Collective dissolution of microbubbles - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review Fluids Année : 2018

Collective dissolution of microbubbles

Résumé

A microscopic bubble of soluble gas always dissolves in finite time in an undersaturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal pressure through Henry's law, and the concentration in the far field. The presence of neighboring bubbles can significantly slow down this process by increasing the effective background concentration and reducing the diffusing flux of dissolved gas experienced by each bubble. We develop theoretical modeling of such diffusive shielding process in the case of small microbubbles whose internal pressure is dominated by Laplace pressure. We first use an exact semianalytical solution to capture the case of two bubbles and analyze in detail the shielding effect as a function of the distance between the bubbles and their size ratio. While we also solve exactly for the Stokes flow around the bubble, we show that hydrodynamic effects are mostly negligible except in the case of almost-touching bubbles. In order to tackle the case of multiple bubbles, we then derive and validate two analytical approximate yet generic frameworks, first using the method of reflections and then by proposing a self-consistent continuum description. Using both modeling frameworks, we examine the dissolution of regular one-, two-, and three-dimensional bubble lattices. Bubbles located at the edge of the lattices dissolve first, while innermost bubbles benefit from the diffusive shielding effect, leading to the inward propagation of a dissolution front within the lattice. We show that diffusive shielding leads to severalfold increases in the dissolution time, which grows logarithmically with the number of bubbles in one-dimensional lattices and algebraically in two and three dimensions, scaling respectively as its square root and 2/3 power. We further illustrate the sensitivity of the dissolution patterns to initial fluctuations in bubble size or arrangement in the case of large and dense lattices, as well as nonintuitive oscillatory effects.
Fichier principal
Vignette du fichier
michelin2018.pdf (8.37 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-02104825 , version 1 (19-04-2019)

Identifiants

Citer

Sébastien Michelin, Etienne Guérin, Eric Lauga. Collective dissolution of microbubbles. Physical Review Fluids, 2018, 3 (4), ⟨10.1103/PhysRevFluids.3.043601⟩. ⟨hal-02104825⟩
45 Consultations
128 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More