Droplet on an elastic substrate: Finite Element Method coupled with lubrication approximation

Gielok, Martin; Lopes, Marcus C.; Bonaccurso, Elmar; Gambaryan‐Roisman, Tatiana

doi:10.1016/j.colsurfa.2016.08.001

Cited by 20 publications

(25 citation statements)

References 21 publications

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“…Using the exponential term also allows for going beyond DVLO theory as it is a fair approximation of the structural (hydration) pressure, which agrees well with the experimental data [40]. In that case, K is the magnitude of the structural disjoining pressure component and χ is the hydration layer thickness [41]. The chosen expression for the disjoining pressure allows to obtain an S-shaped isotherm having both alpha and beta-branches [42] (not to be confused with the inclination angles of the wedge).…”

Section: Governing Equations and System Parameterssupporting

confidence: 68%

Edge Wetting: Steady State of Rivulets in Wedges

Kubochkin,

Gambaryan-Roisman

2022

Preprint

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The geometry of rough, textured, fractured and porous media is topologically complicated. Those media are commonly represented by bundles of capillary tubes when modeled. However, angle-containing geometries can serve as a more realistic portrayal of their inner structure. A basic element abidingly inherent to all of them is an open wedge-like channel. The classical theory of capillarity ignoring intermolecular interactions implies that liquid entering the wedge must propagate indefinitely along its spine when the liquid-gas interface is concave. The latter is well-known as a Concus-Finn condition. In the present paper, we show that steady-state rivulets violating Concus-Finn condition can be formed in such channels when the surface forces are taken into account. We present a simple model based on the disjoining pressure approach and analyze the shape of the rivulets in the wedges. Besides, we consider a case when the walls of the wedge are soft and can be deformed by the liquid.

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Section: Governing Equations and System Parameterssupporting

confidence: 68%

Edge Wetting: Steady State of Rivulets in Wedges

Kubochkin,

Gambaryan-Roisman

2022

Preprint

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“…It is not evident what the thickness of the ring-shape area is over which this force is distributed. Most recently, Gielok et al investigated the elastic deformation of a soft substrate by a sessile droplet using FEM calculations coupled with lubrication approximation [52]. The disjoining pressure approach was applied to model the surface traction on the substrate and the effects of material stiffness, substrate size and the parameters of the disjoining pressure model on deformation profile were explored.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The disjoining pressure approach was applied to model the surface traction on the substrate and the effects of material stiffness, substrate size and the parameters of the disjoining pressure model on deformation profile were explored. The three parameters of the disjoining pressure isotherm used in [52] determine the equilibrium contact angle, the adsorbed film thickness and the length scale a. This scale, which is of the order of the capillary layer thickness w mentioned in the work of Lester [10], is the width of the transition region between the macroscopic droplet and the adsorbed film where the influence of the disjoining pressure is significant.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…This scale, which is of the order of the capillary layer thickness w mentioned in the work of Lester [10], is the width of the transition region between the macroscopic droplet and the adsorbed film where the influence of the disjoining pressure is significant. In [52] the parameters of disjoining pressure have been chosen in such a way that the equilibrium contact angle did not change. It was shown that the dimensionless maximum displacement scales with the dimensionless L ec sin θ/a and the solid angle of the deformed substrate near the contact line scales with L ec /a.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Style et al argued that the effect of substrate stiffness on the apparent contact angle is also dependent on droplet size R [41]. In their work, three wetting regimes have been identified theoretically: However, many experimental studies have reported that the contact angle of millimetre-sized droplets on soft substrates with similar surface stress increases with decreasing substrate stiffness [20,21,32 [52].…”

Section: Effects Of Substrate Deformation On Contact Angle and Contacmentioning

confidence: 99%

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Static and dynamic wetting of soft substrates

Chen

Bonaccurso

Gambaryan‐Roisman

et al. 2018

Current Opinion in Colloid & Interface Science

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a b s t r a c tA survey of recent literature on wetting phenomena reveals that there is a fast-growing interest in wetting of soft or deformable substrates, due to its potential applications in many industrial, technical and biological processes. Unlike rigid substrates, a droplet deposited on a soft substrate deforms the substrate via a combination of the normal component of surface tension and the Laplace pressure, i.e. by capillary force and the action of disjoining pressure. In turn, the capillary and disjoining pressure-induced substrate deformation affects the wetting phenomena on the substrate. In this review, we summarize recent achievements on static and dynamic wetting of soft substrates and provide an outlook to future progress. In static wetting, theoretical, numerical and experimental investigations of capillary and disjoining pressure-induced substrate deformation are introduced, and corresponding effects on contact angle and contact angle hysteresis are discussed. In dynamic wetting, the influence of substrate stiffness on spontaneous wetting, droplet impact dynamics, and other types of forced wetting and dewetting is considered. Finally, other interesting capillarity-controlled phenomena occurring on soft and softlike substrates are briefly introduced.

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