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= ga 2 / , and We Q = Q 2 / ͑ 2 a 3 ͒. Here, a, , , 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 t c = t / ͱ 1+12 1/3 Bo 2/3 where t = ͑a 3 / ͒ 1/2 is the capillary time, valid in the limit We Q → 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 neck radius, R 0 , and the axial curvature at the minimum radius, 2r 1 , using a high speed digital video camera and an appropriate set of microscopic lenses. We find that the dimensionless, asymptotic law, recently obtained for the inviscid pinch-off of a bubble, given by ϰ R 0 2 exp͓ ͱ −ln͑R 0 2 ͔͒, is never achieved down to about 20 m. However, the experimental results are accurately reproduced by a pair of two-dimensional Rayleigh-type equations that include liquid inertia as well as surface tension effects.
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 ␣͑͒ varies during a single pinch-off event from the typical values of inviscid collapse, ␣ Ӎ 0.58, to the value corresponding to a fully viscous dynamics, ␣ Ӎ 1. Consequently, the effective exponent of the power law is not correctly defined in these cases. However, as in the work of Bolaños-Jiménez et al. ͓Phys. Fluids 20, 112104 ͑2008͔͒, 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, R 0 , and half the axial curvature evaluated at the minimum radius, r 1 . 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, 10Յ Յ 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.
Oscillating microbubbles can be used as microscopic agents. Using external acoustic fields they are able to set the surrounding fluid into motion, erode surfaces and even to carry particles attached to their interfaces. Although the acoustic streaming flow that the bubble generates in its vicinity has been often observed, it has never been measured and quantitatively compared with the available theoretical models. The scarcity of quantitative data is partially due to the strong three-dimensional character of bubble-induced streaming flows, which demands advanced velocimetry techniques. In this work, we present quantitative measurements of the flow generated by single and pairs of acoustically excited sessile microbubbles using a three-dimensional particle tracking technique. Using this novel experimental approach we are able to obtain the bubble's resonant oscillating frequency, study the boundaries of the linear oscillation regime, give predictions on the flow strength and the shear in the surrounding surface and study the flow and the stability of a two-bubble system. Our results show that velocimetry techniques are a suitable tool to make diagnostics on the dynamics of acoustically excited microbubbles.
A numerical study on rising bubbles in still liquids employing the Volume of Fluid (VOF) technique to track the interface is presented here. First, a combination of the correlation provided by Rastello et al. [42] for the rectilinear motion of a bubble with that given by Clift et al. [11] in the zig-zag ascension regime, conveniently made dimensionless, is proposed to determine the bubble terminal velocity for a wide range of bubble sizes and fluid properties. Furthermore, the crosspoint of both correlations gives the critical Weber number, We c = (ρ l U 2 T D/σ) c , at which the transition from a rectilinear to a zig-zag bubble motion takes place in a liquid of a given Morton number, Mo = gµ 4 l /σ 3 ρ l . Concerning the numerical simulations, two different open source solvers have been evaluated, i.e. InterFoam and Gerris Flow Solver, to describe the motion of a stable bubble rising with a rectilinear path by performing two-dimensional axisymmetric simulations. The simulations show the presence of parasitic currents and variable results depending on the mesh resolution in the case of InterFoam, whereas no spurious results are observed in Gerris, which is therefore more suitable for these kinds of flows. Finally, the numerical results indicate that the gas properties hardly affect the bubble terminal velocity and shape, although they show that the flow field inside the bubble is highly affected by the gas density and viscosity. This result can be of relevance in heat and mass transfer processes where the mass diffusion or heat exchange can be enhanced by the convective motion induced inside the bubble.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.