R. Bolaños-Jiménez

Axisymmetric bubble collapse in a quiescent liquid pool. II. Experimental study

We present an experimental study of the detachment of a gas bubble growing quasistatically at constant flow rate conditions from a vertical nozzle placed at the bottom of a quiescent pool of water. In particular, we focus on the dynamics of the necking process and on its dependence on both the Bond and Weber numbers, respectively, defined as Bo=ρga2/σ, and WeQ=ρQ2/(π2a3σ). Here, a, ρ, σ, g, and Q are the inner radius of the nozzle, the liquid density, the gas-liquid surface tension, the gravitational acceleration, and the gas flow rate. Our experimental data indicate that the collapse process is not only driven by capillarity but also by the liquid hydrostatic pressure. Good agreement is achieved between the measurements of the collapse time and that given by the scaling proposed as tc=tσ/1+121/3Bo2/3 where tσ=(ρa3/σ)1/2 is the capillary time, valid in the limit WeQ→0. In addition, the details of the final instants previous to pinch-off have been analyzed by recording the time evolution of both the bubble...

The effect of liquid viscosity on bubble pinch-off

The collapse stage of an air bubble immersed in a stagnant viscous liquid is experimentally and theoretically investigated, focusing on the effect of liquid viscosity on the final instants previous to pinch-off. Our experiments are consistent with recent investigations, and at the same time highlight several important limitations of previous works. In particular, it is shown that the use of a power law to describe the collapse dynamics of the bubble is not appropriate in an intermediate range of liquid viscosities, for which a transition from an inviscid to a fully viscous pinch-off takes place. Under these conditions, the instantaneous exponent α(τ) varies during a single pinch-off event from the typical values of inviscid collapse, α ≃ 0.58, to the value corresponding to a fully viscous dynamics, α ≃ 1. Consequently, the effective exponent of the power law is not correctly defined in these cases. However, as in the work of Bolanos-Jimenez et al. [Phys. Fluids 20, 112104 (2008) ], we show that the pinch-off process can be accurately described by the use of a pair of Rayleigh-like differential equations for the time evolution of the minimum radius, R0, and half the axial curvature evaluated at the minimum radius, r1. In particular, the theoretical model is able to describe the smooth transition which takes place from inviscid to viscous-dominated pinch-off in liquids of intermediate viscosity, 10 ≤ μ ≤ 100 cP, and accounts for the fact that the axial curvature remains constant when the local Reynolds number becomes small enough, in close agreement with our experimental measurements.

The necking time of gas bubbles in liquids of arbitrary viscosity

We report an experimental and theoretical study of the collapse time of a gas bubble injected into an otherwise stagnant liquid under quasi-static conditions and for a wide range of liquid viscosities. The experiments were performed by injecting a constant flow rate of air through a needle with inner radius a into several water/glycerine mixtures, providing a viscosity range of 20 cP ≲ μ ≲ 1500 cP. By analyzing the temporal evolution of the neck radius, R0(t), the collapse time has been extracted for three different stages during the collapse process, namely, Ri/a = 0.6, 0.4, and 0.2, being Ri = R0(t = 0) the initial neck radius. The collapse time is shown to monotonically increase with both Ri/a and with the Ohnesorge number, Oh=μ/ρσRi, where ρ and σ represent the liquid density and the surface tension coefficient, respectively. The theoretical approach is based on the cylindrical Rayleigh-Plesset equation for the radial liquid flow around the neck, which is the appropriate leading-order representation o...