Electrohydrodynamic rotation of drops at large electric Reynolds numbers
Electrohydrodynamic rotation of drops at large electric Reynolds numbers
复制标题
大雷诺数下液滴的电流体动力旋转
DOI：
--
复制
发表时间：
2016
影响因子：
3.7
通讯作者：
I. Frankel
中科院分区：
文献类型：
--
作者：
E. Yariv;I. Frankel
当受到足够强的电场作用时，悬浮在弱导电液体中的粒子和液滴表现出自发的旋转运动。这种所谓的昆克旋转是非线性对称破缺现象的一个有趣的例子。为了说明液滴的旋转，我们在二维Taylor-Melcher电流体模型的框架内分析了大电雷诺数的渐近极限。在这个奇异极限中的非平凡的优势平衡导致流体速度和表面电荷密度的标度为$mathit{Re}^{-1/2}$。流动是由一个自包含的非线性边值问题控制的，该边值问题不允许连续的前后对称解，因此需要液滴旋转。此外，热力学论证表明，只有当悬浮液体内的电荷松弛快于液滴内的电荷松弛时，才存在前后不对称溶液。流动问题同时具有镜像对称性(相对于外场方向)和流动反转对称性；它被转化为普适问题，与液滴相和悬浮液相中的电导率和介电常数之比无关。重新标度的角速度与粘性比有微弱的依赖关系。精确方程的相应数值解确实在渐近计算的普适解上完全崩溃。
When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $mathit{Re}gg 1$ , within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $mathit{Re}^{-1/2}$ . The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $mathit{Re}$ upon the asymptotically calculated universal solution.