Deposition of Langmuir-Blodgett layers

Gennes, P. G. de

doi:10.1007/bf01419552

Cited by 170 publications

(154 citation statements)

References 7 publications

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“…Beyond the leading order expansion of h ′ (x) in Ca, however, (13) and (15) are inconsistent. This casts doubts on the original argument for (15), which should also apply to the class of simple slip models considered here, and which has already been reviewed in a critical light in [12]. In particular, this calls into question de Gennes' theory [15] of contact line instability, which crucially uses (15).…”

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confidence: 82%

Toward a description of contact line motion at higher capillary numbers

Eggers

2004

Physics of Fluids

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The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of the microscopic physics on the large-scale shape of the interface.The moving contact line problem is a famous example of hydrodynamics failing to describe a macroscopic flow phenomenon. But it was only in 1971 that Huh and Scriven [1] discovered that the viscous dissipation in the fluid wedge bordered by a solid and a fluid-gas interface is logarithmically infinite if the standard no-slip boundary condition [2] is applied at the solid surface. Thus infinite force would be required to submerge a solid body, and a drop could never spread on a table.This result is of course contradicted by observation, and physical effects that relieve the singularity have to be invoked near the contact line, which go beyond the standard description. A great variety of possible mechanisms have been proposed, and indeed there is no reason to believe that for different solid-fluid-gas systems always the same mechanism is involved. However, a question rarely considered is whether the choice of different microscopic mechanisms would make a great difference when looked at macroscopically.In a recent paper [3] we compared various microscopic models in the case of perfect wetting. We found that the length scale that appears in the expression for the interface shape is strongly speed dependent, in a fashion that depends on the model. Here we are going to show that this dependence is much weaker in the case of partial wetting, and differences only come in at higher order in an expansion in capillary number Ca = U η/γ, where η is the viscosity of the fluid, and γ the surface tension between liquid and gas. Finite capillary number corrections are of interest for various situations of "forced" wetting, in which Ca is no longer asymptotically small, and previous theories for the dynamic interface angle break down [4].For simplicity, we perform our calculations within the framework of lubrication theory, assuming a parabolic flow profile. This limits applications to the case of small contact angles, but without altering the essential structure of the problem. We consider the neighborhood of a contact line moving with speed U across a solid in a frame of reference in which the contact line is fixed at the origin of the coordinate system (see Fig.1). To relieve the corner singularity, we allow the fluid to slide across the solid surface, following the generalized Navier slip law [5,6,7] at the plate, where h(x) is the thickness of the fluid layer, and λ is taken as a constant r...

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confidence: 82%

Toward a description of contact line motion at higher capillary numbers

Eggers

2004

Physics of Fluids

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“…Here θ e is the equilibrium (receding) contact angle and the speed dependence appears through the capillary number Ca = U η/γ, where η and γ denote viscosity and surface tension. We identify the length as the molecular scale associated with the microscopic physics of wetting [23][24][25][26][27][28][29][30][31]. We obtain a length of the order of 10 nm by fitting the experimental data.…”

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confidence: 99%

“…The precise interpretation of this length depends on the physics at molecular scale, which goes beyond hydrodynamics and beyond the purpose of the present paper [23][24][25][26][27][28][29][30][31].…”

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Coexistence of Two Singularities in Dewetting Flows: Regularizing the Corner Tip

et al. 2009

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Entrainment in wetting and dewetting flows often occurs through the formation of a corner with a very sharp tip. This corner singularity comes on top of the divergence of viscous stress near the contact line, which is only regularized at molecular scales. We investigate the fine structure of corners appearing at the rear of sliding drops. Experiments reveal a sudden decrease of tip radius, down to 20 microns, before entrainment occurs. We propose a lubrication model for this phenomenon, which compares well to experiments. Despite the disparity of length scales, it turns out that the tip size is set by the classical viscous singularity, for which we deduce a nanometric length from our macroscopic measurements.

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“…The case of partial wetting, where the liquid has a finite contact angle θ e at equilibrium, has been studied by de Gennes [6,7]. He finds that the velocity v and the dynamic contact angle θ are related as v = c(θ 2 e /θ 2 − 1)/2, and thus argues that a steady state is achieved in which the liquid will partially wet the plate with a nonvanishing dynamic contact angle for pull-out velocities less than c, while a macroscopic Landau-Levich liquid film, formally corresponding to a vanishing θ, will remain on the plate for higher velocities, as depicted in Fig.…”

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Relaxation of a moving contact line and the Landau-Levich effect

Golestanian

Raphaël

2001

Europhys. Lett.

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The dynamics of the deformations of a moving contact line is formulated. It is shown that an advancing contact line relaxes more quickly as compared to the equilibrium case, while for a receding contact line there is a corresponding slowing down. For a receding contact line on a heterogeneous solid surface, it is found that a roughening transition takes place which formally corresponds to the onset of leaving a Landau-Levich film. We propose a phase diagram for the system in which the phase boundaries corresponding to the roughening transition and the depinning transition meet at a junction point, and suggest that for sufficiently strong disorder a receding contact line will leave a Landau-Levich film immediately after depinning.When a drop of liquid spreads on a solid suface, the contact line, which is the common borderline between the solid, the liquid, and the corresponding equilibrium vapor, undergoes a rather complex dynamical behavior. This dynamics is determined by a subtle competition between the mutual interfacial energetics of the three phases, dissipation and hydrodynamic flows in the liquid, and the geometrical or chemical irregularities of the solid surface [1].A most notable feature of contact lines, which is responsible for their novel dynamics, is their anomalous elasticity as noticed by Joanny and de Gennes [2]. For length scales below the capillary length, which is usually of the order of 1 mm, a contact line deformation of wave vector k, denoted as h(k) in Fourier space, will distort the surface of the liquid over a distance |k| −1 . Assuming that the surface deforms instantaneously in response to the contact line, the elastic energy cost for the deformation can be calculated from the surface tension energy stored in the distorted area, and is thus proportional to |k|, namely E cl = γθ 2 2 dk 2π |k||h(k)| 2 , in which γ is the surface tension and θ is the contact angle [2].The anomalous elasticity leads to interesting equilibrium dynamics, corresponding to when the contact line is perturbed from its static position, as studied by de Gennes [3]. Balancing dE cl dt and the dissipation, which for small contact angles is dominated by the hydrodynamic dissipation in the liquid nearby the contact line, he finds that each deformation mode relaxes ( * ) Permanent address: Institute for Advanced Studies in Basic Sciences -Zanjan 45195-159, Iran.

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Deposition of Langmuir-Blodgett layers

Cited by 170 publications

References 7 publications

Toward a description of contact line motion at higher capillary numbers

Toward a description of contact line motion at higher capillary numbers

Coexistence of Two Singularities in Dewetting Flows: Regularizing the Corner Tip

Relaxation of a moving contact line and the Landau-Levich effect

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