Dynamics and rupture of planar electrified liquid sheets

Abstract

We investigate the stability of a thin two-dimensional liquid film when a uniform electric field is applied in a direction parallel to the initially flat bounding fluid interfaces. We consider the distinct physical effects of surface tension and electrically induced forces for an inviscid, incompressible nonconducting fluid. The film is assumed to be thin enough and the surface forces large enough that gravity can be ignored to leading order. Our aim is to analyze the nonlinear stability of the flow. We achieve this by deriving a set of nonlinear evolution equations for the local film thickness and local horizontal velocity. The equations are valid for waves which are long compared to the average film thickness and for symmetrical interfacial perturbations. The electric field effects enter nonlocally and the resulting system contains a combination of terms which are reminiscent of the Kortweg–de-Vries and the Benjamin–Ono equations. Periodic traveling waves are calculated and their behavior studied as the electric field increases. Classes of multimodal solutions of arbitrarily small period are constructed numerically and it is shown that these are unstable to long wave modulational instabilities. The instabilities are found to lead to film rupture. We present extensive simulations that show that the presence of the electric field causes a nonlinear stabilization of the flow in that it delays singularity (rupture) formation.

Newtonian pizza: spinning a viscous sheet

“…Among other problems where similarity solutions of the second kind are encountered for similar reasons, we mention: the spreading groundwater mound of liquid in a porous medium (Wagner 2005); the spreading of insoluble surfactant at the free surface of a deep fluid layer (Jensen 1995); dynamics and rupture of planar electrified liquid sheets (Tilley, Petropoulos & Papageorgiou 2001); the flow in a cylindrical container with a rotating end wall (Muite 2004); the problem of rotary honing (a two-dimensional variant of the Taylor paint-scraper problem) where a similarity solution of the second kind is contained within a similarity solution of the first kind (Hills & Moffatt 2000).…”

Local bifurcation of electrohydrodynamic waves on a conducting fluid

“…The tangential electric field, as opposed to the a) z.wang5@bath.ac.uk normal electric field, has a stabilizing effect on the interface since it provides a dispersive contribution to the linear system. 5,22,27 It can delay the formation of the film rupture 27 and even suppress the Rayleigh-Taylor instability. 5 In the present work, we concentrate on the electrohydrodynamic behavior of a liquid metal in the presence of a strong normal electric field.…”

Влияние Продольного Электрического Поля На Капиллярную Неустойчивость Тонкого Осесимметричного Слоя Жидкого Диэлектрика, Покрывающего Диэлектрическую Нить

“…В электрогидродинамике используется также прибли-жение однородного по температуре и другим физиче-ским характеристикам идеального несжимаемого жид-кого диэлектрика, не содержащего свободных электри-ческих зарядов (см., например, [10,11,[15][16][17]). Осно- вы соответствующей теории были заложены в кон-це XIX в.…”