Martin James E, Solis Kyle J
Sandia National Laboratories, Nanomaterials Sciences, Albuquerque, New Mexico, USA.
Soft Matter. 2015 Sep 28;11(36):7130-42. doi: 10.1039/c5sm00966a. Epub 2015 Aug 7.
We recently reported two methods of inducing vigorous fluid vorticity in magnetic particle suspensions. The first method employs symmetry-breaking rational fields. These fields are comprised of two orthogonal ac components whose frequencies form a rational number and an orthogonal dc field that breaks the symmetry of the biaxial ac field to create the parity required to induce deterministic vorticity. The second method is based on rational triads, which are fields comprised of three orthogonal ac components whose frequency ratios are rational (e.g., 1 : 2 : 3). For each method a symmetry theory has been developed that enables the prediction of the direction and sign of vorticity as functions of the field frequencies and phases. However, this theory has its limitations. It only applies to those particular phase angles that give rise to fields whose Lissajous plots, or principal 2-d projections thereof, have a high degree of symmetry. Nor can symmetry theory provide a measure of the magnitude of the torque density induced by the field. In this paper a functional of the multiaxial magnetic field is proposed that not only is consistent with all of the predictions of the symmetry theories, but also quantifies the torque density. This functional can be applied to fields whose Lissajous plots lack symmetry and can thus be used to predict a variety of effects and trends that cannot be predicted from the symmetry theories. These trends include the dependence of the magnitude of the torque density on the various frequency ratios, the unexpected reversal of flow with increasing dc field amplitude for certain symmetry-breaking fields, and the existence of off-axis vorticity for rational triads, such as 1 : 3 : 5, that do not have the symmetry required to analyze by symmetry theory. Experimental data are given that show the degree to which this functional is successful in predicting observed trends.
我们最近报道了两种在磁性颗粒悬浮液中诱导强烈流体涡度的方法。第一种方法采用破坏对称性的有理场。这些场由两个正交的交流分量组成，其频率形成一个有理数，以及一个正交的直流场，该直流场打破双轴交流场的对称性，以创建诱导确定性涡度所需的奇偶性。第二种方法基于有理三元组，即由三个正交交流分量组成的场，其频率比为有理数（例如1∶2∶3）。对于每种方法，都已开发出一种对称性理论，该理论能够根据场频率和相位预测涡度的方向和符号。然而，该理论有其局限性。它仅适用于那些特定的相位角，这些相位角会产生其李萨如图形或其主要二维投影具有高度对称性的场。对称性理论也无法提供场诱导的转矩密度大小的度量。在本文中，提出了一种多轴磁场的泛函，它不仅与对称性理论的所有预测一致，而且还能量化转矩密度。该泛函可应用于其李萨如图形缺乏对称性的场，因此可用于预测各种对称性理论无法预测的效应和趋势。这些趋势包括转矩密度大小对各种频率比的依赖性、对于某些破坏对称性的场，随着直流场幅度增加流动意外反转，以及对于1∶3∶5等有理三元组存在无法通过对称性理论分析所需对称性的离轴涡度。给出了实验数据，展示了该泛函在预测观察到的趋势方面的成功程度。
