We present scaling laws for the jet velocity resulting from bubble collapse at a liquid surface which bring out the effects of gravity and viscosity. The present experiments conducted in the range of Bond numbers $0.004<Bo<2.5$ and Ohnesorge numbers $0.001<Oh<0.1$ were motivated by the discrepancy between previous experimental results and numerical simulations. We show here that the actual dependence of $We$ on $Bo$ is determined by the gravity dependency of the bubble immersion (cavity) depth which has no power-law variation. The power-law variation of the jet Weber number, $We\sim 1/\sqrt{Bo}$, suggested by Ghabache et al. (Phys. Fluids, vol. 26 (12), 2014, 121701) is only a good approximation in a limited range of $Bo$ values ($0.1<Bo<1$). Viscosity enters the jet velocity scaling in two ways: (i) through damping of precursor capillary waves which merge at the bubble base and weaken the pressure impulse, and (ii) through direct viscous damping of the jet formation and dynamics. These damping processes are expressed by a dependence of the jet velocity on Ohnesorge number from which critical values of $Oh$ are obtained for capillary wave damping, the onset of jet weakening, the absence of jetting and the absence of jet breakup into droplets.

For a floating bubble, in the range of Bond numbers based on an equivalent spherical radius, 0 &lt; Boe &lt; 1, we present analytical expressions for various shape parameters of the bubble as functions of Boe. Expressions are obtained for the radius of the rim Rr, the radius of the thin film cap Rc, the height of the top of the cap from the rim hcap, the height of the rim above the free surface hr, and the depth of the bubble cavity from the free surface Zc. To obtain these expressions, we solve equations formulated in terms of these shape parameters for the meniscus outside the bubble, the force balance of the bubble, the pressure balance at the centre line of the bubble, and geometrical constraints, after neglecting the deformation of the bubble cavity for Boe &lt; 1. The obtained expressions are shown to match well with our experimental measurements of the shape of the bubble. In addition to these expressions, we also present simpler approximations that can be used accurately as scaling laws for these shape parameters up to Boe &lt; 0.5.

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For millimetre to micron sized bubbles, floating at the free surface of different low viscosity fluids with different surface tensions, and then collapsing, we study the ensuing expansion of the outer radius of the hole (ro) at the free surface, as well as its velocity of expansion (uo). Since the thin film cap of the bubble disintegrates before the hole in it reaches the static rim, the hole expansion at intermediate times occurs as if it initiates at the bubble’s static rim of radius Rr; the evolution of ro then results to be a strong function of gravity, since Rr depends strongly on the bubble radius R. A scaling analysis, which includes the increase in the tip radius due to mass accumulation and the resulting change in the retraction force, along with the gravity effects by considering the hole radius in excess of its initial static radius, re = ro − Rr, results in a novel scaling law re/R∼(t/tc)4/7, where tc=ρR3/σ is the capillary time scale; this scaling law is shown to capture the evolution of the hole radii in the present study. The dimensionless velocities of hole expansion, namely, the Weber numbers of hole expansion, Weo=ρuo2R/σ, scale as Weo∼(t/tc)−6/7, independent of gravity effects, matching the observations. We also show that these Weber numbers, which reduce with time, begin with a constant initial Weber number of 64, while the viscous limit of the present phenomena occurs when the bubble Ohnesorge number Oh=μ/σρR≃0.24.