Controlled cavity collapse: scaling laws of drop formation

Abstract

The formation of transient cavities at liquid interfaces occurs in an immense variety of natural processes, among which the bursting of surface bubbles and the impact of a drop on a liquid pool are salient. The collapse of a surface liquid cavity is a well documented natural process that leads to the ejection of a thin and fast jet. Droplets generated through this process can be one order of magnitude smaller than the cavity's aperture, and they are consequently of interest in drop on demand inkjet applications. In this work, the controlled formation and collapse of a liquid cavity is analyzed, and the conditions for minimizing the resulting size and number of ejected drops are determined. The experimental and numerical models are simple and consist of a liquid reservoir, a nozzle plate with the discharge orifice, and a moving piston actuated by single half-sine-shaped pull-mode pulses. The size of the jetted droplet is described by a physical model resulting in a scaling law that is numerically and experimentally validated.

Jetting in finite-amplitude, free, capillary-gravity waves

“…The aforementioned insights obtained through a first principles IVP approach are novel and complement prior seminal studies investigating the problem from a wave-focussing, singularity formation, self-similarity and scaling perspective, cf. MacIntyre (1972), Zeff et al (2000), Duchemin et al (2002), Gordillo (2008), Gañán-Calvo (2017), Gordillo & Rodríguez-Rodríguez (2018), Lai et al (2018), Ismail et al (2018) and Blanco-Rodríguez & Gordillo (2020).…”

“…Predicting the rate and size of droplets from these jets have important applications, e.g. see Blanco-Rodríguez & Gordillo (2020) and the important recent study by Ismail et al (2018) which has elucidated, via experiments and simulations, the criterion for minimising the size and number of ejected droplets from jetting obtained from cavity collapse, in addition to providing scaling laws for the size of drops.…”

On the jets produced by drops impacting a deep liquid pool and by bursting bubbles

“…Recently, it has been also pointed out that the drops emitted from the tip of the jets ejected by the collapse of bubbles might be used in technological applications related with the design of novel printing devices (Castrejón-Pita, Castrejón-Pita & Martin 2012; Basaran, Gao & Bhat 2013; Ismail et al. 2018).

Figure 1.Sequence of images showing the impact of a water drop of radius falling on a deep liquid pool with a velocity such that , , with , and being the gravitational acceleration, the density and the interfacial tension coefficient, respectively, at different instants of time , with the instant the drop touches the surface: ( a ) ( b ) , ( c ) , ( d ) , ( e ) .

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“…It will become clear in what follows that the liquid jets produced in this way originate in a similar manner to those emitted after the bursting of a bubble, a process that has received much attention in the recent literature (Duchemin et al 2002;Ghabache et al 2014;Gañán Calvo 2017;Brasz et al 2018;Deike et al 2018;Gordillo & Rodríguez-Rodríguez 2018;Lai, Eggers & Deike 2018;Gordillo & Rodríguez-Rodríguez 2019;Berny et al 2020) because it plays a key role in the production of the sea spray aerosol (MacIntyre 1972;Bigg & Leck 2008;Veron 2015;Wang et al 2017;Blanco-Rodríguez & Gordillo 2020) and in the dispersion of contaminants and bacteria (Walls, Bird & Bourouiba 2014). Recently, it has been also pointed out that the drops emitted from the tip of the jets ejected by the collapse of bubbles might be used in technological applications related with the design of novel printing devices (Castrejón-Pita, Castrejón-Pita & Martin 2012;Basaran, Gao & Bhat 2013;Ismail et al 2018). Indeed, the high-speed jets formed after the bursting of bubbles (MacIntyre 1972;Duchemin et al 2002;Ghabache et al 2014) or after a drop impacts a free surface (Prosperetti, Crum & Pumphrey 1989;Prosperetti & Oguz 1993;Rein 1996;Ray, Biswas & Sharma 2015;Michon et al 2017;Thoroddsen et al 2018;Yang, Tian & Thoroddsen 2020) share a common feature since they both emerge as a consequence of the axial convergence of the capillary waves that propagate along the collapsing cavity walls.…”

Self-similar jet evolution after drop impact on a liquid surface

“…From the moment of droplet impact, the outburst with rise and fall of a jet takes typically less than 100 ms. Numerous studies on this phenomenon have been carried out [3][4][5][6][7][8][9][10][11][12][13][14], focusing mainly on different fluid responses when a small solid object or a droplet hits the water surface; these include cavity formation, crown splash, central jet rise, and jet tip droplet pinch-off [15][16][17]. Several theories and fluid simulations [7,13,18] have been developed to relate jet shape to fluid from the bath feeding the jet, however the role of surface tension has remained unclear; only drop formation at the tip has been related to surface tension forces [8,13,14,18,19].…”