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.

In the biomedical field, titanium alloys have long been preferred for orthopedic and dental devices due to their excellent biocompatibility and mechanical strength, making them suitable for long-term implantation. However, recent findings indicate that certain alloying elements, such as vanadium, cobalt, and copper, may pose cytotoxic risks when present at higher concentrations or under specific conditions. As a response to these concerns, current research is focused on developing titanium alloys that feature a lower elastic modulus and improved compatibility with bone elasticity. It also aims to exclude potentially cytotoxic elements and incorporate advanced surface modifications, thereby providing effective solutions to these challenges. Based on these identified needs this review highlights the latest advancements in the design of β-Ti alloys through safer and greener methods. It places particular emphasis on pre-clinical in vitro and in vivo studies that evaluate the safety and performance of implants. Additionally, discusses the potential of artificial intelligence and computational methods for predicting and optimizing alloy properties. Unlike previous reviews that focus mainly on microstructure, mechanical behavior or specific clinical niches, this review includes alloy design and processing with pre-clinical evidence, regulatory and intellectual-property dimensions, and life-cycle and sustainability assessments. By linking β-Ti alloy development to circular-economy strategies, biodegradable metallic alternatives and emerging machine-learning tools for alloy prediction, the review provides a framework for the clinical translation of safer and greener titanium implants, offering a complete overview of the critical factors influencing the future development of titanium alloy implants for biomedical applications.