Volume entrained in the wake of a disk intruding into an oil-water interface

Abstract

An object moving through a plane interface into a fluid deforms the interface in such a way that fluid from one side of the interface is entrained into the other side, a phenomenon known as Darwin's drift. We investigate this phenomenon experimentally using a disk which is started exactly at the interface of two immiscible fluids, namely, oil and water. First, we observe that due to the density difference between the two fluids the deformation of the interface is influenced by gravity and show that there exists a time window of universal behavior. Second, we show by comparing with boundary integral simulations that, even though the deformation is universal, our results cannot be fully explained by potential flow solutions. We attribute this difference to the starting vortex, which is created in the wake of the disk. Besides contributing significantly to entrainment directly, the vortex also influences the interface deformation due to Darwin's drift. Universal behavior is preserved, however, because the size and strength of the vortex shows the same universality as the potential flow solution.

Particles, Drops, and Bubbles Moving Across Sharp Interfaces and Stratified Layers

“…Due to the large bending of the interface at the base of the tail, each of these three terms is potentially large in that region, making vorticity generation locally intense under various conditions, as numerical simulations confirm (Pierson & Magnaudet 2018b). This conclusion is also supported by experiments in which a disk was towed across an oil-water interface and the shape of the corresponding tail was compared with potential flow predictions (Peters et al 2016). Another experiment in which a bubble rose across a sharp density interface separating two liquids with negligible interfacial tension (Ar 1 1 and ζ ≈ 1) revealed that V * e decreases with Ar 1 and with the density contrast 1 − ζ , which in particular points to the direct dependency of V * e on the Froude number, i.e., on β (Díaz-Damacillo et al 2016).…”

Inertial settling of a sphere through an interface. Part 1. From sphere flotation to wake fragmentation

“…Hence, the tail dynamics generally dramatically differs from that of a cavity. An example of this may be found in a recent study where a disk initially located at an oil-water interface was pulled down with a constant velocity (Peters et al 2016): the optically determined entrained volume of oil was found to be typically twice as large as Darwin's drift volume (Darwin 1953) predicted by assuming a potential flow throughout the fluid domain. Surprisingly, few systematic studies have been devoted to the tailing configuration, starting with the investigation of Maru et al (1971).…”

Water entry of spheres into a rotating liquid

“…In addition to the experiments, we performed boundary integral (BI) simulations based on potential flow theory Peters et al 2016;Li et al 2020) to better and quantitatively understand the experimental observations. Considering the rotating flow background, we defined a cylindrical coordinate system Orθz, which was fixed to the rotating cylindrical tank.…”

“…The dimensional parameters considered in prior studies are usually the density (or pressure) of the air above the water surface, the impact velocity, the projectile's shape and temperature, and the liquid properties (Enriquez et al 2012;Truscott et al 2014;Mathai, Govardhan & Arakeri 2015;Peters et al 2016;Mansoor et al 2017;Aly & Asai 2018;Zhang et al 2018). Within this parameter space, a variety of splash and cavity types are possible, viz.…”

“…2014; Mathai, Govardhan & Arakeri 2015; Peters et al. 2016; Mansoor et al. 2017; Aly & Asai 2018; Zhang et al.…”