Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotatin g cylinder, air bubbles are entrapped inside the liquid. We propose that th is 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 exp onentially 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 confi rmed by quantitative comparison with numerical simulations of the flow equa tions, and is found to be in qualitative agreement with experimental observ ation.