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Conditions of inertial-viscous transition and related jetting in large cavity collapse
Raja D.K., Hopfinger E.J.,
Published in American Physical Society
Volume: 5
Issue: 12
In this paper, we present results on the effect of viscosity and surface tension on the collapse of large cavities produced by overdriving Faraday waves in a cylindrical container. The forcing amplitude of the container excitation has been increased at a rate such that the last stable wave amplitude b was close to bs, referred to as the singular wave amplitude. The collapse of the wave-depression cavity that follows b⪅bs gives rise to the largest surface jet velocities; when b>bs, cavity collapse occurs with a bubble pinch-off. Viscosity has been varied by two orders of magnitude using water and glycerine-water (GW) solutions. Surface tension effects are highlighted by comparing with previously obtained results with FC 72, a low-surface-tension and low-viscosity liquid. The main objective has been to clarify how these fluid properties affect the cavity shape and cavity collapse dynamics. It is shown that the initial cavity depth depends only weakly on fluid properties, whereas the initial radius decreases with increasing viscosity and increases with decreasing surface tension. The collapse of the cavity is initially inertial with minimum cavity radius rm varying with time in the form rm∼τα, with α≃0.5, where τ=(t0-t), with t0 being the time at singular collapse. In high-viscosity fluids, there is an inertial-viscous transition to α=1, whereas in water the transition is to α>1/2 and is close to 2/3, indicating an inertial-capillary transition. In low-viscosity and low-surface-tension fluid (FC 72), collapse remains inertial up to singular collapse. The transitions are characterized by the evolution of the relevant dimensionless flow parameters. It is shown that inertial-viscous transition occurs when the capillary number, Ca=Urμ/σ, defined with the local radial velocity, Ur, changes from Ca<1 to Ca>1, while the local Ohnesorge number is large, Oh=μ/ρσrm≳0.1. The local Reynolds number at transition remains large and decreases with decreasing τ to Re∼1. The velocity of the jet, emerging from the free surface following singular collapse, increases with viscosity, and reaches a maximum in GW. Numerical simulations give an indication of the increase and localization of the pressure that drives the liquid jet with a high-speed precursor air jet. © 2020 American Physical Society.
About the journal
JournalData powered by TypesetPhysical Review Fluids
PublisherData powered by TypesetAmerican Physical Society
Open AccessNo