Abstract
Here we characterize the origin and subsequent disintegration into droplets of the type of high-speed jets formed after the sudden implosion of a locally spherical cavity. The full spatio-temporal evolution of these types of impulsively generated jets is described here making use of just the initial values of the interfacial normal velocity at the axis of symmetry and of its corresponding second derivative along the azimuthal direction, obtained straightforwardly from the solution of the Laplace equation subjected to standard boundary conditions. The predicted time evolutions of the jet tip radius and velocity, and of the radii of the ejected droplets, are shown to agree well with experimental observations.
Highlights
In this paper we have provided a theoretical description of the type of impulsive jets issued from the base of curved cavities as a consequence of the so-called flow focusing effect, which has been fully quantified and characterized by providing a set of algebraic equations expressing the jet tip velocities and the radii of the droplets ejected in terms of the material properties of the liquid, of the geometry of the device, of the radius of curvature of the interface and of the liquid velocity which is suddenly imposed upstream of the cavity
Since the predicted values agree with experimental measurements, we believe that our results could find applicability in the design of new printing or needle-free drug delivery devices using different geometries to those investigated here
Summary
Recent technological applications related with the needle-free injection of drugs (Mitragotri 2006) or printing (Brown et al 2012; Basaran, Gao & Bhat 2013; Delrot et al 2016; Jalaal et al 2019) resort to the impulsively generated and highly focused jets produced either after the sudden acceleration of a liquid column limited by a curved meniscus (Antkowiak et al 2007; Kiyama et al 2016) or by the velocities induced by the rapidly expanding vapour bubble created after the almost instantaneous vaporization of the liquid or solid volume absorbing a concentrated laser pulse (Tagawa et al (2012), Peters et al (2013), Brasz et al (2015), Delrot et al (2016), Kyriazis, Koukouvinis & Gavaises (2019), Turkoz et al (2019), Oyarte Galvez et al (2020), see figure 1a left) This type of unsteady liquid ligament, which can even reach supersonic velocities (Tagawa et al 2012), experience a strong stretching in the downstream direction until a drop, with a noticeably smaller diameter than the width of the cavity from which the jet emanates, is ejected from its tip (see figure 1b). The paper is structured as follows: in § 2 we present the theoretical results and compare the predictions with both our own experimental results and with those found in the literature and § 3 is devoted to summarize our main findings in this contribution
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