The high-speed impingement of droplets on a wall occurs widely in nature and industry. However, there is limited research available on the physical mechanism of the complicated flow phenomena during impact. In this study, a simplified multi-component compressible two-phase fluid model, coupled with the phase-transition procedure, is employed to solve the two-phase hydrodynamics system for high-speed cylindrical droplet impaction on a solid wall. The threshold conditions of the thermodynamic parameters of the fluid are established to numerically model the initiation of phase transition. The inception of cavitation inside the high-speed cylindrical droplets impacting on the solid wall can thus be captured. The morphology and dynamic characteristics of the high-speed droplet impingement process are analysed qualitatively and quantitatively, after the mathematical models and numerical procedures are carefully verified and validated. It was found that a confined curved shock wave is generated when the high-speed cylindrical droplet impacts the wall and this shock wave is reflected by the curved droplet surface. A series of rarefaction waves focus at a position at a distance of one third of the droplet diameter away from the top pole due to the curved surface reflection. This focusing zone is identified as the cavity because the local liquid state satisfies the condition for the inception of cavitation. Moreover, the subsequent evolution of the cavitation zone is demonstrated and the effects of the impact speed, ranging from $50$ to $200~\text{m}~\text{s}^{-1}$ , on the deformation of the cylindrical droplet and the further evolution of the cavitation were studied. The focusing position, where the cavitation core is located, is independent of the initial impaction speed. However, the cavity zone is enlarged and the stronger collapsing wave is induced as the impaction speed increases.

Bulk nanobubbles (NBs) have received considerable attention because of their extensive potential applications, such as in ultrasound imaging and water management. Although multiple types of experimental evidence have supported the existence and stabilization of bulk NBs, the underlying mechanism remains unclear. This study numerically investigates the bulk NB stabilization with molecular dynamics (MD) methods: the all-atom (AA) MD simulation is used for NBs of several nanometers diameter; the coarse-grained (CG) MD simulation is for the NBs of about 100 nm. The NB properties are statistically obtained and analyzed, including the inner density, inner pressure, surface charge, interfacial hydrogen bond (HB), and gaseous diffusion. The results show that the gas inside an NB has ultrahigh density (tens of kilograms per cubic meter). A double-layer surface charge exists on the NB. The inner/outer layer is positively/negatively charged, and the electrostatic stress can counteract part of the surface tension. In addition, the interfacial HB is weakened by the interaction between gas and water molecules, causing less surface tension. The above features are beneficial to NB stabilization. The NB equilibrium radii solved by the interfacial mechanical equilibrium equation agree with the MD results, indicating that this equation can describe the force balance of an NB as small as several nanometers. Besides, supersaturation appears to be necessary for the NB thermodynamic equilibrium. Based on Henry’s law and the ideal gas law, the theoretical analysis suggests that the stability of the NB thermodynamic equilibrium is conditional: the number of gas molecules in NBs should be more than half that dissolved in liquid. This study unravels a stabilized bulk NB’s properties and discusses the NB equilibrium and stabilization mechanism, which will advance the understanding and application of bulk NBs.

Abstract

The high-speed impingement of hollow droplets embedded with a cavity has fundamental applications in various scenarios, such as in spray coating and biomedical engineering. The impingement dynamics is modulated by the wrapping medium, different from that of denser solid droplets. With air and vapour cavities, the impingement of two kinds of hollow cylindrical droplets is simulated in the present study to investigate the morphology and physical mechanisms regarding droplet and cavity dynamics. The compressible two-phase Eulerian model is used to couple with the phase transition procedure. The results detail the evolution of droplets and collapsing dynamics of the two kinds of cavities. Processes are captured in which the impinging water-hammer shock wave interacts with the cavity, and vertical liquid jets are induced to impact the embedded cavity. For the case of the air cavity, a transmitted shock wave is formed and propagates inside the cavity. The air cavities are compressively deformed and broken into a series of small cavities. Subsequently, a range of intermittent collapsing compression wavelets are generated due to the interface collapse driven by local jets. As for the vapour cavity in the saturated state, initially, once it is impacted by the impinging shock wave, it gradually shrinks accompanied by local condensation but without generation of transmitted waves. Following the first interaction between the lower and upper surfaces of the cavity, the vapour cavity undergoes continuous condensation and collapse with repeated interface fusion. The vapour cavity finally turns into liquid water blended into the surroundings, and the strong collapsing shock waves are expanded inside the droplet. The radius ratios and initial impinging speeds are chosen to analyse the variation of the collapsing time, maximum collapsing pressure and mean pressure on the rigid wall. The pressure withstood by the wall due to the collapsing cavity increases with the initial size of the cavity and initial impinging speed. The maximum local pressures in the entire fluids and the mean pressure on the wall during the collapsing of the vapour cavities are higher than those for the air cavities.

Abstract