It is well known that the water entry of a sphere causes cavity formation above a critical impact velocity as a function of the solid–liquid contact angle; Duez et al. (Nat. Phys., vol. 3 (3), 2007, pp. 180–183). Using a rough sphere with a contact angle of $120^{\circ }$ , Aristoff & Bush (J. Fluid Mech., vol. 619, 2009, pp. 45–78) showed that there are four different cavity shapes dependent on the Bond and Weber numbers (i.e., quasistatic, shallow, deep and surface). We experimentally alter the Bond number, Weber number and contact angle of smooth spheres and find two key additions to the literature: (1) cavity shape also depends on the contact angle; (2) the absence of a splash crown at low Weber number results in cavity formation below the predicted critical velocity. In addition, we use alternate scales in defining the Bond, Weber and Froude numbers to predict the cavity shapes and scale pinch-off times for various impacting bodies (e.g., spheres, multidroplet streams and jets) on the same plots, merging the often separated studies of solid–liquid and liquid–liquid impact in the literature.
We present new observations from an experimental investigation of the classical problem of the crown splash and sealing phenomena observed during the impact of spheres onto quiescent liquid pools. In the experiments, a 6 m tall vacuum chamber was used to provide the required ambient conditions from atmospheric pressure down to 1/16th of an atmosphere, whilst high-speed videography was exploited to focus primarily on the above-surface crown formation and ensuing dynamics, paying particular attention to the moments just prior to the surface seal. In doing so, we have observed a buckling-type azimuthal instability of the crown. This instability is characterised by vertical striations along the crown, between which thin films form that are more susceptible to the air flow and thus are drawn into the closing cavity, where they atomize to form a fine spray within the cavity. To elucidate to the primary mechanisms and forces at play, we varied the sphere diameter, liquid properties and ambient pressure. Furthermore, a comparison between the entry of room-temperature spheres, where the contact line pins around the equator, and Leidenfrost spheres (i.e. an immersed superheated sphere encompassed by a vapour layer), where there is no contact line, indicates that the buckling instability appears in all crown sealing events, but is intensified by the presence of a pinned contact line.
Water entry has been studied for over a century, but few studies have focused on multiple droplets impacting on a liquid bath sequentially. We connect multi-droplet streams, jets and solid objects with physical-based scaling arguments that emphasize the intrinsically similar cavities. In particular, the cavities created by the initial impact of both droplet streams and jets on an initially quiescent liquid pool exhibit the same types of cavity seal as hydrophobic spheres at low Bond number, some of which were previously unseen for jets and droplet streams. Low-frequency droplet streams exhibit an additional three new cavity seal types unseen for jets or solid spheres that can be predicted with a new non-dimensional frequency. The cavity depth and cavity velocity for both droplet and jet impact are rationalized by an energy scaling analysis and the Bernoulli equation.
We investigate the impact and penetration of a solid sphere passing through gelatine at various impact speeds up to 143.2 m s −1 . Tests were performed with several concentrations of gelatine. Impacts for low elastic Froude number Fr e , a ratio between inertia and gelatine elasticity, resulted in rebound. Higher Fr e values resulted in penetration, forming cavities with prominent surface textures. The overall shape of the cavities resembles those observed in water-entry experiments, yet they appear in a different order with respect to increasing inertia: rebound, quasi-seal, deep-seal, shallow-seal and surface-seal. Remarkably, similar to the We-Bo phase diagram in water-entry experiments, the elastic Froude number Fr e and elastic Grashof number Gr e (a ratio between gravity and gelatine elasticity) classify all five different phenomena into distinguishable regimes. We find that Fr e can be a good indicator to describe the cavity length H, particularly in the shallow-seal regime. Finally, the evolution of cavity shape, pinch-off depth, and lower cavity radius are investigated for different Fr e values.
The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise largely from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on a rigid sphere by placing the sphere inside a jet of water so that the jet strikes the quiescent water surface prior to entry of the sphere into the pool. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high-speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.
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