Abstract:Water-entry ofobject is a type of fluid-structure interaction problem withcomplex physics, which has a wide range of engineeringapplications. During the water-entry process, as the object passesthe water-air interface, the possible air entrapment may formcavity under specific conditions and the dynamic movement ofcavity can generate a jet pointing towards the object. Both thecavity and jet can greatly influence the force on the object andtherefore influence its movement. Moreover, the super-hydrophobicsurface can form multi-scale fluid-solid coupling phenomena in theprocess of water-entry of object, which in turn affects the motionof the object and the macroscopic fluid flow. For small scalewater-entry problem, the surface or interfacial force rather thanbody force is usually dominant. The objective of present study isto obtain the cavity behaviors and motion of characteristics forthe problem of water-entry of small super-hydrophobic spheres in awider parameter space. Based on such purposes, the high-speedphotography experiment method is used to study the low-speedwater-entry and cavity dynamics of super-hydrophobic spheres witha radius of 0.175\sim 10 mm. Five dynamic modes are obtainedincluding sphere floating oscillation, quasi-static impact cavity,shallow seal impact cavity, deep seal impact cavity and surfaceseal impact cavity. The relationship between these dynamic modeswith the Weber number and Bond number is discussed, and thedimensionless relationship between the floating oscillation andsinking behaviors of the sphere is derived. The results show thatthe cavity behaviors of water-entry of super-hydrophobic spheresare mainly related to the Weber number and the Bond number. In therange of Bo O(1), the shallow seal state also does not happen. Thecritical relationship between the floating oscillation and thesinking of sphere can be described by the scaling laws. A formulais developed to categorize the floating oscillation andquasi-static impact cavity phenomena.