Hydrodynamics of wetting

Voinov, O. V.

doi:10.1007/bf01012963

Cited by 866 publications

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“…In the capillary-dominated regime, the Cox-Voinov law describes the dependence of the dynamic contact line on the spreading rate [4][5][6]. Our model indeed displays an excellent agreement with the Cox-Voinov law for different equilibrium contact angles θ Y [ Fig.…”

Section: Fig 2 (Color Online) Comparison Of the Mobility With And Wsupporting

confidence: 64%

“…To extend the classical description to the partial-wetting regime, one can supplement it with nonhydrodynamic interactions as a boundary condition at the contact line [1,4]. When capillary forces are the dominant driving mechanism, the dynamic contact angle, [4][5][6], where Ca ¼ ηU=γ is the capillary number with liquid viscosity η and contact-line velocity U; l M and l μ are characteristic macroscopic and microscopic length scales in the problem. Despite its success in matching experimental data, invoking this boundary condition does not address the question of how the nonhydrodynamic forces determine the emerging dynamics at the macroscopic scale.…”

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confidence: 99%

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Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

et al. 2015

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When a liquid touches a solid surface, it spreads to minimize the system's energy. The classic thin-film model describes the spreading as an interplay between gravity, capillarity, and viscous forces, but it cannot see an end to this process as it does not account for the nonhydrodynamic liquid-solid interactions. While these interactions are important only close to the contact line, where the liquid, solid, and gas meet, they have macroscopic implications: in the partial-wetting regime, a liquid puddle ultimately stops spreading. We show that by incorporating these intermolecular interactions, the free energy of the system at equilibrium can be cast in a Cahn-Hilliard framework with a height-dependent interfacial tension. Using this free energy, we derive a mesoscopic thin-film model that describes the statics and dynamics of liquid spreading in the partial-wetting regime. The height dependence of the interfacial tension introduces a localized apparent slip in the contact-line region and leads to compactly supported spreading states. In our model, the contact-line dynamics emerge naturally as part of the solution and are therefore nonlocally coupled to the bulk flow. Surprisingly, we find that even in the gravity-dominated regime, the dynamic contact angle follows the Cox-Voinov law. Pour a glass of water on a table; what happens? It spreads for a while and stops. This process seems simple enough to be described by a reduced-order model, and indeed the classic thin-film model is a step in this direction [1]. This model can be derived from the Stokes equations using the lubrication approximation, but it contains no information about the interactions between the liquid and the underlying solid surface. While these interactions are of nonhydrodynamic origin and only become significant at heights less than ∼100 nm [2], they have pronounced macroscopic implications: the classic model, which does not incorporate these intermolecular interactions, predicts that the liquid never stops spreading, in stark contrast to the basic observation of a static puddle that forms in the partialwetting regime.A liquid is said to be partially wetting to a surface when it forms a contact angle in the range of 0 < θ Y ≤ π=2 at equilibrium. This equilibrium contact angle is well described by the Young equation, cos θ Y ¼ ðγ sg − γ sl Þ=γ, where γ sg , γ sl and γ are solid-gas, solid-liquid, and liquidgas interfacial energies [3]. To extend the classical description to the partial-wetting regime, one can supplement it with nonhydrodynamic interactions as a boundary condition at the contact line [1,4]. When capillary forces are the dominant driving mechanism, the dynamic contact angle, [4][5][6], where Ca ¼ ηU=γ is the capillary number with liquid viscosity η and contact-line velocity U; l M and l μ are characteristic macroscopic and microscopic length scales in the problem. Despite its success in matching experimental data, invoking this boundary condition does not address the question of how the nonhydrodynamic forces determine the emer...

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Section: Fig 2 (Color Online) Comparison Of the Mobility With And Wsupporting

confidence: 64%

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confidence: 99%

Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

et al. 2015

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“…We do currently not have any explanation for this behavior. Possible approaches to include the effect of the liquid viscosity include the growth of a viscous boundary layer from the solid substrate into the accelerating liquid as well as viscous friction in the vicinity of the moving three phase contact line during spreading [23]. The latter would introduce a dynamic contact angle that modifies the shape of the liquid-vapor interface around the contact area.…”

