Numerical study on droplets impacting solid spheres: Effect of fluid properties and sphere diameter

This study adopts the phase-field method to investigate the dynamics of droplet impact on spherical surfaces at various Reynolds numbers Re and Weber numbers We. Five liquids are studied in the present simulation, which expands the research scope of viscosity (1-970 mPa.s) and surface tension (20-500 mN/m) compared with previous works. The temporal evolution of the spreading factor beta and the dimensionless center thickness h* is systematically analyzed. The results indicate that beta(proportional to)(max)We(alpha) suggested by previous works does not apply to viscous fluids. Thus, we adopt the impact factor P = We/Re-0.8, which has been used to study droplet impact on flat surfaces, to decide the dominating force of beta(max) for impact on spheres. We first find that beta(max).Reb exists in the viscous regime (P > 1), whereas beta(proportional to)(max)We(alpha) mainly exists in the capillary regime (P < 1). Although the fluid properties of incident droplets vary widely, the variation in h* with dimensionless time tau always has three distinct phases. The first phase follows h* = 1-tau, and the second phase basically conforms to h*alpha tau (-1.6). The minimum dimensionless center thickness h* min scales as Re-c. Furthermore, the exponents a, b, and c are found to be strongly related to the diameter ratio of spheres and droplets, and prediction models of the three exponents are proposed.

Automated summary

This study investigates the dynamics of droplet impact on spherical surfaces at various Reynolds and Weber numbers using the phase-field method. It explores the temporal evolution of spreading factor and dimensionless center thickness, and concludes that different forces dominate in different regimes. The study also proposes prediction models for the exponents a, b, and c, which are strongly related to the diameter ratio of spheres and droplets.