The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free-slip), about one half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is send to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on "slippery" or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet-droplet collisions) and for impacts on no-slip surfaces

Technologies including (3D-) (bio-)printing, diesel engines, laser-induced forward transfer, and spray cleaning require optimization and therefore understanding of micrometer-sized droplets impacting at velocities beyond 10 m s(-1). However, as yet, this regime has hardly been addressed. Here we present the first time-resolved experimental investigation of microdroplet impact at velocities up to V0 = 50 m s(-1), on hydrophilic and -phobic surfaces at frame rates exceeding 10(7) frames per second. A novel method to determine the 3D-droplet profile at sub-micron resolution at the same frame rates is presented, using the fringe pattern observed from a bottom view. A numerical model, which is validated by the side- and bottom-view measurements, is employed to study the viscous boundary layer inside the droplet and the development of the rim. The spreading dynamics, the maximal spreading diameter, the boundary layer thickness, the rim formation, and the air bubble entrainment are compared to theory and previous experiments. In general, the impact dynamics are equal to millimeter-sized droplet impact for equal Reynolds-, Weber- and Stokes numbers (Re, We, and St, respectively). Using our numerical model, effective scaling laws for the progression of the boundary layer thickness and the rim diameter are provided. The dimensionless boundary layer thickness develops in time (t) according to δBL ~ D0/√Re(t/τ)0.45, and the diameter of the rim develops as DRim ~ D0/√We(t/τ)0.68, with drop diameter D0 and inertial time scale τ = D0/V0. These scalings differ from previously assumed, but never validated, values. Finally, no splash is observed, at variance with many predictions but in agreement with models including the influence of the surrounding gas. This confirms that the ambient gas properties are key ingredients for splash threshold predictions.

A drop of water that freezes from the outside-in presents an intriguing problem: the expansion of water upon freezing is incompatible with the self-confinement by a rigid ice shell. Using high-speed imaging we show that this conundrum is resolved through an intermittent fracturing of the brittle ice shell and cavitation in the enclosed liquid, culminating in an explosion of the partially frozen droplet. We propose a basic model to elucidate the interplay between a steady build-up of stresses and their fast release. The model reveals that for millimetric droplets the fragment velocities upon explosion are independent of the droplet size and only depend on material properties (such as the tensile stress of the ice and the bulk modulus of water). For small (sub-millimetric) droplets, on the other hand, surface tension starts to play a role. In this regime we predict that water droplets with radii below 50 µm are unlikely to explode at all. We expect our findings to be relevant in the modeling of freezing cloud and rain droplets.

The dissolution process of small (initial (equivalent) radius R 0 < 1 mm) long-chain alcohol (of various types) sessile droplets in water is studied, disentangling diffusive and convective contributions. The latter can arise for high solubilities of the alcohol, as the density of the alcohol-water mixture is then considerably less than that of pure water, giving rise to buoyancy-driven convection. The convective flow around the droplets is measured, using micro-particle image velocimetry (µPIV) and the schlieren technique. When non-dimensionalizing the system, we find a universal Sh ∼ Ra 1/4 scaling relation for all alcohols (of different solubilities) and all droplets in the convective regime. Here Sh is the Sherwood number (dimensionless mass flux) and Ra is the Rayleigh number (dimensionless density difference between clean and alcohol-saturated water). This scaling implies the scaling relation τ c ∝ R 5/4 0 of the convective dissolution time τ c , which is found to agree with experimental data. We show that in the convective regime the plume Reynolds number (the dimensionless velocity) of the detaching alcohol-saturated plume follows Re p ∼ Sc −1 Ra 5/8 , which is confirmed by the µPIV data. Here, Sc is the Schmidt number. The convective regime exists when Ra > Ra t , where Ra t = 12 is the transition Ra number as extracted from the data. For Ra Ra t and smaller, convective transport is progressively overtaken by diffusion and the above scaling relations break down.