The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a 'tank treading' motion. These observations are apprehended at the light of a variant of Wagner theory for liquid impact. This framework offers a simple analogy where the fluid motion within the impacting drop may be viewed as the flow induced by a flat rising expanding disk. The theoretical predictions are found to be in very close agreement both qualitatively and quantitatively with the numerical observations for about three decades in time. Interestingly the inviscid self-similar impact pressure and velocities are shown to depend solely on the self-similar variables (r/ √ t, z/ √ t). The structure of the boundary layer developing along the wet substrate is investigated as well, and is proven to be formally analogous to that of the boundary layer growing in the trail of a shockwave. Interestingly, the boundary layer structure only depends on the impact self-similar variables. This allows to construct a seamless uniform analytical solution encompassing both impact and viscous effects. The depiction of the different dynamical fields enables to quantitatively predict observables of interest, such as the evolution of the integral viscous shearing force and of the net normal force. IntroductionThe impact of a liquid drop onto a rigid surface results in a rapid sequence of events ending, in the inertial limit, in spreading (Eggers et al. 2010) or splashing (Stow & Hadfield 1981), interface tearing (Villermaux & Bossa 2011) and ultimate fragmentation (Stow & Stainer 1977). A large number of studies have investigated the many facets of drop impact, with a special attention to the description of its late stages (Rein 1993;Yarin & Weiss 1995). The literature on the early stages of impact is however scarce in comparison. Detailed experimental data depicting the instants following impact can nonetheless be found in the work of Rioboo et al. (2002), that evidenced a "kinematic phase" where the drop merely resembles a truncated sphere and spreads as the squareroot of time. This phase precedes the apparition of the liquid lamella.Probably one of the first depiction of the very first instants of drop impact dates back to Engel (1955). With the help of high-speed cinematography, Engel captured the chronology of events triggered by drop impact. He noted in particular the unvarying shape of the drop apex during the earliest moments of impact, which might be surprising due to the incompressible character of the liquid. Engel put forward the possible roles of inertia, viscosity or surface tension to explain this observation. Actually, the physical mechanism underpinning this behaviour is best illustrated with Figure 1a. There, the numerically...

The dissolution of minerals into water becomes significant in geomorphology, when the erosion rate is controlled by the hydrodynamics transport of the solute. Even in absence of an external flow, dissolution itself can induce a convection flow due to the action of gravity. Here we perform a study of the physics of solutal convection induced by dissolution. We simulate numerically the hydrodynamics and the solute transport, in a 2D geometry, corresponding to the case, where a soluble body is suddenly immersed in a quiescent solvent. We identify three regimes. At short timescale, a concentrated boundary layer grows by diffusion at the interface. After a finite onset time, the thickness and the density reach critical values which starts the destabilization of the boundary layer. Finally, the destabilization is such as we observe the emission of intermittent plumes. This last regime is quasi-stationnary: the structure of the boundary layer as well as the erosion rate fluctuate around constant values. Assuming that the destabilization of the boundary layer occurs at a specific value of the solutal Rayleigh number, we derive scaling laws both for fast and slow dissolution kinetics. Our simulations confirm this scenario by validating the scaling laws both for onset, and the quasi-stationary regime. We find a constant value of the Rayleigh number during the quasi-stationary regime showing that the structure of the boundary layer is well controlled by the solutal convection. Finally, we apply the scaling laws previously established to the case of real dissolving minerals. We predicts the typical dissolution rate in presence of solutal convection. Our results suggest that solutal convection could occur in more natural situations than expected. Even for minerals with a quite low saturation concentration, the erosion rate would increase as the dissolution would be controlled by the hydrodynamics.