Insights on the impact of a plane drop on a thin liquid film

Abstract

Numerical simulations of early and intermediate instants of a plane two-dimensional drop impact on a pre-existing thin film of the same liquid are performed. The evolution of the phenomenon is analyzed by solving the free-surface Navier-Stokes equations by means of a Volume of Fluid (VOF) method. Viscous, inertial and surface tension forces are taken into account; gravity is neglected. The so-called splashing regime is emphasised, where the emergence of an initial horizontal ejecta sheet is followed by the formation of an almost vertical lamella sheet, which is the planar counterpart of the well known splashing-crown of spherical geometry. Overall velocity and pressure fields as well as detailed interface shapes are presented, and several insights on the relevant scaling laws are furnished. In the ejecta sheet (jet) regime a major result is the finding of a deviation from the standard square root behavior for the dependence on time of the contact length of sheet first emergence, which is proved to be crucial in the subsequent original application of the potential theory of Howison et al. [J. Fluid Mech., 542, 1 (2005)]. In the lamella sheet regime, the outwards expansion of its base is discussed in connection with the theory of the formation of a kinematic discontinuity within the underneath film of Yarin and Weiss [J. Fluid Mech., 283, 141 (1995)]. Analogies between planar and axysymmetric configurations are discussed

von Kármán Vortex Street within an Impacting Drop

“…It is only recently that numerical simulations managed to identify the ejecta sheet [8,14,15], because of the extreme range of scales involved and the challenges of interfacial flow simulations [16]. The intricate shapes observed herein were beyond reach in previous studies.…”

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

“…For threedimensional modeling of droplet splashing and axisymmetric modeling of droplet splashing, Josseranda and Zaleskib found that C ≈ 1.1 [47]. For two-dimensional modeling of droplet splashing, as can be seen in previous studies [17,27,49], the coefficient C will be larger than 1.1 owing to the fact that a two-dimensional planar droplet is a liquid cylinder rather than a spherical droplet in three-dimensional space. In Fig.…”

“…In addition, previous research [47][48][49] has shown that the spread radius r generally obeys the power law r/D ≈ C √ Ut/D at short times after the impact. The sketch of the definition of the spread radius can be found in Ref.…”

“…Actually, splashing can occur at widely different scales, from the astronomical scale when a comet impacts a planet to the microscopic scale in laboratory experiments [47][48][49]. The splashing of droplets on liquid or solid surfaces is a crucial event in a wide variety of phenomena in natural process and industrial applications, such as a raindrop splashing on the ground, the impact of a fuel droplet on the wall of a combustion chamber, and nanoprinting using the laser induced forward transfer technique.…”

Evolution of the ejecta sheet from the impact of a drop with a deep pool

“…The primary points of comparison for our results are the inviscid simulation of Weiss & Yarin (1999) and Davidson (2002), the experiments of Thoroddsen (2002) and the volume-of-fluid simulations of Coppola, Rocco & de Luca (2011). In our experiments the threshold for the formation of ejecta sheets is a curve in the Re-We plane, as shown in figure 3.…”