Section: Prl 108 074505 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Dynamics of Collapse of Air Films in Drop Impact

et al. 2012

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Liquid drops hitting solid surfaces deform substantially under the influence of the ambient air that needs to be squeezed out before the liquid actually touches the solid. Nanometer-and microsecond-resolved dual wavelength interferometry reveals a complex evolution of the interface between the drop and the gas layer underneath. For intermediate impact speeds (We $ 1 . . . 10) the layer thickness can develop one or two local minima-reproduced in numerical calculations-that eventually lead to the nucleation of solidliquid contact at a We-dependent radial position, from a film thickness >200 nm. Solid-liquid contact spreads at a speed involving capillarity, liquid viscosity and inertia. DOI: 10.1103/PhysRevLett.108.074505 PACS numbers: 47.55.DÀ, 47.55.nd, 47.55.np Liquid drops deform substantially upon impact onto a solid surface. Depending on impact speed they rebound, get deposited on the surface, or disintegrate in a splash (for a review, see Ref.[1]). Following experimental reports of tiny air bubbles being incorporated into drops [2][3][4][5] as well as the suppression of splashing upon reducing the ambient air pressure [6] it became clear that the ambient air plays a non-negligible role in the impact process. To describe the expulsion of the air that initially separates the drop from the solid, several models were formulated [7-9] that describe the drop impact primarily in terms of a balance between the inertia of the decelerating liquid and the excess pressure arising from the viscous squeezeout of the thin air layer. A local pressure maximum right under the drop leads to the formation of a ''dimple'', which should eventually evolve into the enclosed air bubble [9]. Using this model and including corrections due to capillary forces, it was shown that a thin air film of almost constant thickness should develop under the drop [10], and the formation of a thin liquid jet was observed using an axisymmetric, curvilinear description [11]. Mandre et al. [10] suggested that this air film plays an important role, e.g., for the splashing process, but recent experiments by Discroll and Nagel [12] question this scenario: while the presence of interference fringes right under the drop indeed confirms the formation of a dimple, their measurements suggest that direct liquid-solid contact forms very quickly around the dimple, separating dimple from splashing dynamics. Whether air films do play an important role in other regimes of drop impact, how they collapse to establish direct liquid-solid contact, and to what extent the proposed visco-inertial models describe these processes remains unexplored at this stage.In this letter, we address these issues by monitoring the evolution and the collapse of the air film for a wide range of liquid properties (interfacial tension , viscosity l , density l ) at moderate impact speeds. To do so, we develop an advanced high-speed dual wavelength interferometry technique that allows us to extract full thickness profiles with an unprecedented resolution of % 10 nm and 50 s. Focusing on...

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“…The most popular law for drop spreading is certainly the so-called Tanner law [23,22] with n = 1/10. This evolution can be simply obtained by considering that the shape of the drop is a thin spherical cap and that the contact angle follows the Cox-Voinov relation.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of spreading drops

Legendre

Maglio

2013

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 10539Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr g r a p h i c a l a b s t r a c t• Numerial simulation of spreading drops on a wettable surface.• We discuss the effect of the main parameters (density, viscosity, surface tension, drop radius and wettability).• Power law evolutions observed in experiments (t 1 /2, t 1 /10) are recovered and discussed.• The combined effect of viscosity and wettability has a significant effect on the spreading. Keywords:Drop spreading Numerical simulation a b s t r a c tWe consider a liquid drop that spreads on a wettable surface. Different time evolutions have been observed for the base radius r depending of the relative role played by inertia, viscosity, surface tension and the wetting condition. Numerical simulations were performed to discuss the relative effect of these parameters on the spreading described by the evolution of the base radius r(t) and the spreading time t S . Different power law evolutions r(t) ∝ t n have been observed when varying the parameters. At the early stage of the spreading, the power law t 1/2 (n = 1/2) is observed as long as capillarity is balanced by inertia at the contact line. When increasing the viscosity contribution, the exponent n is found to increase despite the increase of the spreading time. The effect of the surface wettability is observed for liquids more viscous than water. For a small contact angle, the power law t 1/2 is then followed by the famous Tanner law t 1/10 once the drop shape has reached a spherical cap. IntroductionWhen a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid (some milli-seconds for millimeter sized water drops) while it takes a much longer time for viscous liquids to completely spread. From the literature [22,17,9,1,6,3,2,24,7], it appears that several time evolutions can be observed for the base radius depending if inertia, viscosity and/or * Corresponding authors.

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Hydrodynamics of wetting

Cited by 866 publications

References 9 publications

Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

Dynamics of Collapse of Air Films in Drop Impact

Numerical simulation of spreading drops

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