Numerical study and predictions of evolution behaviors of evaporating pinned droplets based on a comprehensive model

In this paper, an evaporation model, which comprehensively considers transport mechanisms that include vapor diffusion in air, evaporative cooling at liquid-air interface, conjugate heat transfer in solid, liquid and air, buoyancy-induced convection and Marangoni convection in both liquid and air, is established to study the evaporation of pinned droplets on both unheated and heated substrates. Based on this model and using the adaptive evolution algorithm proposed by the authors, the temporal evolution behaviors of pinned droplets are simulated. Numerical results show that the temporal evolutions of contact angle and volume of pinned droplets with an initial contact angle θ0 = π/2, when normalized, follow the same laws, respectively, though there exist great differences in the droplet base radius, substrate temperature and ambient humidity. From the numerical results, the simple normalized correlations for the temporal evolutions of contact angle and volume of pinned droplets with θ0 = π/2 are developed, and further, the general expressions in closed forms applicable for predicting the evolution behaviors of evaporating pinned droplets with θ0 ≤ π/2 on both unheated and heated substrates are deduced by considering the evaporation process of droplets with θ0 ≤ π/2 as a part of the evaporation process of droplets with θ0 = π/2. Finally, the proposed expressions are compared and validated with the theoretical and experimental results in the literature.