Droplet coalescence kinetics: Thermodynamic non-equilibrium effects and entropy production mechanism

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescences are studied in detail via the discrete Boltzmann method. Temporal evolutions of the total TNE strength D* and the total entropy production rate can both provide concise, effective, and consistent physical criteria to distinguish different stages of droplet coalescence. Specifically, when the total TNE strength * and the total entropy production rate reach their maxima, it corresponds to the time when the liquid-vapor interface length changes the fastest; when the total TNE strength D* and the total entropy production rate reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. Throughout the merging process, the force contributed by surface tension in the coalescence direction acts as the primary driving force for droplet coalescence and reaches its maximum simultaneously with coalescent acceleration. In contrast, the force arising from non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as the total TNE strength D*. In the coalescence of two unequal-sized droplets, contrary to the larger droplet, the smaller droplet exhibits higher values for total TNE strength D*, merging velocity, driving force contributed by surface tension, and resistance contributed by the NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to the stronger non-equilibrium driving forces stemming from larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet are consistently smaller than those in the larger droplet and diminish with the radius ratio. This study offers kinetic insights into the complexity of thermodynamic non-equilibrium effects during the process of droplet coalescence, advancing our comprehension of the underlying physical processes in both engineering applications and the natural world.