Limit for Small Spheres To Float by Dynamic Analysis

Small spheres released above the liquid surface experience a dynamic process to ultimately float or sink, and thus, their behaviors should be considered by dynamic analysis instead of static equilibrium. This study numerically investigates the motion of small spheres after contacting the liquid surface with zero velocity, and the flotation condition is proposed based on the analyses of acting forces and the sphere's motion. Whether the small spheres float is determined by the density ratio, Bond number, and contact angle. A critical contact angle exists, below which the flotation of small spheres is impossible. The decrease in Bond number and increase in hydrophobicity enlarge the limit density ratio for small spheres to float, while exerting little effect on large spheres. The theoretical formulas of the limit density ratio are obtained based on energy balance and agree well with numerical results. The limit density ratio predicted in consideration of a dynamic process is far less than the maximum density ratio predicted by static equilibrium.