Crater evolution after the impact of a drop onto a semi-infinite liquid target

Abstract

This paper is devoted to an experimental and theoretical investigation of the crater formed by the impact of a single drop onto a semi-infinite target of the same liquid. The shape of the crater at various time instances after impact has been observed using a high-speed video system and then accurately characterized. A theoretical model for the crater expansion has been developed, which is able to predict the temporal variation of the crater depth for sufficiently high Weber, Froude, and Reynolds numbers. The flow around the crater is approximated by an irrotational velocity field past a moving and expanding sphere. The equations describing the propagation of the surface of the crater have been obtained from the balance of stresses at the crater interface, accounting for inertia, gravity, and surface tension. The temporal evolution of the crater depth has been calculated by numerical solution of the equations of motion. The agreement between the theoretical predictions and experimental data are rather good.

Liquid jet eruption from hollow relaxation

“…In particular, most of these works have considered steady cavity profiles to be decently fitted with a parabola. Conversely, unsteady liquid cratering dynamics have been investigated mainly in the case of point source, obtained for example by means of drop impact (Bisighini et al 2010). In this type of experiment, the cavity shape is very close to an hemisphere and the dynamics of expansion-retraction is well described by Rayleigh-Plesset equation.…”

“…This phenomenon has been extensively studied, from the initial stages of contact (Korobkin & Pukhnachov 1988), through the dynamics of transient cavities produced thereof (see e.g. Bisighini et al 2010 for drop impact or Birkhoff & Zarantonello 1957;Duclaux et al 2007 for solid body impact) up to jet formation (Hogrefe et al 1998;Gekle et al 2009). Such a jet is a classic signature of hollow crater-like relaxation, and appears at scales ranging from champagne bubbles (Liger-Belair et al 2009) to geological craters central peak (Melosh 1989).…”

The Effect of Film Temperature on crater morphology during the impact of a single droplet

“…Film temperature is shown to have little effect in the initial stages of the droplet impact. In this region, more commonly called the "inertial self-similar" region, the impact is dominated by momentum exchange [4], and the track of the crater evolution follows a similar pattern for all impact velocities and film temperatures. In the second region, the crater becomes deeper and wider as the temperature increase.…”

“…Each droplet size and velocity was individually measured to eliminate errors from movement of the camera or film between tests. The dimensions as well as time (t) were non-dimensionalised for comparison with the work from [8] and [4]using the following relationships.…”

“…This study is therefore relevant to industry by developing an understanding to how temperature may affect the outcome of droplet impact onto liquid films. There are several reviews of the droplet impact outcomes, such as [3] , and there are a number of theories about the crater evolution [4] for droplets of same temperature and liquid impacting on a film [5]. However there are few studies on droplets of different temperature to the film [6,7].…”