Droplet squeezing through a narrow constriction: Minimum impulse and critical velocity

Models of a droplet passing through narrow constrictions have wide applications in science and engineering. In this paper, we report our findings on the minimum impulse (momentum change) of pushing a droplet through a narrow circular constriction. The existence of this minimum impulse is mathematically derived and numerically verified. The minimum impulse happens at a critical velocity when the time-averaged Young-Laplace pressure balances the total minor pressure loss in the constriction. Finally, numerical simulations are conducted to verify these concepts. These results could be relevant to problems of energy optimization and studies of chemical and biomedical systems.