The Dynamics of Drop Impact

Inkjet printing, rainfall, droplet collision in combustion chambers are different forms of drop impacts. The whole dynamics of these impacts is complex and remains far to be fully understood. In particular the role of the viscosity of the drop liquid is still hard to exhibit. In one hand, the early time of the impact should be considered inviscid, and viscous free calculation give a fair approximation of the short time dynamics. On the other hand, experimental evidences show that the transition between splashing dynamics and deposition is controlled by a so-called splashing parameter K = We · sqrt(Re), where the viscosity enter through the Reynolds number Re (We being the Weber number). Therefore the role of the viscosity for the early time of the impact needs to be elucidated. We will present numerical simulations of the impact of a drop on a liquid layer thanks to a volume of fluid technique (VOF), where the Navier-Stokes equations are solved for both liquid and gas phases. For a given Weber number, we will vary only the viscosity so that viscous effects can be emphasized. The calculation will also determine the relative spreading of the drop inside the liquid layer. For splashing behaviors, a jet is emitted soon after the initiation of the impact; contrarily, no jets are present when deposition happens. The pressure field and the velocity field are studied near the neck of the impact and show no specific dependance on the viscosity. However, viscous effects are observed through the diffusion of the vorticity from the interface into the liquid bulk. Therefore, the viscous length l_v = sqrt(vt) controls the gradient fields at the impact and we observe that the width of the emitted jet is determined by this length. Therefore, applying mass conservation to a dynamical solution where a jet of width l_v is created, we can estimate the balance between mass ejected by the falling drop with mass coming from a retracting jet. The growth of a jet is thus controlled by this mass balance and the splashing parameter law is retrieved. In particular, the viscous effects appear in the theory as a singular perturbation of the inviscid impact dynamics. Self-similar solutions of the impact are therefore considered in specific gometries. More information at http://www.lmm.jussieu.fr/MEMBRES/JOSSERAND/josserand.html.