High energy dissipation rates from the impingement of free paper-thin sheets of liquids: A study of the coefficient of restitution of the collision

The micromixing time of impinging thin liquid sheets depends upon the energy dissipation rate, which is typically 104 to 106 W/kg. The energy dissipation rate in the impingement zone is a function of the coefficient of restitution (COR) of the collision. In this study the COR was investigated both theoretically and experimentally. An analytical expression was developed that consists of a term that accounts for an inelastic collision of impinging sheets and a term that quantifies the “elasticity” imparted to the collision once the critical velocity for backflow is reached. The theoretical results were compared with experiments that determined the COR by measuring the velocity of single sheets and mixed sheets. Not only do the experimental results show a jump in the COR at the critical velocity, as predicted by theory, but calculated values of the COR from the analytical expression compare well with measured values.