The photographs show instantaneous realizations of electrostatic disruption of room-temperature parafin oil, a liquid that is used to finish furniture among other applications. The oil emerges at 5 milliliters (mL) per second through a smooth 1-mm-diameter circular orifice (not shown) after having been injected with negative charge, giving the oil a charge density of 0.15 Coulombs per cubic meter.
The liquid is charged by a submerged electrode, which is positioned immediately upstream of the grounded orifice through which the fluid issues. In absence of charge injection the liquid would exit as a glassy smooth cylindrical stream. The elegant filamentary structure and subsequent droplet development is purely electrostatic. No mechanical or aerodynamic forces are involved.
Droplet development starts with collapse of the cylindrical charged column into the thick-rimmed, ribbon-like structure seen at the top of the images. The charged cylindrical column of fluid is unstable to small disturbances in the circular cross-section of the column. Upon small distortion, the charge, and therefore the fluid that carries it, tends to rapidly migrate to the extremities pulling the column into a thin sheet. The concentration of charged fluid at the extremities accounts for the thick rim of the ribbon. The rim, in turn, is unstable to longitudinal waves. Again the charge rushes to the extremities, this time the crests of the waves, stretching them into rapidly growing, periodically occurring thin filaments.
As the charged fluid moves towards their tips, the filaments are typically capped by growing fluid lumps. These subsequently break off in the form of mutually repelling and rapidly dispersing droplets. As seen towards the bottom of the images, occasionally the filaments themselves break off form the maternal ribbon and subsequently break up into droplets on either end, by means of the same basic mechanism.
Description of the large-scale electrohydrodynamic motion has yet to be attempted. However the resulting droplet spray is quantitatively described by statistical thermodynamics; the system is well mixed and in its most probable state, namely that of maximum entropy (disorder). The description reveals the existence of an abrupt change in properties known as a first-order phase transition.
First-order phase transitions occur, for example, when water freezes to ice. To bring about this phase transition in water, you simply adjust its "temperature", specifically by cooling it to below its freezing point. The phase transition predicted in the droplets is a little different. This abrupt change in properties occurs for charged droplets below a certain "size"--about a micron (millionth of a meter). Mean charge on droplets larger than a micron is simply the ratio of mean droplet size to the first Bohr radius, the distance of a electron from the nucleus of a hydrogen atom. One interpretation of this independence of droplet size on fluid properties is that spray behavior is determined by the physics of the two-dimensional surface charge; the transition being the point at which the surface charge freezes into a crystal of electrons, analogous to an ice crystal of water molecules. The droplets in the image are most probably coated with electron ice crystals.
The electrostatically atomized working fluid is EXXON Marcol 87 with viscosity ~ 35 cp, surface tension = 0.031 N/m, density = 850 kg/m3, and electrical conductivity ~ 0.1 cu.
Reported by: Dimitris E. Nikitopoulos, Louisiana State University, and Arnold J. Kelly, CIC Inc., 52nd Annual APS Division of Fluid Dynamics Meeting, November 21-23, 1999, New Orleans