Effect of transient pinning on stability of drops sitting on an inclined plane

Berejnov, Viatcheslav; Thorne, Robert

doi:10.1103/physreve.75.066308

Cited by 48 publications

(63 citation statements)

References 24 publications

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“…On the other hand, droplet B moves very slightly downhill as its associated stable state is displaced to the left and macroscopically it appears to be pinned at the substrate. These behaviours are consistent with the experiments reported by Berejnov & Thorne (2007), in which they observed a transient pinning and depinning of the contact line as the inclination angle was varied. Figure 7(f ) shows that when the inclination angle exceeds some critical angle, φ crit , all equilibria disappear and the droplets freely move downhill.…”

Section: N Savva and S Kalliadasissupporting

confidence: 82%

“…We demonstrated the existence of a critical inclination angle and confirmed qualitatively the transient dynamics reported in the work of Berejnov & Thorne (2007). We also examined in detail how the critical angle is affected by topographical and/or chemical heterogeneities and their orientation and deduced an approximate relation for the critical inclination angle, which is valid when we have small-amplitude, single-wavelength, periodic heterogeneities.…”

Section: Discussionsupporting

confidence: 60%

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Droplet motion on inclined heterogeneous substrates

Savva

Kalliadasis

2013

J. Fluid Mech.

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We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasistatic dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick-slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.

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Section: N Savva and S Kalliadasissupporting

confidence: 82%

Section: Discussionsupporting

confidence: 60%

Droplet motion on inclined heterogeneous substrates

Savva

Kalliadasis

2013

J. Fluid Mech.

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“…We resolve this by noting that in the course of tilting, the width does not change: there is no force to move the contact line perpendicular to the direction of gravity and the critical width W c equals the initial width. A second problem is that contact line shapes assumed in earlier work [7], i.e., circles or curves connected by straight segments parallel with gravity, are at odds with experimental observations [8] and our simulated critical shapes (Fig. 4).…”

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confidence: 57%

“…Simplifications that have allowed theoretical progress in predicting the tilted droplet shape and the roll-off angle include fixing the contact line or the contact angle distribution along the contact line [7]. However, these simplified geometries are at odds with experimental observations [8]. Another approach has been to ignore the constraints entirely and analyze the problem as if the contact line is free to move [9].…”

mentioning

confidence: 99%

Droplets on Inclined Plates: Local and Global Hysteresis of Pinned Capillary Surfaces

et al. 2014

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Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as an example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history. The diverse and complex shapes of raindrops on a window strikingly illustrate the difficulty in understanding shapes of droplets under the influence of surface tension and gravity. Early theoretical work by Laplace, Young, and Gauss [1] showed that at equilibrium, a droplet touches a solid surface at a unique angle, the Young contact angle θ Y . In practice, however, the contact angle of static droplets often deviates from the Young angle, because the contact line gets pinned on physical or chemical defects before it has equilibrated to the lowest energy [2]. This results in a net force at the contact line, which can, akin to friction, balance gravity or shear in static droplets or slow down moving droplets. The range over which the angle can vary is bracketed by a receding angle θ r and an advancing angle θ a , as has been observed for stationary droplets and moving droplets alike [3]. They depend on the density of surface defects [4] and are often treated as constants for a given liquid-substrate combination, although it is observed and understood that these parameters are in fact asymptotes for vanishing defect size relative to droplet size [5]. Contact lines with angles in the hysteresis range ½θ r ; θ a do not move, and this explains qualitatively why droplets can remain stuck. These immobile drops are not only fascinating to observe; the minimal force to set them in motion is highly relevant technically, e.g., for condensers, pesticide spraying and water-repelling surfaces [6].

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“…The evaporation method is http://dx.doi.org/10.1016/j.apsusc.2015.07.078 0169-4332/© 2015 Elsevier B.V. All rights reserved. a simple modification of the above method and Â r is acquired as the evaporating drop begins to shrink [10][11][12][13][14][15][16][17]. In general, CAH on a real surface is attributed to two mechanisms: (i) adhesion hysteresis associated with molecular rearrangement on solid surfaces by wetting [7,18,19], (ii) localized defects associated with hydrophilic blemishes or surface roughness [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Facile manipulation of receding contact angles of a substrate by roughening and fluorination

Sheng

et al. 2015

Applied Surface Science

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Effect of transient pinning on stability of drops sitting on an inclined plane

Cited by 48 publications

References 24 publications

Droplet motion on inclined heterogeneous substrates

Droplet motion on inclined heterogeneous substrates

Droplets on Inclined Plates: Local and Global Hysteresis of Pinned Capillary Surfaces

Facile manipulation of receding contact angles of a substrate by roughening and fluorination

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