We report on singular jets in a free-falling liquid tin droplet following nanosecond laser-pulse impact. Following impact, the droplet (with diameter $D_0=50$ or 70\,$μ$m) undergoes rapid radial expansion and subsequent retraction, resulting in the formation of an axisymmetric jet. Using numerical simulations in tandem with our experiments, we reveal that a delicate interplay between radial flow and the curvature of the retracting droplet governs jet formation. The resulting dynamics is characterized using the impact Weber number, $\We$ (in the experiments $2 \lesssim \We \lesssim 16$), and a pressure width, W (typically $1 \lesssim \W \lesssim 2$), which describes the angular distribution over the droplet surface of the instantaneous pressure impulse exerted by the transient laser-produced plasma. %, within the range $0-20$. For values $\We<10$, the droplet presents a pronounced forward curvature during the retraction, leading to the formation of a cavity. The collapse of such a cavity leads to a singular jet that greatly enhances the jetting velocity up to ten times the impact propulsion velocity, an effect that narrowly peaks around $\We\sim6-8$, reminiscent of singular jets in droplet-solid impact. We identify a further sensitivity of the jet velocity enhancement on the pressure width W and capture the dynamics in a phase diagram connecting the various deformation morphologies with jet velocity.
Liquid jet formation at the macroscale is observed across a wide range of flow conditions. Notable examples include droplet impact on a solid surface [1][2][3][4][5][6][7][8] and on a liquid bath [9][10][11][12][13], bubble bursting at a liquid interface [14][15][16][17][18][19][20], and cavity collapse resulting from the impact of a solid object on a liquid surface [9,[21][22][23]. These jetting phenomena have important industrial applications, such as inkjet printing [24,25], laser-induced forward transfer [26][27][28], and needlefree medical injection devices [29,30]. They also embody complex fluid dynamics present in nature, for instance, in raindrop impacts on leaves [31], or aerosol exchange between ocean and atmosphere during wave breaking [32,33].
The jetting dynamics observed in droplet impact on non-wetting surfaces is of particular interest in this study. At sufficiently low impact velocities, the radially converging surface waves upon impact lead to the formation of an air cavity that collapses during the droplet’s recoil phase [1,4,7,8,11,[34][35][36]. For low radial flows the droplet retracts and breaks axially, while for higher radial flows the initial spreading leads to the formation of a thin film. Within a narrow range of impact velocities, the cavity collapse and droplet recoil can lead to a fast singular jet, often with a velocity several times greater than the initial impact velocity. Similar jetting behavior is observed when solid objects fall into liquid pools [12,22]. The emergence of such jets critically depends on the convergence of surface capillary waves generated after the impact, resulting in a toroidal droplet shape, combined with the radial recoil motion, both of which enhance the jetting process [1,4,37]. On non-wetting hydrophobic or superhydrophobic surfaces, bubbles may become trapped beneath the droplet during impact. These bubbles can migrate upward and burst at the surface, also producing high-speed jets [1,4,38]. Wettability further influences the dynamics: On certain surfaces, the entrapped cavity may become pinned, resulting in asymmetric closure. This asymmetry can promote necking and pinch-off of the cavity, significantly amplifying jet velocities [1,4]. Furthermore, highly focused microjets produced within a closing cavity after droplet impact on a liquid pool can interact with the surrounding air, influencing the jet velocity due in the confined geometry [13]. Together, these phenomena illustrate a complex interplay between the radial flow within the droplet, the cavity closure mechanism, and the propagation and focusing of capillary waves, leading to jet formation.
In this work, we find singular jets arising from the interaction of a nanosecond laser pulse with a free-falling liquid tin droplet in vacuum. Here, the droplet undergoes rapid expansion due to the recoil pressure of the plasma formed on the laser-facing surface [39,40]. The relevant parameters used to characterize these dynamics include the Weber number based on the center-of-mass propulsion velocity, U cm , defined as We = ρD 0 U 2 cm /σ ; deformation Weber number based on the radial expansion rate Ṙ, defined as We d = ρD 0 Ṙ/σ following Ref. [41]; and a pressure distribution width W, modeled as a raised cosine function ∝ 1cos θ π W , with azimuthal angle θ , to represent the angular distribution of the applied surface pressure following Ref. [42]. Here, D 0 is the initial droplet diameter, ρ = 7000 kg/m 3 is the density of liquid tin, and σ = 0.544 N/m is the surface tension [43]. For low We, the droplet undergoes radial expansion followed by contraction, resembling the recoil-driven flow observed in droplet impact scenarios. Due to the angular distribution of the surface pressure, the droplet acquires an effective curvature during retraction [40,42]. This curvature can facilitate the entrapment of a cavity (containing a vacuum), which, upon collapse, produces a strong jet directed along the laser propagation axis. Additionally, based on the jet’s tip velocity, Û we define the corresponding jetting Weber number We Û = ρD 0 Û2 /σ that permits us to define breakup criteria. The absence of a substrate and a contact line offers an ideal system for droplet flow analysis, eliminating any dependence of the jetting dynamics on substrate wettability. Moreover, the drag forces that arise from interactions with the surrounding air are minimal as experiments are performed in vacuum. These conditions enable the production of singular jetting within a remarkably simplified system, where an effectively instantaneous touch of a laser fully determines the droplet dynamics. The additional control parameter (that is, besides We) in this laser-droplet interaction is the width of the spatial distribution of the recoil pressure generated by the plasma formed at the droplet surface, denoted by W [42,44].
The two governing parameters, We and W, can be tuned via the laser energy [42,44], leading to a precise control of
This content is AI-processed based on open access ArXiv data.