论文标题
在随时间变化的梯度磁场中悬浮纳米颗粒的动力学：分析结果
Dynamics of Suspended Nanoparticles in a Time-varying Gradient Magnetic Field: Analytical Results
论文作者
论文摘要
从理论上讲，我们研究了稀铁流体中单域铁磁纳米颗粒的确定性动力学，该动力学是由时变梯度磁场引起的。使用力和扭矩平衡方程，我们得出了一组一组一阶微分方程，描述了以小雷诺数为特征的这种粒子的翻译和旋转运动。由于梯度磁场同时生成颗粒的翻译和旋转，因此这些运动是耦合的。基于派生的方程组，我们通过通过粒子方向角度表达粒子位置来明确证明这一事实，反之亦然。获得的表达式用于表明基本方程组的解在时间上是周期性的，并确定粒子坐标和方向角振荡的间隔。另外，对于粒子振荡的特征频率较小的情况，这组方程近似求解。在这种情况下，我们发现所有粒子在其初始位置附近执行小的翻译振荡。相反，仅当粒子位于梯度磁场的零点附近时，方向角才在初始角度附近振荡。还讨论了所获得的结果在生物医学和分离过程中的可能应用。
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.
