applied sciences  
The Splashing of Melt upon the Impact of Water Droplets and Jets  
[PERSON]*(c), [PERSON], [PERSON] and [PERSON]  
Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia; [EMAIL_ADDRESS] (Y.D.C. ); [EMAIL_ADDRESS] (A.Y.I. ); [EMAIL_ADDRESS] (V.A.U.) * Correspondence: [EMAIL_ADDRESS]; Tel. : +7. (495)-434-95-25  
S.E. ; Y.; I.  
arises with regard to the mechanisms governing the melt-water premixing in this seemingly stable, stratified, flow with the heavy melt layer located under an of order-of-magnitude less dense water. A hypothesis on the possible mechanisms for the premixing was proposed in [5] on the basis of experimental observations of melt spreading prior to a steam explosion. It was observed that hot melt did not spread as a smooth layer, rather, quite intensive sporadic melt splashes were observed, which formed a dynamically existing premixing layer above the average melt surface. An idea suggested in [5] was that the melt splashes could be caused by the impact of cumulative water jets generated by the collapse of vapor bubbles in subcooled water, which were observed intermittently near the melt-water interface. While independent confirmation of the feasibility and efficiency of this mechanism is still a matter of ongoing study (e.g., theoretical estimates of the water energy and impulse that develop upon the collapse of a hot vapor bubble in subcooled water were performed in [6]), the problem of the impact of water on the melt surface is interesting in itself, both from a fundamental and an applied point of view. Droplet impact on a liquid surface is a classical research topic [7; 8; 9] that can be approached from the perspective of fluid dynamics, thermodynamics, and surface physics because it provides an example of a simple, yet phenomena-rich interaction. It is known that the collision of a drop with a liquid surface can involve different regimes, including floating, bouncing, coalescence or splashing [9]. A characteristic feature of the splashing regime, where the surface of the pool liquid is significantly disturbed, is the formation of a deep crater with a crown-like cylindrical liquid film ejected from its rim (e.g., [10]). Also, in this regime, the so-called Rayleigh [11] or Worthington [7; 8] central jet, or a liquid column rising above the center of the crater is formed after impact (also called a cumulative jet in Russian literature). The boundaries between different regimes have been researched by many authors in terms of the primary non-dimensional parameters, the Weber number, We \(=\rho u^{2}D/\sigma\), and the Froude number \(\mathrm{Fr}=u^{2}/gD\), where \(\rho\) and \(\sigma\) are the density and surface tension of the liquid droplet, \(D\) is the droplet diameter, and \(u\) is the impact velocity. A large amount of experimental data indicate that droplet bouncing and coalescence occur for low Weber and Froude numbers, whereas splashing occurs at high values, see review in [12]. The total coalescence, rebound and fast partial bounce regimes of free-falling droplet interaction with the receiving liquid were studied experimentally in [13]. For high impact velocities, numerous fine droplets (spray) are formed including multiple splashes [14]. Experiments have also shown that sometimes a large bubble becomes entrapped when the crown closes at the top [10; 12]. In addition to finding the regime boundaries, experimental studies and numerical simulations have revealed the fine details of the droplet-pool interaction in different regimes. Cavity development in a shallow liquid pool upon droplet impact was studied numerically by the VOF method in [15] in conditions where the cavity depth was comparable to the thickness of the liquid layer. For example, in the work of [16; 17], the material distribution on the cavity surface and in the crown was studied by using contrasting droplet (ink-colored) and pool (transparent) liquids.