Investigation of the effect of curvature on the local mass flux of evaporating droplets using a phase field method

Abstract

Droplet evaporation, a fundamental process with wide-ranging applications, involves complex physical mechanisms that significantly influence mass transfer rates and droplet lifetimes. Despite its significance, the influence of droplet deformation induced by capillary forces on local saturation conditions and its subsequent impact on phase change have received limited attention. This study delves into the impact of capillary-induced droplet deformation on local saturation conditions and its subsequent effect on phase change within a quiescent vapor environment. Contrary to most analytical and numerical studies that impose temperature and heat flux conditions at the vapor–liquid interface, our investigation employs direct numerical simulations based on the thermal Navier–Stokes–Korteweg model, capturing the dynamics of the droplet and its interface without relying on ad-hoc interface conditions. Our findings demonstrate that droplet deformation induces free oscillatory motion, which, although not significantly altering droplet lifetime due to viscous damping, leads to non-uniform mass fluxes along the droplet interface. We observe that areas of higher curvature are associated with increased local pressure and reduced temperatures, a discrepancy primarily attributed to evaporative cooling. This effect is further elucidated through an analysis of pressure and energy fluxes, revealing that regions of high curvature experience significant heat consumption, driving evaporative cooling and creating temperature gradients along the interface. Conversely, areas with negative curvature exhibit a reverse trend, indicating the complex interplay of capillarity, deformation, and phase change in droplet evaporation. Our results highlight the intricate relationship between droplet deformation, local pressure, mass flux, and temperature, underscoring the necessity for improved modeling of these factors in future studies on droplet evaporation dynamics.