Drygiannakis A I, Papathanasiou A G, Boudouvis A G
School of Chemical Engineering, National Technical University of Athens, Athens, GR-15780, Greece.
J Colloid Interface Sci. 2008 Oct 15;326(2):451-9. doi: 10.1016/j.jcis.2008.06.061. Epub 2008 Jul 9.
Liquid droplets bridging the gap between two dielectric-coated horizontal electrode plates suffer breakup instabilities when a voltage applied between the electrodes exceeds a threshold. Interestingly enough, broken liquid bridges (i.e. a pair of a sessile and a pendant drop) can spontaneously rejoin if the voltage is still applied to the electrodes. Here we study the electro-hydrostatics of the liquid bridges in the joined or broken state and we illuminate the mechanisms of the shape transitions that lead to bridge rupture or droplet joining. The governing equations of the capillary electro-hydrostatics form nonlinear and free boundary problems which are solved numerically by the Galerkin/finite element method. On one hand, we found that capillary bridges become unstable at a turning point bifurcation in their solution space. The solutions past the turning point are unstable and the instability signals the bridge rupture. On the other hand, the separate droplets approach each other as the applied voltage increases. However, solutions become unstable past a critical voltage at a turning point bifurcation and the droplets join. By studying the relative position of the turning points corresponding to bridge rupture and droplet joining, respectively, we define parameter regions where stable bridges or separate droplets or oscillations between them can be realized.
当施加在两个涂有介电层的水平电极板之间的电压超过阈值时，跨越两电极间间隙的液滴会遭受破裂不稳定性。有趣的是，如果仍然对电极施加电压，破裂的液桥（即一个附着液滴和一个悬垂液滴组成的一对液滴）可以自发重新连接。在这里，我们研究处于连接或破裂状态的液桥的电流体静力学，并阐明导致桥破裂或液滴连接的形状转变机制。毛细电流体静力学的控制方程构成非线性自由边界问题，通过伽辽金/有限元方法进行数值求解。一方面，我们发现毛细桥在其解空间的一个转折点分岔处变得不稳定。超过转折点的解是不稳定的，这种不稳定性预示着桥的破裂。另一方面，随着施加电压的增加，分离的液滴相互靠近。然而，在一个转折点分岔处超过临界电压后，解变得不稳定，液滴会连接在一起。通过分别研究对应于桥破裂和液滴连接的转折点的相对位置，我们定义了可以实现稳定桥、分离液滴或它们之间振荡的参数区域。
