2023/03/07 by J. M. Gordillo, Gordillo, J. M., Francisco J. Blanco–Rodríguez +1
Engineering · Materials Science · #Particle Dynamics in Fluid Flows #Fluid Dynamics and Heat Transfer #Ultrasound and Cavitation Phenomena
paper · pdf · doi:10.48550/arxiv.2303.03815
Motivated by the results in Gordillo and Blanco-Rodriguez, 'Bubble bursting jets are driven by the purely inertial collapse of gas cavities', Phys. Rev. Lett., Submitted (2023) \citePRL2023, where it is found that bubble bursting jets are driven by a purely inertial mechanism, here we present a study on the dynamics of the jets produced by the collapse of gas cavities of generic shape when the implosion is forced by a far field boundary condition expressing that the flow rate per unit length, q_∞, remains constant in time. Making use of theory and of numerical simulations, we first analyze the case of a conical bubble with a half-opening angle β when the value of q_∞ is fixed to a constant, finding that this type of jets converge towards a purely inertial β-dependent self-similar solution of the equations in which the jet width and velocity are respectively given, in the limit β≪ 1, by rjet≈ 2.25tanβ√(q_∞τ) and vjet≈ 3 q_∞/(2tanβ√(q_∞τ)) respectively, with τ indicating the dimensionless time after the jet is ejected. For the case of parabolic cavities with a dimensionless radius of curvature at the plane of symmetry rc our theory predicts that rjet∝ (2 rc)-1/2(q_∞ τ)3/4 and vjet∝ q_∞ (2rc)1/2 (q_∞τ)-3/4, a result which is also in good agreement with numerical simulations. The present results might find applications in the description of the very fast jets, with velocities reaching up to 1000 m s-1, produced after a bubble cavitates very close to a wall and in the quantification of the so-called bazooka effect.