卷曲对于精确加载和靶向运输小材料很有前景，然而有效的实现需要理解场参数和链性质对卷曲特征的作用。在这里，我们使用数值模拟研究了半刚性顺磁链中的线圈形成。我们证明了初始线圈的大小和形状由 Mason 和 elastoviscous 数决定，这两个数与场参数和链弯曲刚度有关。初始线圈的大小遵循非单调行为与 Mason 数，从中可以识别出两个区域：（1）一个依赖于弹性的非线性区域，其中线圈尺寸随磁场强度的增加而减小，并且环的形状趋于圆形，（2）一个独立于弹性的线性区域，其中尺寸随磁场强度的增加而增大，形状变得更加椭圆形。根据与这些区域相关的时间尺度，我们为每种情况确定了不同的卷曲机制，这些机制将卷曲动力学与顺磁链的另外两种构象动力学：摆动和折叠行为联系起来。
