Analysis of Droplet Evaporation Dynamics Using Computational Singular Perturbation and Tangential Stretching Rate

Computational singular perturbation (CSP) has been successfully used in the analysis of complex chemically reacting flows by systematically identifying the intrinsic timescales and slow invariant manifolds that capture the essential subprocesses driving the dynamics of the system. In this article, the analytical and computational framework is applied for the first time to analyze the Lagrangian droplets undergoing evaporation and dispersion in the surrounding gases. First, a rigorous mathematical formulation is derived to adapt the CSP tools into the droplet dynamics equations, including the formal definition of the tangential stretching rate (TSR) that represents the explosive/dissipative nature of the system. A steady ammonia and a falling water droplet studies are then conducted to demonstrate the utility of the CSP methodology in identifying various physical mechanisms driving the evolution of the system, such as the distinction of thermal-driven and mass-driven regimes. Various definitions of the importance indices are also examined to provide in-depth analysis of different subprocesses and their interactions in modifying the droplet dynamics.