Dynamics of sphere entry into dilute viscoelastic polymer solutions

This study experimentally investigates the effects of viscoelastic dilute aqueous polyethylene oxide solutions on the water entry of spheres. The solutions are modified to manipulate viscoelastic properties which influence cavity dynamics and the behavior of the Worthington jet. The effects of viscoelasticity and impact velocity are quantified using dimensionless numbers, including the Deborah number (De), the Reynolds number (Re), and the Froude number (Fr). Three distinct cavity patterns are identified, and transitions between these patterns occur as De and Re change. As Re increases, the cavity patterns emerge sequentially in a specific order, with the critical transition points between patterns dependent on De. The combined influence of De and Fr determines the dimensionless pinch-off time and depth of the deep seal cavity. Higher De or Fr values result in increased dimensionless pinch-off time and depth. Furthermore, energy analysis of the Worthington jet reveals that kinetic energy transforms into potential, surface tension, and elastic energy, with the Deborah number (De) influencing this conversion. In viscoelastic solutions, unlike in filtered water, elastic energy constitutes a significant portion of the total mechanical energy, leading to a much more complex energy conversion process.