Abstract :
The present work deals with the cone-jet mode of electrospray atomization of liquids at sufficiently low flow rates. In this case, the meniscus shape almost coincides with Taylor’s cone and the emitted jet is extremely thin. Its diameter is many orders of magnitude smaller than meniscus dimensions, while the jet length is usually comparable with them. These features of the meniscus and jet allow their theoretical description to be derived directly from the basic equations of fluid dynamics and electrodynamics. To do that we use asymptotic expansions in the small parameter which is proportional to the Weber number of the meniscus-jet. the basic equations also take into account nonequilibrium relaxation of the ion distribution in the surface charge layer and the influence of surface ions on surface tension (electrocapillary effect) at the meniscus-jet surface.
In this work asymptotic systems of differential equations have been obtained by perturbation methods in the regions of the meniscus, jet, and surrounding gas. The solutions to these equations have been found, matched with each other, and applied to the investigation of the cone-jet mode of electrospray atomization. Using the developed asymptotic approach we have been able:
1. to find distributions of electrodynamic and hydrodynamic variables in all regions (the meniscus, jet, and surrounding gas);
2. to study the sturcture of electrohydrodynamic flow inside the meniscus and jet;
3. to determine and analyze the shape of the perturbed meniscus and jet;
4. to obtain the electric charge and normal electric field strength at the surface of the meniscus and jet.
These characteristics are of vital importance for the gas-phase ion production by means of the field evaporation. It also follows from the developed theory that the non-dimensional current f=I(γKQ/ )-1/2 carried by the jet depends only on the dielectric constant epsilon as where γ and K are the surface tension coefficient and electrical conductivity of the liquid, I and Q are the electric current and volume flow rate of the liquid. This dependence is consistent with the scaling law found experimentally by Fernandez de la Mora and Loscertales (1994) J. Fluid Mech. 260, 155–184.
