论文标题
调整磁场以通过非线性周期性界面波生成具有可控速度的旋转铁氟利液滴
Tuning a magnetic field to generate spinning ferrofluid droplets with controllable speed via nonlinear periodic interfacial waves
论文作者
论文摘要
Hele-Shaw构型中的二维不自由表面流是探索非线性物理学的肥沃地面。由于Saffman和Taylor在流体界面的线性不稳定性方面的工作，因此已经花费了很大的努力来确定物理学和迫使设定线性生长速率。但是，线性稳定性并不总是意味着非线性稳定性。我们演示了径向和方位角外部磁场的组合如何在Hele-Shaw构型中操纵线性不稳定的铁氟滴的界面形状。我们表明，弱非线性理论可用于调整最初的不稳定生长。然后，非线性阻止了不稳定性，并导致永久性变形的液滴形状。具体而言，我们表明可以以可预测的旋转速度将变形的液滴设置为运动，这表明流体流体界面上的非线性行进波。最线性不稳定的波数和所施加的外部磁场的组合强度决定了行动波形，这可能是不对称的。
Two dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid--fluid interfaces, significant effort has been expended to determining the physics and forcing that set the linear growth rate. However, linear stability does not always imply nonlinear stability. We demonstrate how the combination of a radial and an azimuthal external magnetic field can manipulate the interfacial shape of a linearly unstable ferrofluid droplet in a Hele-Shaw configuration. We show that weakly nonlinear theory can be used to tune the initial unstable growth. Then, nonlinearity arrests the instability, and leads to a permanent deformed droplet shape. Specifically, we show that the deformed droplet can be set into motion with a predictable rotation speed, demonstrating nonlinear traveling waves on the fluid-fluid interface. The most linearly unstable wavenumber and the combined strength of the applied external magnetic fields determine the traveling wave shape, which can be asymmetric.
