Revision of Bubble Bursting: Universal Scaling Laws of Top Jet Drop Size and Speed

The collapse of a bubble of radius R-o at the surface of a liquid generating a liquid jet and a subsequent first drop of radius R is universally scaled using the Ohnesorge number Oh = mu/(rho sigma R-o)(1/2) and a critical value Oh* below which no droplet is ejected; rho, sigma, and mu are the liquid density, surface tension, and viscosity, respectively. First, a flow field analysis at ejection yields the scaling of R with the jet velocity V as R/l(mu) similar to (V/V-mu)(-5/3), where l(mu) = mu(2)/(rho sigma) and V-mu = sigma/mu. This resolves the scaling problem of curvature reversal, a prelude to jet formation. In addition, the energy necessary for the ejection of a jet with a volume and averaged velocity proportional to RoR2 and V, respectively, comes from the energy excess from the total available surface energy, proportional to sigma R-o(2), minus the one dissipated by viscosity, proportional to mu(sigma R-o(3)/rho)(1/2). Using the scaling variable phi = (Oh* - Oh)Oh(-2), it yields V/V-mu = k(nu)phi(-3/4) and R/l(mu) = k(d)phi(5/4), which collapse published data since 1954 and resolve the scaling of R and V with k(v) = 16, k(d) = 0.6, and Oh* = 0.043 when gravity effects are negligible.