We study the motion of a drop lying on a plate simultaneously submitted to horizontal and vertical harmonic vibrations. The two driving vibrations are adjusted to the same frequency, and, according to their relative amplitude and phase difference DeltaPhi, the drop experiences a controlled directed motion with a tunable velocity. We present a simple model putting in evidence the underlying mechanism leading to this ratchetlike motion of the drop. Our model includes the particular case DeltaPhi=pi corresponding to the climbing of a drop on a vertically vibrated inclined substrate, as recently observed by Brunet et al. [Phys. Rev. Lett. 99, 144501 (2007)10.1103/PhysRevLett.99.144501]. This study gives insights in the fundamental issue of wetting dynamics and offers new possibilities of controlled motion in droplet microfluidics applications.

We put in evidence the unexpected behavior of Leidenfrost droplets at the later stage of their evaporation. We predict and observe that, below a critical size Rl, the droplets spontaneously take off due to the breakdown of the lubrication regime. We establish the theoretical relation between the droplet radius and its elevation. We predict that the vapor layer thickness increases when the droplets become smaller. A satisfactory agreement is found between the model and the experimental results performed on droplets of water and of ethanol.

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate γ-plot with rounded cusps that can approach arbitrarily closely the true γ-plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude δ for a γ-plot of the form γ = γ0[1 + δ(| sin θ| + | cos θ|)]. The phase-field results are consistent with the scaling law Λ ∼ V −1/2 observed experimentally, where Λ is the facet length and V is the growth rate. In addition, the variation of V and Λ with δ is found to be reasonably well predicted by an approximate sharpinterface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.