TRANSITION OF SCALING FOR PINCH-OFF OF AN AXISYMMETRIC LIQUID LIGAMENT IN ANOTHER IMMISCIBLE LIQUID

摘要

Scaling for pinch-off of an axisymmetric liquid ligament in another immiscible liquid is studied computationally for inter-mediate Reynolds number, where both inertial and viscous forces are dominant. Interface motion near pinch-off is traced by a front tracking /finite difference method with higher resolution. When the ligament breaks up, a thin thread forms between a bulb of the tip and the rest of the ligament. Computational results show that the minimum radius of the thread decreases with time and the ex-ponent of time shifts from 2/3 to 1. This shift corresponds to the transition from potential flow scaling law to the scaling law for viscous thread in another viscous fluid. The rate of the thinning down of the thread is in good agreement with the one obtained from experiments for very small Reynolds number range, where viscous force is dominant. Since the length scale becomes very small close to the pinch-off, the viscous effect overcomes the in-ertial effect and the scaling alters from the potential flow scaling law to the viscous scaling law.