Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface

Pigeonneau, Franck; Sellier, Antoine

doi:10.1063/1.3629815

Cited by 27 publications

(67 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the low-Reynolds-number limit, the various computational studies based on the BIM (Chi & Leal 1989;Manga & Stone 1995;Pigeonneau & Sellier 2011) consistently show that increasing Bo and B I up to O(10) values slows down the film drainage, while no significant influence of interfacial forces is observed for larger values. Indeed, increasing Bo and B I allows the two boundaries of the film to deform more easily, causing the film thickness to remain more uniform during the drainage process.…”

Section: A Toroidal Bubblementioning

confidence: 77%

“…Among the two situations involving O(1) viscosity ratios (solid and dash-dotted lines in figure 16), the smaller B I the faster the drainage, in agreement with previous low-Reynolds-number findings. In those two cases, the drainage is found to be significantly slower than in the free-surface situations recently considered by Pigeonneau & Sellier (2011), as shown by comparing the solid line with the squares (B I ≈ 3 in both cases) and the dash-dotted line with the triangles (B I 12 in both cases). As this trend is observed for any B I , we can conclude that the difference is due to the viscosity ratio: the smaller Λ, the more efficient the drainage since the stretching of the upper film surface does not induce any significant stress (hence no dissipation) when Λ 1.…”

Section: A Toroidal Bubblementioning

confidence: 85%

See 1 more Smart Citation

Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

et al. 2012

View full text Add to dashboard Cite

The dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid-fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier-Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.

show abstract

Section: A Toroidal Bubblementioning

confidence: 77%

Section: A Toroidal Bubblementioning

confidence: 85%

Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

et al. 2012

View full text Add to dashboard Cite

show abstract

“…This acceleration region is observed far all different bubbles tested, suggesting the development of a positive temperature gradient upstream of the bubble that could result from the interaction between the bubble and the molten glass in the heat transfer balance. Near the top of the crucible, the bubble slowdown may also be due to the hydrodynamic interaction between the bubble and the free surface …”

Section: Resultsmentioning

confidence: 99%

X‐ray imaging of a high‐temperature furnace applied to glass melting

et al. 2019

Self Cite

View full text Add to dashboard Cite

The dynamics of soda‐lime‐silica glass grain melting is investigated experimentally using a nonintrusive technique. A cylindrical alumina crucible is filled with glass cullet and placed into a furnace illuminated by an X‐ray source. This glass granular bed is gradually heated up to 1100°C, leading to its melting and the generation of a size‐distributed population of bubbles rising in the molten glass. An image processing algorithm of X‐ray images of the cullet bed during melting allows the characterization of bubbles size distribution in the crucible as well as their velocity. The introduction of tin dioxide μ‐particles in the glass matrix before melting enhances the texture of the images and makes possible the determination of the bubble‐induced molten glass velocity field by an optical flow technique. The bubble size distribution can be fitted by a log‐normal law, suggesting that it is closely related to the initial size distribution in the cullet bed. The liquid motion induced by the bubbles in Stokes' regime is strongly affected by the flow confinement and the determination of bubble rising velocity along its trajectory unveils the existence of local tiny temperature fluctuations in the crucible. Overall, the measuring techniques developed in this work seem to be very promising for the improvement of models and optimization of industrial glass furnaces.

show abstract

“…During the experiments, bubble motion underwent two stages. The first stage was the buoyant ascent of the bubble toward the interface and the second was the drainage of the interfacial film above the stationary bubble [ Pigeonneau and Sellier , ]. Once the bubble approached the surface, its rise velocity rapidly decreased, forming a protruding hemispherical cap of radius,

R_{cap} \sim R = {(3 V / 4 π)}^{1 / 3}

, where V is the volume of the bubble.…”

Section: Methodsmentioning

confidence: 99%

Film drainage and the lifetime of bubbles

Nguyen

Gonnermann

Chen

et al. 2013

Geochem Geophys Geosyst

View full text Add to dashboard Cite

[1] We present the results of new laboratory experiments that provide constraints on inter bubble film thinning and bubble coalescence as a consequence of liquid expulsion by gravitational and capillary forces. To ensure dynamic similarity to magmatic systems, the experiments are at small Reynolds numbers Re ( 1 ð Þand cover a wide range of Bond numbers (10 À3Bo 10 2 ). Results indicate that at Bo < 0.25 film drainage is due to capillary forces, whereas at Bo > 0.25 gravitational forces result in film thinning. The film drainage time scale is given by t $ C ln () and is orders of magnitude faster than often assumed for magmatic systems. Here, C $ 10 is an empirical constant and is the ratio of initial film thickness to film thickness at the time of rupture and is the characteristic capillary or buoyancy time scale at values of Bo < 0.25 and Bo > 0.25, respectively.

show abstract

Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface

Cited by 27 publications

References 23 publications

Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

X‐ray imaging of a high‐temperature furnace applied to glass melting

Film drainage and the lifetime of bubbles

Contact Info

Product

Resources

About