Higuera F J
E. T. S. Ingenieros Aeronáuticos, UPM Plaza Cardenal Cisneros 3, 28040 Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016314. doi: 10.1103/PhysRevE.78.016314. Epub 2008 Jul 23.
Numerical computations and order-of-magnitude estimates are used to describe the time evolution of a drop of a very viscous liquid of finite electrical conductivity attached to a metallic plate which is suddenly subject to a uniform electric field. Under the action of the electric stresses induced at its surface, the drop elongates in the direction of the field, and charged droplets are emitted when the strength of the field is higher than a certain critical value. A stationary emission mode exists in which the attached drop develops a conical tip and a thin jet, with small droplets emitted from the end of the jet in a process that involves the formation of a long ligament. The flow rate and the electric current carried by the stream of droplets emitted in this mode are determined by the flow and the transfer of charge in the attached drop, in particular in a small region around its tip and in a leading stretch of the jet, where the solution is nearly stationary despite the transient character of the jet further downstream. A simplified analysis of the stationary regions is carried out to elucidate the effects of the physical properties of the liquid (electrical conductivity, permittivity, viscosity, and surface tension), the volume of the drop, and the strength of the applied field. For high electrical conductivities and applied fields well above its critical value, the electrical and viscous stresses are large compared to surface tension stresses, and their balance gives a flow rate proportional to the square of the applied field. The electric current is then that of a stationary electrified jet fed with this flow rate.
数值计算和量级估计被用于描述附着在金属板上的具有有限电导率的高粘性液体滴的时间演化，该金属板突然受到均匀电场作用。在其表面感应出的电应力作用下，液滴沿电场方向伸长，当电场强度高于某个临界值时，带电液滴会发射出来。存在一种稳态发射模式，其中附着的液滴会形成一个锥形尖端和一条细射流，在涉及形成长韧带的过程中，小液滴从射流末端发射出来。以这种模式发射的液滴流的流速和电流由附着液滴中的流动和电荷转移决定，特别是在其尖端周围的小区域以及射流的前端部分，尽管射流下游具有瞬态特性，但在这些区域解几乎是稳态的。对稳态区域进行了简化分析，以阐明液体的物理性质（电导率、介电常数、粘度和表面张力）、液滴体积和外加电场强度的影响。对于高电导率和远高于其临界值的外加电场，电应力和粘性应力比表面张力应力大得多，它们的平衡给出了与外加电场平方成正比的流速。此时电流就是以该流速供给的稳态带电射流的电流。
