On bubble motion in a Hele-Shaw cell, a possibility to study two-phase flows under reduced gravity

Eck, W.; Siekmann, J.

doi:10.1007/bf01047407

Cited by 24 publications

(31 citation statements)

References 7 publications

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“…Any element of length d of the contact line thus experiences a force normal to itself and proportional to γca 2/3 d . Following the work of Eck & Siekmann (1978) on the motion of bubbles in Hele-Shaw cells, one can project the force contribution from all elements of the contact line and sum them to yield a global force proportional to γCa 2/3 . The drop has two circular contact lines of length 2πR each, so that the associated force is…”

Section: Contact Line Dragmentioning

confidence: 99%

“…For a receding meniscus, the viscous stress applied by the solid on the moving meniscus can be computed exactly. Cantat (2013) gives the force f r per unit length on a receding meniscus with a local capillary number ca, f r = 3.84γca 2/3 = 3.84γ (Ca cos ϕ) We integrate this force along the rear boundaries of the drop to obtain the corresponding viscous force (Eck & Siekmann 1978),…”

Section: Contact Line Dragmentioning

confidence: 99%

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Drops and bubbles in wedges

Reyssat

2014

J. Fluid Mech.

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We investigate experimentally the spontaneous motion of drops and bubbles confined between two plates forming a narrow wedge. Such discoidal objects migrate under the gradient in interfacial energy induced by the non-homogeneous confinement. The resulting capillary driving force is balanced by viscous resistance. The viscous friction on a drop bridging parallel plates is estimated by measuring its sliding velocity under gravity. The viscous forces are the sum of two contributions, from the bulk of the liquid and from contact lines, the relative strength of which depends on the drop size and velocity and the physical properties of the liquid. The balance of capillarity and viscosity quantitatively explains the dynamics of spontaneous migration of a drop in a wedge. Close the tip of the wedge, bulk dissipation dominates and the migrating velocity of drops is constant and independent of drop volume. The distance between the drop and the tip of the wedge is thus linear with time t: x(t) ∼ t 0 − t, where t 0 is the time at which the drop reaches the tip of the wedge. Far away from the apex, contact lines dominate the friction, the motion is accelerated toward the tip of the wedge and velocities are higher for larger drops. In this regime, it is shown that x(t) ∼ (t 0 −t) 4/13 . The position and time of the crossover between the two dissipation regimes are used to write a dimensionless equation of motion. Plotted in rescaled variables, all experimental trajectories collapse to the prediction of our model. In contrast to drops, gas bubbles in a liquid-filled wedge behave as non-wetting objects. They thus escape the confinement of the wedge to reduce their surface area. The physical mechanisms involved are similar for drops and bubbles, so that the forces acting have the same mathematical structures in both cases, except for the sign of the capillary driving force and a numerical factor. We thus predict and show experimentally that the trajectories of drops and bubbles obey the same equation of motion,except for a change in the sign of t 0 − t.

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Section: Contact Line Dragmentioning

confidence: 99%

Section: Contact Line Dragmentioning

confidence: 99%

Drops and bubbles in wedges

Reyssat

2014

J. Fluid Mech.

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“…No velocity data were reported. Eck and Siekmann (1978) conducted gravity driven bubble experiments in a Hele-Shaw cell. They observed circular-shaped bubbles at low Capillary number, defined as:…”

Section: Introductionmentioning

confidence: 99%

The velocity and shape of convected elongated liquid drops in narrow gaps

Shad

Salarieh

Maini

et al. 2010

Journal of Petroleum Science and Engineering

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“…This regime is applicable for gas bubbles in a horizontal Hele-Shaw cell involving a highly viscous liquid, which has been studied analytically and experimentally. [1][2][3][4][5][6] When the bubble Reynolds number is moderate or high, i.e., Re ≥ 1, the inertial forces cannot be neglected, and all three forces are significant. The moderate Re regime (Re in the order of 100) refers to a gas bubble in a tilted Hele-Shaw cell filled with a low viscous a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell

et al. 2014

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Buoyancy-driven single bubble behaviour in a vertical Hele-Shaw cell with various gap Reynolds numbers Re(h/d)2 has been studied. Two gap thicknesses, h = 0.5 mm (Re(h/d)2 = 1.0–8.5) and 1 mm (Re(h/d)2 = 6.0–50) were used to represent low and high gap Reynolds number flow. Periodic shape oscillation and path vibration were observed once the gap Reynolds number exceeds the critical value of 8.5. The bubble behaviour was also numerically simulated by taking a two-dimensional volume of fluid method coupled with a continuum surface force model and a wall friction model in the commercial computational fluid dynamics package Fluent. By adjusting the viscous resistance values, the bubble dynamics in the two gap thicknesses can be simulated. For the main flow properties including shape, path, terminal velocity, horizontal vibration, and shape oscillation, good agreement is obtained between experiment and simulation. The estimated terminal velocity is 10%–50% higher than the observed one when the bubble diameter d ≤ 5 mm, h = 0.5 mm and 9% higher when d ≤ 18 mm, h = 1.0 mm. The estimated oscillation frequency is 50% higher than the observed value. Three-dimensional effects and spurious vortices are most likely the reason for this inaccuracy. The simulation confirms that the thin liquid films between gas bubbles and the cell walls have a limited effect on the bubble dynamics.

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On bubble motion in a Hele-Shaw cell, a possibility to study two-phase flows under reduced gravity

Cited by 24 publications

References 7 publications

Drops and bubbles in wedges

Drops and bubbles in wedges

The velocity and shape of convected elongated liquid drops in narrow gaps

Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell

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