We study numerically liquid-vapor phase separation in two-dimensional, nonisothermal, van der Waals (vdW) liquid drops using the method of smoothed particle hydrodynamics (SPH). In contrast to previous SPH simulations of drop formation, our approach is fully adaptive and follows the diffuse-interface model for a single-component fluid, where a reversible, capillary (Korteweg) force is added to the equations of motion to model the rapid but smooth transition of physical quantities through the interface separating the bulk phases. Surface tension arises naturally from the cohesive part of the vdW equation of state and the capillary forces. The drop models all start from a square-shaped liquid and spinodal decomposition is investigated for a range of initial densities and temperatures. The simulations predict the formation of stable, subcritical liquid drops with a vapor atmosphere, with the densities and temperatures of coexisting liquid and vapor in the vdW phase diagram closely matching the binodal curve. We find that the values of surface tension, as determined from the Young-Laplace equation, are in good agreement with the results of independent numerical simulations and experimental data. The models also predict the increase of the vapor pressure with temperature and the fitting to the numerical data reproduces very well the Clausius-Clapeyron relation, thus allowing for the calculation of the vaporization pressure for this vdW fluid.

The rapid evaporation and explosive boiling of a van der Waals (vdW) liquid drop in microgravity is simulated numerically in two-space dimensions using the method of smoothed particle hydrodynamics. The numerical approach is fully adaptive and incorporates the effects of surface tension, latent heat, mass transfer across the interface, and liquid-vapor interface dynamics. Thermocapillary forces are modeled by coupling the hydrodynamics to a diffuse-interface description of the liquid-vapor interface. The models start from a nonequilibrium square-shaped liquid of varying density and temperature. For a fixed density, the drop temperature is increased gradually to predict the point separating normal boiling at subcritical heating from explosive boiling at the superheat limit for this vdW fluid. At subcritical heating, spontaneous evaporation produces stable drops floating in a vapor atmosphere, while at near-critical heating, a bubble is nucleated inside the drop, which then collapses upon itself, leaving a smaller equilibrated drop embedded in its own vapor. At the superheat limit, unstable bubble growth leads to either fragmentation or violent disruption of the liquid layer into small secondary drops, depending on the liquid density. At higher superheats, explosive boiling occurs for all densities. The experimentally observed wrinkling of the bubble surface driven by rapid evaporation followed by a Rayleigh-Taylor instability of the thin liquid layer and the linear growth of the bubble radius with time are reproduced by the simulations. The predicted superheat limit $\left(T_s\approx 0.96\right)$ is close to the theoretically derived value of $T_s=1$ at zero ambient pressure for this vdW fluid.

We present experimental observations of Faraday wave patterns when a liquid in a square recipient is submitted to vertical vibrations with forcing frequencies and amplitudes in the intervals 10 ≤ F ≤ 80 Hz and 0.1 ≤ A ≤ 3 mm, respectively. A sweep of the forcing parameter space is performed to investigate the surface patterns that form for two different sizes of the recipient. The waveforms are obtained by means of a Pearson correlation analysis of a sequence of liquid surface images for each experiment. The Pearson correlation coefficients are then fast Fourier transformed to obtain the power spectra. For 10 ≤ F ≤ 15 Hz, tessellation patterns consisting of ordered arrays of rhomboid-shaped tiles are observed; whereas, for 20 ≤ F ≤ 25, the tessellation patterns become irregular over the entire surface where square, rhomboidal, andhexagonal tilings coexist. At 30 ≤ F ≤ 45 Hz, the patterns correspond to a mixed state where ordered and irregular quadrilateral tessellation patterns coexist. At frequencies between 50 and 80 Hz, the tessellated patterns that form consist of irregularly distributed square-shaped tiles. In all cases, the excited waves are periodic with a dominant subharmonic frequency f = F/2. However, for given forcing parameters, the waveforms and their amplitudes differ markedly when the size of the recipient is changed.