Global models for moving contact lines

This paper proposes a simple scenario to describe the coalescence of sessile droplets. This scenario predicts a power-law growth of the bridge between the droplets. The exponent of this power law depends on the driving mechanism for the spreading of each droplet. To validate this simple idea, the coalescence is simulated numerically and a basic experiment is performed. The fluid dynamics problem is formulated in the lubrication approximation framework and the governing equations are solved in the commercial finite element software COMSOL. Although a direct comparison of the numerical results with experiment is difficult because of the sensitivity of the coalescence to the initial and operating conditions, the key features of the event are qualitatively captured by the simulation and the characteristic time scale of the dynamics recovered. The experiment consists of inducing coalescence by pumping a droplet through a substrate which grows and ultimately coalesces with another droplet resting on the substrate. The coalescence was recorded using high-speed imaging and also confirmed the power-law growth of the neck.

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“…This result was later confirmed by others. 14,15 In the symmetric case for which R 1 = R 2 , Eq. ͑3͒ reduces to…”

Section: A Simple View On the Coalescence Dynamicsmentioning

confidence: 99%

Modeling the coalescence of sessile droplets

Sellier

Trelluyer

2009

Biomicrofluidics

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“…While it might appear that imposing perturbations of this kind is rather restrictive since a precursor film is not always present in physical experiments or technological applications, this approach is actually quite general. As mentioned earlier, a number of works [11,17,19] have shown that the main features of the flow are not influenced significantly by the choice of the regularizing method at the contact line; for the macroscopic flow properties (in particular, instability development), the main factor is the actual length-scale that is introduced at the front, and not the regularizing method itself. This lengthscale determines the degree of energy dissipation at the front, and one expects that its spatial variation can have significant influence on the macroscopic flow properties.…”

Section: Stability Of the Flowmentioning

confidence: 99%

“…The assumptions of this approach, as well as the details of our computational methods are given elsewhere [8,9,17]. For completeness, here we give the basic outline, and refer the interested reader to these earlier works for details.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Greenspan [18] Dussan [20] or Hocking and Rivers [21]). Diez et al [17] have recently performed an extensive analysis of the computational performance of these regularizing mechanisms applied to the spreading drop problem. In that paper it is shown that the results are rather insensitive to the choice of the model, consistently with, e.g.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Flow of thin films on patterned surfaces

Kondic

Diez

2003

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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We present fully nonlinear time-dependent simulations of the gravity driven flow of thin wetting liquid films. The computations of the flow down a homogeneous substrate show that the contact line where liquid, solid, and gas phase meet becomes unstable and develops patterns. These computations are extended to inhomogeneous surfaces, and show that inhomogeneity can induce instability of the fluid front. In particular, we analyze flow on patterned surfaces, where surface inhomogeneity is introduced in a controllable manner. We discuss the conditions that need to be satisfied so that surface patterns, lead to predictable selective wetting of the substrate. Applications of these results to technologically relevant flows are discussed. #

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“…(5) using standard finite differences [34] and adaptive mesh refinement. The disparate length scales involved in this problem make the numerical computations prohibitively expensive.…”

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confidence: 99%

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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Global models for moving contact lines

Cited by 103 publications

References 39 publications

Modeling the coalescence of sessile droplets

Modeling the coalescence of sessile droplets

Flow of thin films on patterned surfaces

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

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