Drop dynamics after impact on a solid wall: Theory and simulations

Abstract

We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier-Stokes equation.

Water colliding with oil

“…There are currently debates in the literature about the characteristics of the transient axisymmetric objects forming during an impact (Eggers et al 2010). Beyond their intrinsic relevance, these questions are also practical: Planchette et al (2012) found that fragmentation occurs if the aspect ratio of the cylinder is larger than π, that is, the criterion discovered by Plateau (and discussed by Delaunay and Rayleigh) for the instability of a liquid cylinder.…”

A solvable model of axisymmetric and non-axisymmetric droplet bouncing

“…Note that the constraint on incompressibility leads to an initial velocity that already has components in the transverse directions. Physically this models times after the initial crush phase of impact, which is a short but highly compressible regime, when incompressibility again becomes a good approximation 24 .…”

The dynamics of Leidenfrost drops

“…6.9b), inversely scaling with U (inset). The velocity dependency of τ th arises from the fact that, for higher impact velocities, the drop is forced more strongly onto the plate for early times [30,35,39]. Sinceh ≈…”

“…Prior to impact a high pressure region is formed between the drop and the substrate, a result of the viscosity of the escaping air [76]. This causes a deceleration of the drop and the formation of a dimple in the drop before touchdown [30,39]. Touchdown of the drop on the substrate can be prevented completely in the case of a heated substrate, because the escaping air is replenished by the evaporation of the drop [8,36,45].…”

“…Once contact has established, the wetted area starts to grow, depending on the Weber number (W e = 2ρU 2 R/γ, where R is the drop radius) [36][37][38][39]. For W e < 1 the wetting radius R w grows due to capillary action, while for W e > 1 the inertia of drops forces the spreading.…”