The onset of electrospray: the universal scaling laws of the first ejection.

The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field.

Global stability of the focusing effect of fluid jet flows.

The global stability of the steady jetting mode of liquid jets focused by coaxial gas streams is analyzed both theoretically and experimentally. Numerical simulations allow one to identify the physical mechanisms responsible for instability in the low viscosity and very viscous regimes of the focused liquid. The characteristic flow rates for which global instability takes place are estimated by a simple scaling analysis. These flow rates do not depend on the pressure drop (energy) applied to the system to produce the microjet. Their dependencies on the liquid viscosity are opposite for the two extremes studied: the characteristic flow rate increases (decreases) with viscosity for very low (high) viscosity liquids. Experiments confirmed the validity of these conclusions. The minimum flow rates below which the liquid meniscus becomes unstable are practically independent of the applied pressure drop for sufficiently large values of this quantity. For all the liquids analyzed, there exists an optimum value of the capillary-to-orifice distance for which the minimum flow rate attains a limiting value. That limiting value represents the lowest flow rate attainable with a given experimental configuration in the steady jetting regime. A two-dimensional stability map with a high degree of validity is plotted on the plane defined by the Reynolds and capillary numbers based on the limiting flow rate.