School of Mechanical Engineering, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Republic of Korea.
Soft Matter. 2019 Mar 13;15(11):2328-2335. doi: 10.1039/c8sm01750f.
We study the mechanism of stretching and breaking of a mono-emulsion droplet under a direct current electric field using theoretical and experimental approaches aided by numerical simulation. Axisymmetric straining flow driven by an electric field results in the equilibrium deformation of the droplet along the direction of the electric field if the electric capillary number Cae that is the ratio of electric stresses to capillary stresses, is less than a critical value (Cae)crit. At (Cae)crit, the droplet breaks either before showing the slow deformation stage or rapidly. Furthermore, we developed a theoretical model to understand the mechanism of the transition from equilibrium deformation to non-equilibrium breaking. The Cae that can induce Taylor's deformation D = (α - β)/(α + β) ≈ 0.295; where α and β are the lengths of semi-major and semi-minor axes of the droplet, corresponds to (Cae)crit. At this stage, the maximum flow velocity shifts to the outside of the droplet along the electric field direction and large electric stresses are mainly concentrated at the droplet's side apex causing daughter droplet ejection. Finally, we compare the values of (Cae)crit obtained from the theoretical model ((Cae)crit ≈ 0.25) for which the conductivity ratio (R) between the droplet and ambient liquid i.e., R ∼ O(10) with our experimental results ((Cae)crit ≈ 0.245) and realize that (Cae)crit decreases as R increases. We also observe that even though the viscosity ratio can alter the emulsion breakup modes, it has no effect on (Cae)crit for the onset of breaking.
我们通过理论和实验方法，并结合数值模拟，研究了直流电场下单乳液液滴拉伸和断裂的机理。如果电毛细数 Cae（即电场应力与毛细应力的比值）小于临界值（Cae）crit，电场驱动的轴对称拉伸流将导致液滴沿电场方向平衡变形。在（Cae）crit 时，液滴要么在表现出缓慢变形阶段之前就发生断裂，要么快速断裂。此外，我们还开发了一个理论模型来理解从平衡变形到非平衡断裂的转变机制。能诱导泰勒变形 D = (α - β)/(α + β) ≈ 0.295 的 Cae（其中 α 和 β 分别是液滴的半长轴和半短轴的长度）对应于（Cae）crit。在这个阶段，最大流速沿电场方向向液滴外部移动，并且大的电场应力主要集中在液滴的侧面顶点，导致子液滴的喷射。最后，我们比较了理论模型得出的（Cae）crit 值（（Cae）crit ≈ 0.25），其中液滴和环境液体之间的电导率比（R）即 R ∼ O(10)，与我们的实验结果（（Cae）crit ≈ 0.245），并意识到（Cae）crit 随着 R 的增加而减小。我们还观察到，即使粘度比可以改变乳液的破裂模式，但它对破裂起始时的（Cae）crit 没有影响。
