Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose that this is due to air being drawn into the narrow channel of a cusp singularity that generically forms on free surfaces. Since the width of the cusp is exponentially small in the driving strength, even the minute viscosity of air is enough to destroy the stationary solution, and a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory is confirmed by quantitative comparison with numerical simulations of the flow equations, and is found to be in qualitative agreement with experimental observation.