Trapping of air in impact between a body and shallow water

Abstract

Near-impact behaviour is investigated for a solid body approaching another solid body with two immiscible incompressible viscous fluids occupying the gap in between. The fluids have viscosity and density ratios which are extreme, the most notable combination being water and air, such that either or both of the bodies are covered by a thin film of water. Air–water interaction and the commonly observed phenomenon of air trapping are of concern in the presence of the two or three thin layers and one or two interfaces. The subcritical regime is of most practical significance here and it leads physically to the effect of inviscid water dynamics coupling with a viscous-dominated air response locally. This physical mechanism induces touchdown (or an approach to touchdown), which is found to occur in the sense that the scaled air-gap thickness shrinks towards zero within a finite scaled time according to analysis performed hand in hand with computation. A global influence on the local touchdown properties is also identified. Comparisons with computations prove favourable. Air trapping is produced between two touchdown positions, at each of which there is a pressure peak; an oblique approach would not affect the finding unless the approach itself is extremely shallow. The mechanism of air–water interaction leading to air trapping is suggested as a quite wide-ranging result.

Air cushioning in droplet impacts with liquid layers and other droplets

“…A similar relationship between the free-surface height and the pressure holds for the air cushioning of solid bodies coated by shallow liquid layers. 35 The leading order behavior for small h is shown in Figure 5(a) and is identical to the case of droplet impact with a solid wall. This figure shows the maximum deformation of the droplet free-surface and the largest pressures at each integer time-step of the five layer depths considered.…”

Two mechanisms of droplet splashing on a solid substrate

“…In particular, it has been explained that dimple formation leading to the bubble entrapment was due as a first approximation to the viscous cushioning of the gas beneath the drop (Smith et al 2003;Purvis & Smith 2004;Korobkin et al 2008;Mandre et al 2009;Mani et al 2010;Duchemin & Josserand 2011). The lubrication pressure in the gas deforms the drop before contact, forming a dimple, so that contact occurs along a circle entrapping a gas bubble, as observed experimentally (Thoroddsen et al 2005;Driscoll & Nagel 2011;Bouwhuis et al 2012;Kolinski et al 2012;Tran et al 2013).…”

“…Since then, numerous studies have investigated the mechanism by which gas pressure influences the splash dynamics. These studies have involved and combined theoretical, experimental and numerical approaches (Korobkin et al 2008;Mandre et al 2009;Mani et al 2010;Hicks & Purvis 2010;Duchemin & Josserand 2011;Driscoll & Nagel 2011;Kolinski et al 2012;Duchemin & Josserand 2012;Hicks et al 2012;Riboux & Gordillo 2014;Kim et al 2014;Liu et al 2015;Guo et al 2016). It has been demonstrated that splashing was closely linked with the dynamics of the thin film of gas, either beneath the drop before impact but also during the fast spreading of the drop after impact.…”

“…Indeed, by varying only the gas density and viscosity, we seek to isolate the gas inertia correction to the cushioning since neither compressibility nor non-continuum effects are taken into account by our numerics. The key point of our approach lies in solving the full Navier-Stokes equations and not a reduced model involving the lubrication approximation for the gas cushioning and the inviscid dynamics for the liquid, as done by most of the numerical and analytical studies of this problem until now (Smith et al 2003;Purvis & Smith 2004;Korobkin et al 2008;Mandre et al 2009;Duchemin & Josserand 2011;Hicks et al 2012), which consist of completely neglecting the gas inertia. Solving the full incompressible Navier-Stokes equations for both the gas and the liquid phase remains nowadays a real challenge in the context of drop impact in order to capture the dimple and the bubble entrapment correctly (Guo et al 2016;) which explains why reduced models have been mostly used until now.…”

Probing the nanoscale: the first contact of an impacting drop

“…The theoretical treatment of the air-cushioning, started by Smith et al (2003), is based on balancing the viscous lubrication in the thin air layer and the rapid deceleration of the drop inertia. Korobkin et al (2008) added two deformable surfaces and Hicks & Purvis (2010) reformulated the above 2-D theories for the axisymmetric case, to allow quantitative comparison with theory. They predicted the initial radius of the air-disc L o at first contact, as (Hicks et al (2012), Hicks & Purvis (2013))…”