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arXiv 2012.10491cond-mat.soft
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时变梯度磁场中悬浮纳米颗粒的动力学分析

Dynamics of Suspended Nanoparticles in a Time-varying Gradient Magnetic Field: Analytical Results

S. I. Denisov, T. V. Lyutyy, A. T. Liutyi

摘要:

从理论上研究了在时变梯度磁场作用下,稀磁流体中单畴铁磁纳米颗粒的确定性动力学行为。使用力和扭矩平衡方程,我们推导出一组的一阶微分方程描述的平移和旋转运动的小雷诺数的特点,这样的颗粒。由于梯度磁场产生粒子的平移和旋转,因此这些运动是耦合的。基于推导出的方程组,我们证明了这一事实明确表示通过粒子的取向角的粒子的位置,反之亦然。所得到的表达式被用来表明,基本方程组的解决方案是周期性的时间和确定的间隔,其中粒子坐标和取向角振荡。此外,这组方程近似求解的情况下,小的特征频率的粒子振荡。在这个条件下,我们发现所有的粒子在它们的初始位置附近都有很小的平移振荡。相反,只有当粒子位于梯度磁场的零点附近时,取向角才在初始角附近振荡。最后讨论了所得结果在生物医学和分离过程中的可能应用。

英文摘要:

We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particles characterized by small Reynolds numbers. Since the gradient magnetic field generates both the translations and rotations of particles, these motions are coupled. Based on the derived set of equations, we demonstrate this fact explicitly by expressing the particle position through the particle orientation angle, and vice versa. The obtained expressions are used to show that the solution of the basic set of equations is periodic in time and to determine the intervals, where the particle coordinate and orientation angle oscillate. In addition, this set of equations is solved approximately for the case of small characteristic frequency of the particle oscillations. With this condition, we find that all particles perform small translational oscillations near their initial positions. In contrast, the orientation angle oscillates near the initial angle only if particles are located in the vicinity of zero point of the gradient magnetic field. The possible applications of the obtained results in biomedicine and separation processes are also discussed.

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