Pinching Dynamics and Satellite Droplet Formation in Symmetrical Droplet Collisions

International audienceIn head-on collisions between two droplets, reflexive separation is frequently formed, showing tentative coalescence followed by disintegration into two primary drops. With higher impact inertia relative to surface tension, characterized by a Weber number (We), more satellite droplets are created between the primary drops. In the symmetric configuration, the existing phenomenological models indicate the absence of satellite droplets at the onset We when the coalesced drops start to break. Supported by experimental and simulation evidence, here we demonstrate the exclusive formation of at least one droplet after pinch of the thread connecting the colliding drops. In accordance with the universal features of a thinning liquid filament approaching singularity as predicted by scaling theories of pinch-off, the mechanism of satellite droplet formation in the symmetrical impact of droplets is clarified. Via slight breaking of the symmetry, no satellite droplet can be observed, thus providing a possible interpretation for the discrepancy in the literature and implications for controlling undesirable drop formation. Droplet collision plays a critical role in classical fluid mechanical research not only for the fundamental significance but also for its high relevance to many natural disciplines and practical processes. Examples are seen in raindrop formation [1,2], combustion in spray engines [3,4], operation of nuclear reactors [5,6], and medical treatments such as inhalation therapy [7,8]. For mastering the mass distribution of liquid in the targeted systems, the collision dynamics of two droplets have been studied extensively in recent decades [9-15]. Regarding the symmetrical collision of droplets, reflexive separation (RS) occurs when the impact inertia is large enough to overcome the surface tension force, as indicated by the Weber number, We ¼ 2ρU 2 R=σ. Here U is the relative velocity of two droplets, R the radius, and ρ and σ, respectively, the density and surface tension of the liquid. RS features a strong internal flow with a rebounding motion, which elongates the coalesced drop and leads to a dumbbell shape followed by fragmentation. As shown in Ref. [9], collisions of near-inviscid (water) droplets at the critical We (We c) at the onset of RS led to the formation of only two drops after rupturing, with nearly identical sizes. For slightly viscous drops (hydrocarbons), as studied in Ref. [10,11], however, a satellite droplet with a much smaller size was observed along with two primary drops when the We slightly exceeded We c. Despite the discrepant results for various Ohnesorge numbers (Oh ¼ μ= ffiffiffiffiffiffiffiffi ffi ρRσ p , where μ is the fluid viscosity) of droplet collisions upon the onset of RS, phenomenological models were proposed along the same lines. That is, they all indicated the occurrence of pinch-off right at the center of the ligament connecting the primary drops, without any satellite droplet produced afterward [9,11-13]. On the other hand, satellite droplets were observed in the breakup of Newtonian liquid filaments for a wide range of Oh (0.0018-1.81) [16-18]. The formation of satellite droplets was attributed to the asymmetrical singularity of pinch-off [19-22]. To depict the dynamics of the thinning liquid filaments, scaling theories of inertial (I) [23], viscous (V) [24], and inertial-viscous (IV) [19] regimes have been developed. While inertial and capillary forces balance in the I regime, viscous and capillary forces balance in the V regime, and all three forces (inertial, viscous, and capillary) balance in the IV regime. A recent study [18] demonstrated that, for a liquid filament with slightly viscous (Oh ¼ 0.07) and highly viscous liquids (Oh > 1.0), the IV regime dominated the last stage of pinching. For nearly inviscid liquid, however, the experiments and simulations showed that the thinning liquid filament followed the I regime when it finally approached singularity [25,26]. This scenario remained valid even when Oh was up to ∼0.02 [27]. In fact, depending on the Oh and also the initial conditions, the observed dynamics can alternate between the different regimes (I, V, and IV) [18,28]. To correlate with the pinching processes and resolve the puzzle regarding the creation of satellite drops, in this Letter, the breakup of RS in a considerable range of Oh (0.0061-0.152) was experimentally studied for a We close to We c (within AE15%). Furthermore, full-field numerical simulations have been performed to understand the pinching dynamics during the head-on droplet impact. To identify the generic behaviors of RS for a wide range of Oh, drops of water, alkanes, and silicone oils with different diameters have been tested. Collisions of two identical droplets with the desired We and Oh were carried PHYSICAL REVIEW LETTERS 123, 234502 (2019) 0031-9007=19=123(23)=234502(6) 234502-