Temperature- and curvature-dependent surface tensions and Tolman lengths for real fluids: A mesoscopic investigation

The curvature and temperature dependency of the liquid-vapor surface tension has a significant influence on the accurate prediction of the nanobubble/nanodrop nucleation process. In this work, a mesoscopic approach combining the pseudo-potential multiphase lattice Boltzmann method (LBM), the principle of dynamic similarity, and the van der Waals theory of corresponding states is adopted to quantitatively investigate the curvature and temperature dependency of the surface tension and Tolman length for real fluids (water and R134a). By Tolman length, we mean the distance from the surface of tension to the equimolar surface, which measures the extent by which the surface tension of a nanodrop/nanobubble deviates from the corresponding flat interface limit. We show that the Tolman lengths for flat liquid-vapor interfaces (δF) increase with the increase of temperature and are proportional to (1−Tr)−1.044. Equations for predicting surface tensions of water and R134a with effects of temperature and curvature radius taken into consideration are proposed. We demonstrate that the surface tensions increase while the Tolman lengths (δB) decrease with the increase of curvature for nanobubbles. For nanodroplets, however, the surface tensions decrease while the Tolman lengths (δD) increase with the increase of curvature. Effects of the equation of state for real fluids, which determines the interparticle interaction force in the pseudo-potential LBM, are also discussed. This mesoscopic approach can quantify the curvature dependency of liquid-vapor surface tensions for various real fluids in a wide temperature range with low computation costs, providing a new avenue for the accurate prediction of nucleation processes in micro-/nanoscale phase change heat transfer with applications to boiling, evaporation, and condensation.