A study of the advancing interface

Hoffman, Richard L.

doi:10.1016/0021-9797(83)90287-4

Cited by 151 publications

(70 citation statements)

References 46 publications

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“…For example, one can measure the interface angle at some distance to the contact line or use the angle formed by extrapolating the interface to the solid wall. 22 Various experiments 11,[23][24][25] have adopted the latter scheme by assuming the interface in the bulk to be spherical, which is a good approximation for CaӶ 1. We take the same scheme to facilitate the comparison.…”

Section: Resultsmentioning

confidence: 99%

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

2011

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The Cahn–Hilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the near-wall layer by the relaxation of a wall energy. The first part of the paper elucidates the role of the wall relaxation in a flowing system, with two main results. First, we show that wall energy relaxation produces a dynamic contact angle that deviates from the static one, and derive an analytical formula for the deviation. Second, we demonstrate that wall relaxation competes with Cahn–Hilliard diffusion in defining the apparent contact angle, the former tending to “rotate” the interface at the contact line while the latter to “bend” it in the bulk. Thus, varying the two in coordination may compensate each other to produce the same macroscopic solution that is insensitive to the microscopic dynamics of the contact line. The second part of the paper exploits this competition to develop a computational strategy for simulating realistic flows with microscopic slip length at a reduced cost. This consists in computing a moving contact line with a diffusion length larger than the real slip length, but using the wall relaxation to correct the solution to that corresponding to the small slip length. We derive an analytical criterion for the required amount of wall relaxation, and validate it by numerical results on dynamic wetting in capillary tubes and drop spreading.

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Section: Resultsmentioning

confidence: 99%

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

2011

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“…For drop moving on a dry solid, this integration gives a logarithmic singularity near the tip of the wedge, which must be modeled by a molecular cut-off length. 19 This integration yields μV rl/θ , where the factor l arises from the logarithmic cut-off. 8 Hoffman 19 showed l 15 for liquid spreading on a dry surface, while Bico and Quéré 20 obtained l 5 for liquid spreading on a wet surface, a value we will use herein.…”

Section: 11mentioning

confidence: 99%

“…19 This integration yields μV rl/θ , where the factor l arises from the logarithmic cut-off. 8 Hoffman 19 showed l 15 for liquid spreading on a dry surface, while Bico and Quéré 20 obtained l 5 for liquid spreading on a wet surface, a value we will use herein. The reduction of the viscous friction in the latter case results from the wedge slipping on the pre-wetted film.…”

Section: 11mentioning

confidence: 99%

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The fastest drop climbing on a wet conical fibre

Thoroddsen

2013

Physics of Fluids

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We use high-speed video imaging to study the capillary-driven motion of a micro-droplet along the outside of a pre-wetted conical fiber. The cones are fabricated on a glass-puller with tip diameters as small as 1 μm, an order of magnitude smaller than in previous studies. The liquid is fed through the hollow fiber accumulating at the fiber tip to form droplets. The droplets are initially attached to the opening as they grow in size before detaching and traveling up the cone. This detachment can produce a transient oscillation of high frequency. The spatial variation of the capillary pressure drives the droplets towards the wider side of the cone. Various liquids were used to change the surface tension by a factor of 3.5 and viscosity by a factor of 1500. Within each droplet size and viscous-dissipation regime, the data for climbing speeds collapse on a single curve. Droplets traveling with and against gravity allow us to pinpoint the absolute strength of the driving capillary pressure and viscous stresses and thereby determine the prefactors in the dimensionless relationships. The motions are consistent with earlier results obtained from much larger cones. Translation velocities up to 270 mm/s were observed and overall the velocities follow capillary-viscous scaling, whereas the speed of the fastest droplets is limited by inertia following their emergence at the cone tip.

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“…Rose and Heins (1962) were among the first who highlighted the relation between the advancing contact angle and average velocity U avg of three-phase contact line. Later, various researchers like Hoffman (1975), Tanner (1979) and Blake (2006) studied the wetting behavior and dependency of the advancing contact angle on Ca and the static contact angle.…”

Section: Frontiers In Heat Pipesmentioning

confidence: 99%

Hydrodynamics of a Confined Meniscus in a Square Capillary Tube at Low Capillary Numbers

Rana¹,

Sikarwar²,

Khandekar³

et al. 2014

Frontiers in Heat Pipes

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In microchannel fluid flow, understanding of the liquid-gas interface behavior is vital for developing a wide range of microfluidic devices. The dynamic contact angle of the liquid-air meniscus varies with its velocity and the ensuing meniscus shape has profound effect on the local transport characteristics in its vicinity. Depending on the application, dynamic menisci shapes eventually control the momentum, heat and mass transport coefficients in two-phase microchannel flow geometries, where such conditions are often encountered. To better understand the effect of dynamic contact angle on meniscus shape, high speed visualization of menisci of four different liquids (water, ethanol, glycerin and silicon oil) has been undertaken at different Capillary numbers. Quantitative information of the velocity field and its distribution near the moving liquid-air interface has been done using micro-PIV measurements in a 1 mm × 1 mm dry square capillary having deionized water as the working fluid. This provides vital information on the local flow transport characteristics (two-dimensional velocity fields on a longitudinal plane) in the wake of the meniscus. To augment and complement the study, three-dimensional simulation of the flow field near the liquid-air meniscus has also been performed on Comsol ® , applying the two-phase flow level-set method. The results clearly demonstrate that, while the u-velocity profile in the liquid domain is parabolic (Poiseuille-type flow) in nature away from the interface, it drastically changes (become flatter) as we approach the meniscus. Close to the meniscus the flow becomes three-dimensional with both v and w velocities showing a double-vortex, the strength of the latter being lower than the former. This observation is clearly noted both by PIV data as well as the simulations. The characteristic of the flow field in the meniscus wake is the most important parameter which affects the viscous stress generated due to the meniscus motion. The study reveals that controlling the wettability of the liquid can be an effective tool to control the overall transport behavior of the moving confined meniscus.

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A study of the advancing interface

Cited by 151 publications

References 46 publications

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

The fastest drop climbing on a wet conical fibre

Hydrodynamics of a Confined Meniscus in a Square Capillary Tube at Low Capillary Numbers

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