Draining Collars and Lenses in Liquid-Lined Vertical Tubes

Jensen, Oliver E.

doi:10.1006/jcis.1999.6551

Cited by 30 publications

(37 citation statements)

References 39 publications

(162 reference statements)

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“…1, where the velocity V is plotted as a function of the slug length L (the horizontal dashed line illustrates Eq. [1]). Because of a film left behind, the drop gets shorter during the fall-but we checked that this variation remained always smaller than 5%, which allowed us to consider the slug velocity a constant during the whole motion.…”

Section: Dry Versus Wetmentioning

confidence: 93%

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Falling Slugs

Bico

Quéré

2001

Journal of Colloid and Interface Science

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The fall of viscous slugs in vertical capillary tubes is described. Deviations toward Poiseuille law are analyzed by taking into account the dissipation in menisci, together with the existence of a film behind the slug. Slugs are found to fall slower in dry tubes than in prewetted ones, which is quantitatively discussed in term of viscous friction. A criterion for the minimal length of the slug obeying the Poiseuille solution is finally derived. C 2001 Academic Press

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Section: Dry Versus Wetmentioning

confidence: 93%

“…Equation [1] is independent of the slug length L, since the latter quantity fixes both the weight and the viscous force. If it is obeyed, the liquid viscosity can be simply deduced from the slug velocity.…”

Section: Introductionmentioning

confidence: 99%

Falling Slugs

Bico

Quéré

2001

Journal of Colloid and Interface Science

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“…͑13͒, has been estimated by assuming h w = b and h m = 1.5 nm ͑the typical molecular size obtained of the silicone oil employed, which has molar mass 1500 g/mol and density 950 kg/ m 3 ͒. Although we did not address the prewetted-tube case-throughly investigated by Jensen 22 -we observe that the theoretical curve derived for small contact angles also fits these data with ␣ = 5.2.…”

Section: Scaling Laws For a Slug Falling At Constant Velocitymentioning

confidence: 86%

Gravity-driven slug motion in capillary tubes

Lunati

2009

Physics of Fluids

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The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier-Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists ͑i.e., due to hydrodynamic deformation of the interface͒. Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug ͑i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines͒. Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quéré ͓J. Bico and D. Quéré, J. Colloid Interface Sci. 243, 262 ͑2001͔͒, the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci ͑not considered in previous studies͒ has to be considered for large contact angles.

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“…Increasing the precursor film thickness to η = 0.01 has marginal effect; increasing by a further order of magnitude (Figure 11(c)) increases drop speeds but again causes drops in vertical tubes to fall increasingly slowly compared to tilted tubes. We infer that the drop dynamics are controlled by a balance between dissipation at the advancing contact line and release of potential energy (as in [5,10]), so that wider drops are subject to greater dissipation and therefore travel slower. (In the most extreme case, α = π/2 in figure 11(d), the front of the drop wraps entirely around the interior of the tube to become a collar for t 8.)…”

Section: Motion Of An Isolated Dropmentioning

confidence: 99%

“…Blow-up may be regularized by retaining the fully nonlinear expression for the interfacial curvature in the governing evolution equation. This captures the growth of a collar on the exterior of a tube into an isolated bead or drop [7,8], or the growth and snap-off of a collar on the interior of a tube to form an occlusive liquid bridge [9,10]. Beads or bridges form on vertical tubes only if the Bond number is sufficiently small; strong gravitational forcing suppresses the initial collar growth by saturating the primary Plateau-Rayleigh instability at small amplitudes [11,12].…”

Section: Introductionmentioning

confidence: 99%

Liquid film dynamics in horizontal and tilted tubes: Dry spots and sliding drops

et al. 2007

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Using a model derived from lubrication theory, we consider the evolution of a thin viscous film coating the interior or exterior of a cylindrical tube. The flow is driven by surface tension and gravity and the liquid is assumed to wet the cylinder perfectly. When the tube is horizontal, we use large-time simulations to describe the bifurcation structure of the capillary equilibria appearing at low Bond number. We identify a new film configuration in which an isolated dry patch appears at the top of the tube and demonstrate hysteresis in the transition between rivulets and annular collars as the tube length is varied. For a tube tilted to the vertical, we show how a long initially uniform rivulet can break up first into isolated drops and then annular collars, which subsequently merge. We also show that the speed at which a localized drop moves down the base of a tilted tube is non-monotonic in tilt angle.

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Draining Collars and Lenses in Liquid-Lined Vertical Tubes

Cited by 30 publications

References 39 publications

Falling Slugs

Falling Slugs

Gravity-driven slug motion in capillary tubes

Liquid film dynamics in horizontal and tilted tubes: Dry spots and sliding drops

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