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.

We aim to establish the scaling laws for both the minimum rate of flow attainable in the steady cone-jet mode of electrospray, and the size of the resulting droplets in that limit. Use is made of a small body of literature on Taylor cone-jets reporting precise measurements of the transported electric current and droplet size as a function of the liquid properties and flow rate. The projection of the data onto an appropriate non-dimensional parameter space maps a region bounded by the minimum rate of flow attainable in the steady state. To explain these experimental results, we propose a theoretical model based on the generalized concept of physical symmetry, stemming from the system time invariance (steadiness). A group of symmetries rising at the coneto-jet geometrical transition determines the scaling for the minimum flow rate and related variables. If the flow rate is decreased below that minimum value, those symmetries break down, which leads to dripping. We find that the system exhibits two instability mechanisms depending on the nature of the forces arising against the flow: one dominated by viscosity and the other by the liquid polarity. In the former case, full charge relaxation is guaranteed down to the minimum flow rate, while in the latter the instability condition becomes equivalent to 3

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.

We study both numerically and experimentally the steady cone-jet mode of electrospraying close to the stability limit of minimum flow rate. The leaky dielectric model is solved for arbitrary values of the relative permittivity and the electrohydrodynamic Reynolds number. The linear stability analysis of the base flows is conducted by calculating their global eigenmodes. The minimum flow rate is determined as that for which the growth factor of the dominant mode becomes positive. We find a good agreement between this theoretical prediction and experimental values. The analysis of the spatial structure of the dominant perturbation may suggest that instability originates in the cone-jet transition region, which shows the local character of the cone-jet mode. The electric relaxation time is considerably smaller than the residence time of a fluid particle in the cone-jet transition region (defined as the region where the surface and bulk intensities are of the same order of magnitude) except for the high-polarity case, where these characteristic times are commensurate with each other. The superficial charge is not relaxed within the cone-jet transition region except for the high-viscosity case, because significant inner electric fields arise in the cone-jet transition region. However, those electric fields are not large enough to invalidate the scaling laws that do not take them into account. Viscosity and polarization forces compete against the driving electric shear stress in the cone-jet transition region for small Reynolds numbers and large relative permittivities, respectively. Capillary forces may also play a significant role in the minimum flow rate stability limit. The experiments show the noticeable stabilizing effect of the feeding capillary for diameters even two orders of magnitude larger than that of the jet. Stable jets with electrification levels higher than the Rayleigh limit are produced. During the jet break-up, two consecutive liquid blobs may coalesce and form a bigger emitted droplet, probably due to the jet acceleration. The size of droplets exceeds Rayleigh’s prediction owing to the stabilizing effect of both the axial electric field and viscosity.

A new technique is proposed in this paper to produce jets, droplets, and emulsions with sizes ranging from tens of microns down to the submicrometer scale. Liquid is injected at a constant flow rate through a hypodermic needle to form a film over the needle's outer surface. This film flows toward the needle tip until a liquid ligament is steadily ejected. Both the film motion and the liquid ejection are driven by the viscous and pressure forces exerted by a coflowing fluid stream. If this stream is a high-speed gas current, the outcome is a capillary jet which breaks up into droplets due to the Rayleigh instability. Micrometer emulsions are also produced by this instability mechanism when the injected liquid is focused by a viscous liquid stream. The minimum flow rates reached with the proposed technique are two orders of magnitude lower than those of the standard flow focusing configuration. This sharp reduction of the minimum flow rate allows one to form steady jets with radii down to the submicrometer scale. The stability of this new configuration is analyzed experimentally for both gas-liquid and liquid-liquid systems. In most of the cases, the loss of stability must be attributed to the liquid source because the critical Weber (capillary) number for the gas-liquid (liquid-liquid) case was significantly greater than the value corresponding to the convective/absolute instability transition in the jet.