The Impact of a Solid on a Liquid Surface

Richardson, E. G.

doi:10.1088/0959-5309/61/4/308

Cited by 114 publications

(56 citation statements)

References 10 publications

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“…The study of impacts of solids onto the surface of a fluid bath is motivated by several applications, including the impacts of sea landing planes, the behaviour of projectiles entering water (Richardson 1948), slamming of boat hulls (Howison, Ockendon & Oliver 2002) and bio-locomotion mechanisms for water striders (Bush & Hu 2006). Interest in the detailed study of these phenomena was sparked by Worthington over a hundred years ago (see Worthington 1882Worthington , 1897.…”

Section: Introductionmentioning

confidence: 99%

Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

2017

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We present a fully predictive model for the impact of a smooth, convex and perfectly hydrophobic solid onto the free surface of an incompressible fluid bath of infinite depth in a regime where surface tension is important. During impact, we impose natural kinematic constraints along the portion of the fluid interface that is pressed by the solid. This provides a mechanism for the generation of linear surface waves and simultaneously yields the pressure applied on the impacting masses. The model compares remarkably well with data of the impact of spheres and bouncing droplet experiments, and is completely free of any of impact parametrisation.

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Section: Introductionmentioning

confidence: 99%

Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

2017

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“…The creation and collapse of an underwater cavity has been studied extensively for a solid impacting a liquid surface (Richardson 1948;Gaudet 1998;Lee et al 1997;Bergmann et al 2006;Ducleaux et al 2007;Bergmann et al 2009), as well as the formation of jets resulting from the collapse of this cavity (Longuet-Higgins 1983;Hogrefe et al 1998;Zeff et al 2000;Duchemin et al 2002;Gekle et al 2009;. The first event that is visible after an object hits a liquid is however the splash.…”

Section: Introductionmentioning

confidence: 99%

Splash wave and crown breakup after disc impact on a liquid surface

2013

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In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash -giving rise to what is known as the crown splash-if the impact Weber number exceeds a threshold value We crit ≃ 140. We explain this threshold by defining a local Bond number Bo tip based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when Bo tip 1, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-numberdependent self-similar structure for every Weber number. From this we demonstrate that Bo tip ∝ We, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for W e crit ≃ 140.Next, including the effect of air, we have developed a theory which predicts the timevarying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, F D . The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when W e > We crit .

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“…Subsequent studies by Mallock (1918) and Bell (1924) provided some qualitative explanation for the observed cavity shapes and sphere trajectories. The advent of high-speed cine-photography allowed for quantitative measurements, the first series of which explored the influence of the atmospheric pressure on the water entry of missiles (Gilbarg & Anderson 1948;Richardson 1948). Additional investigations of the water-entry cavity and surrounding flow field were performed by Birkhoff & Caywood (1949), Birkhoff & Isaacs (1951), Birkhoff & Zarantonello (1957) and Abelson (1970), but the most extensive ones were conducted by May (1951May ( , 1952May ( , 1975 with a view to naval ordinance applications.…”

Section: Introductionmentioning

confidence: 99%

Water entry of small hydrophobic spheres

2009

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We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the low Bond number limit, where cavity collapse is driven principally by surface tension rather than gravity. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description based on the solution to the Rayleigh-Besant problem is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time in the zero Bond number limit. The sphere's depth at cavity pinch-off is also computed in the low Weber number, quasi-static limit. Theoretical predictions compare favourably with our experimental observations in the low Bond number regime, and also yield new insight into the high Bond number regime considered by previous investigators. Discrepancies are rationalized in terms of the assumed form of the velocity field and neglect of the longitudinal component of curvature, which together preclude an accurate description of the cavity for depths less than the capillary length. Finally, we present a theoretical model for the evolution of the splash curtain formed at high Weber number and couple it with the underlying cavity dynamics.

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The Impact of a Solid on a Liquid Surface

Cited by 114 publications

References 10 publications

Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

Splash wave and crown breakup after disc impact on a liquid surface

Water entry of small hydrophobic spheres

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