Events Before Droplet Splashing on a Solid Surface

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Madhav Mani, hreyas Mandre and Michael Brenner J. Fluid Mechanics, vol. 647, pp 163-185


droplet dynamics deformation surface tension


This paper articulates in detail simulations of an idea from a previous paper regarding splashing dynamics: Precursors to droplet splashing on a solid surface. It has been observed that a drop falling on a surface ejects a thin liquid sheet into the air as it splashes, but the dynamics of this phenomenon are problematic. Previously, it was thought that a drop hitting a surface faster than some critical velocity would contact the surface at a single point and this singularity caused sheet ejection. One theory was that the contact line velocity is much larger than the speed of sound in the liquid, so the pressure disturbance form impact is pinned to the contact line and the movement of the pressure wave through the drop causes sheet formation. However, this might produce a sheet along the solid surface, which is not what is observed. Another recent experiment demonstrated that the splashing criteria depend on ambient gas pressure, as well as impact parameters (velocity and droplet radius).

Snapshots from simulation of droplet deformation as it approaches a solid surface. a.) cross-section of drop showing dimple formation. b.) pressure dynamics as trapped gas film becomes thin

An alternate approach assumes that the droplet is deformed before contacting the surface, and a layer of air is trapped between the drop and the surface before impact. This suggests that the liquid inertia, liquid viscosity, surface tension, gas pressure, gas viscosity, compressibility of the gas, heat transfer in the gas, mass transfer between the gas and the liquid and the mean free path of the gas are all potentially relevant effects in splash formation. For this paper the model assumes that the nonlinear inertia in the liquid, surface tension forces at the liquid-gas interface, and viscous forces in the fluid are all negligible and that the gas film trapped between the drop and the surface is very thin. Each of these approximations breaks down at some time before contact with the wall, but can still be used to understand the dynamics of a drop as it approaches the surface.

The dynamics in the liquid are modeled using a 2D cylinder (rather than a sphere) and the incompressible Euler equations. The dynamics of the gas fit into 3 regimes; the gas is supercompressible, compressible, and incompressible depending on the ambiant pressure of the gas and the impact paramenters of the problem. The formulas primarily used were the compressible lubrication equations. As the drop approaches the surface, a small dimple is formed and a pocket of gas is trapped between the drop and the surface; the theory is that this gas film is a major factor in splashing dynamics.