Splashing velocity of a viscous liquid squeezed between two parallel disks

Abstract

Squeezing of a liquid film between two approaching solid surfaces can generate a high-speed peripheral splash. Despite extensive studies on squeeze-film hydrodynamics, quantitative prediction of the splash velocity remains unresolved, with existing theory significantly overestimating experiments. Here, we present a theoretical framework to predict the ejection velocity of viscous liquid squeezed between two parallel circular disks. We show that discrepancy of theory from experiments arise due to incomplete treatment of liquid inertia and from using peak ejection velocity to represent splash velocity. By accounting for both local and convective inertia, and introducing a momentum-averaged ejection velocity, we obtain good agreement with experiments over a wide range of parameters.