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

Abstract

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 β and the dimensionless center thickness h * is systematically analyzed. The results indicate that β max ∝ We a 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 β max for impact on spheres. We first find that β max ∝ Re b exists in the viscous regime ( P > 1), whereas β max ∝ We a mainly exists in the capillary regime ( P < 1). Although the fluid properties of incident droplets vary widely, the variation in h * with dimensionless time τ always has three distinct phases. The first phase follows h * = 1- τ , and the second phase basically conforms to h * ∝ τ −1.6 . The minimum dimensionless center thickness h * min scales as Re c . Furthermore, the exponents a , b , and c are found to b e strongly related to the diameter ratio of spheres and droplets, and prediction models of the three exponents are proposed.