Revision of capillary cone-jet physics: Electrospray and flow focusing

Abstract

Capillary cone jets are natural microfluidic structures arising in steady capillary tip streaming, whose paradigms are electrospray and flow focusing phenomena. In this work, we make a profound revision of the basic underlying physics of generic cone jets from thousands of experimental measurements, most of them reported in the literature. First, the boundaries of the stability region of steady jetting are calculated. We describe these limitations by instability mechanisms associated with the local flow structure in the tip and the issuing jet and with the global behavior of the meniscus. Second, to undertake a general physical treatment of cone jets in steady regime, we analyze the energy balance taking place in the tips of both flow focusing and electrospray. This analysis yields a fundamental result: if the electrospray data are expressed in terms of an effective pressure drop, both phenomena satisfy the same scaling law for the droplet size, which exhibits nearly complete similarity in the parameter window where quasimonodisperse sprays are produced. That effective pressure drop is a function of the liquid properties exclusively, i.e., it does not depend on the operational parameters (flow rate and applied voltage). Moreover, the stability limits of the operational regimes are analyzed in detail, finding fundamental coincidences between flow focusing and electrospray as well. These results provide most useful general description and predictive scaling laws for nearly monodisperse microspraying or nanospraying based on steady cone jets, of immediate applicability in analytical chemistry, chemical engineering, biochemistry, pharmaceutical and food technologies, painting, and many other technological fields.