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 β and the dimensionless center thickness h* is systematically analyzed. The results indicate that βₘₐₓ∝Weᵃ suggested by previous works does not apply to viscous fluids. Thus, we adopt the impact factor P = We/Re⁰.⁸, which has been used to study droplet impact on flat surfaces, to decide the dominating force of βₘₐₓ for impact on spheres. We first find that βₘₐₓ∝Reᵇ exists in the viscous regime (P > 1), whereas βₘₐₓ∝Weᵃ 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 Reᶜ. 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.