Velocity scaling and breakup criteria for jets formed due to acceleration and deceleration process

We investigate the formation of a liquid jet due to an impact. The fluid contained in a completely wettable tube undergoes a constant acceleration-deceleration motion with the acceleration time being much smaller than the deceleration time duration. During the impact, the fluid near the wall rises up. For a small deceleration time and liquid viscosity, the velocity of the contact line between the liquid and the wall approximates the tube velocity. Later, the tube deceleration causes the flow to focus at the center of the tube, forming a liquid jet. The velocity of the liquid jet is mainly characterized by five dimensionless numbers: the Weber number (We), the Ohnesorge number (Oh), the Bond number (Bo), the dimensionless acceleration (tau(a)), and the deceleration time (tau(d)). For zero Bond numbers and small acceleration time, our numerical simulations show that the jet velocity V-j scales with Oh(-1/4) We(1/8) tau(-2/3)(d) for large Oh. For a wide range of Bond numbers, the kinetic energy reduction due to viscous dissipation in the jet tip [1 - V-j(2)/V-j,0(2)] scales with Oh(2/3) f(We, Bo)(2/3) for small Oh, where V-j,V-0 is the inviscid jet velocity, and f (We, Bo) is an empirical function of We and Bo obtained from a least-squares fit of numerical results. At small Bo, the jet forms due to the focusing flow and the jet velocity decreases with surface tension. On the other hand, at large Bo, when the initial interface is flatter, focusing of surface waves enhances the jet formation and jet velocity increases with surface tension. For the Bond number in experiments, we also investigate the breakup criteria for the liquid jets. By denoting the critical Weber number for breakup as We e , we find that f (We(c), Bo)(-2/3) linearly increases with Oh(2/3) for a wide range of Oh, and has a nonmonotonic dependence on tau(d).