The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei-Eotvos plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions.

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Dynamics of an initially spherical bubble rising in quiescent liquid

Review of direct numerical simulation of fluid–particle mass, momentum and heat transfer in dense gas–solid flows

Bubbly flows involve bubbles randomly distributed within a liquid At large Reynolds number, they experience an agitation that can combine shear-induced turbulence (SIT), large-scale buoyancy-driven flows, and bubble-induced agitation (BIA) The properties of BIA strongly differ from those of SIT They have been determined from studies of homogeneous swarms of rising bubbles Regarding the bubbles, agitation is mainly caused by the wake-induced path instability Regarding the liquid, two contributions must be distinguished The first one corresponds to the anisotropic flow disturbances generated near the bubbles, principally in the vertical direction The second one is the almost isotropic turbulence induced by the flow instability through a population of bubbles, which turns out to be the main cause of horizontal fluctuations Both contributions generate a k−3 spectral subrange and exponential probability density functions The subsequent issue will be to understand how BIA interacts with SIT

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Agitation, Mixing, and Transfers Induced by Bubbles

Two-phase bubbly flow simulation using CFD method: A review of models for interfacial forces

The present work focuses on the collective effect on both bubble dynamics and mass transfer in a dense homogeneous bubble swarm for gas volume fractions alpha up to 30 %. The experimental investigation is carried out with air bubbles rising in a square column filled with water. Bubble size and shape are determined by means of a high-speed camera equipped with a telecentric lens. Gas volume fraction and bubble velocity are measured by using a dual-tip optical probe. The combination of these two techniques allows us to determine the interfacial area between the gas and the liquid. The transfer of oxygen from the bubbles to the water is measured from the time evolution of the concentration of oxygen dissolved in water, which is obtained by means of the gassing-out method. Concerning the bubble dynamics, the average vertical velocity is observed to decrease with alpha in agreement with previous experimental and numerical investigations, while the bubble agitation turns out to be weakly dependent on alpha. Concerning mass transfer, the Sherwood number is found to be very close to that of a single bubble rising at the same Reynolds number, provided the latter is based on the average vertical bubble velocity, which accounts for the effect of the gas volume fraction on the bubble rise velocity. This conclusion is valid for situations where the diffusion coefficient of the gas in the liquid is very low ( high Peclet number) and the dissolved gas is well mixed at the scale of the bubble. It is understood by considering that the transfer occurs at the front part of the bubbles through a diffusion layer which is very thin compared with all flow length scales and where the flow remains similar to that of a single rising bubble.

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H.M. Slagter

Papers

On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers