ALBERT

Beschreibung: When a liquid meniscus held at the exit of a metallic capillary tube is charged to a high voltage V, the free surface often takes the form of a cone whose apex emits a steady microjet, and thus injects a certain charge I and liquid volume Q per unit time into the surrounding gas. This work deals with liquids with relatively large conductivities K, for which the jet diameter dj is much smaller than the diameter dn of the capillary tube. In the limit dj/dn → 0, the structure of the jet (dj and I, in particular) becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the measured current is given approximately by I = f(ε) (γQK/ε)½ for a wide variety of liquids and conditions (ε, and γ are, respectively, the dielectric constant of the liquid and the coefficient of interfacial tension; f(ε) is shown in figure 11). The following explanation is proposed for this behaviour. Convection associated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distribution slightly at distances r from the apex large compared to a certain charge relaxation length λ, but substantially when r ∼ λ. When the fluid motion is modelled as a sink flow, λ is of the order of r* = (Qεε0/K)[formula omitted] (ε0 is the electrical permittivity of vacuum). If, in addition, the surface charge density is described through Taylor's theory, the corresponding surface current convected towards the apex scales as Is ∼ (γQK/ε)½, as observed for the spray current. The sink flow hypothesis is shown to be realistic for sufficiently small jet Reynolds numbers. In a few photographs of ethylene glycol cone jets, we find the rough scaling dj ∼ 0.4r* for the jet diameter, which shows that the jet forms as soon as charge relaxation effects set in. In the limit ε ≫ 1, an upper bound is found for the convected current at the virtual cone apex, which accounts for only one-quarter of the total measured spray current. The rest of the charge must accordingly reach the head of the jet by conduction through the bulk. © 1994, Cambridge University Press. All rights reserved.

Beschreibung: An investigation is carried out on the effects of Brownian agitation in the motion of small particles in a carrier gas in situations far from equilibrium. Although the standard near-equilibrium closure of the hydrodynamic equations is not valid for the heavy particles, the smallness of their speed of thermal agitation allows an alternative systematic hypersonic closure. The hypersonic equations are solved for two known instances where the kinetic Fokker—Planck equation describing the nonequilibrium particle distribution function admits exact solutions. These problems are characterized by a null or a spatially constant value for the gradient of the velocity field in the carrier gas, both being free from boundary surfaces. In the first case, where the background velocity is uniform, a fundamental solution (expressed as an integral) is obtained for the steady flow of particles from a point source; this result has obvious applications for the description of the Brownian broadening of particle streamlines. An asymptotic integration of the fundamental solution yields analytical expressions for the particle hydrodynamic properties valid everywhere except near the source, where a direct integration of the Vlasov equation completes the description. The exact solution for the second example, where the background velocity field gradient is uniform, is taken from the literature. Once these reference solutions have been established, the hypersonic equations are attacked by a variety of methods. In particular, for the uniform steady flow, a boundary-layer analysis yields analytical results identical to those obtained from the asymptotic evaluation of the kinetic fundamental solution. In both problems, the agreement found between kinetic and hydrodynamic solutions is excellent even for values of order one of the inverse particle Mach number, the expansion parameter of the hypersonic theory. © 1990, Cambridge University Press. All rights reserved.