Contact line singularity at partial wetting during evaporation driven by substrate heating

Janecek, Vladislav; Nikolayev, Vadim

doi:10.1209/0295-5075/100/14003

Cited by 33 publications

(48 citation statements)

References 13 publications

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“…where the right hand side is finite. The integral in the left hand side can only be convergent if Q(r) → 0 when r → ∞ which proves equation (24). It means that the overall mass flux transferred to the gas environment is zero, which is consistent with the assumption of thermodynamic equilibrium at r → ∞.…”

Section: Mass Conservation Issuesupporting

confidence: 68%

“…We propose a rigorous solution for the case of diffusioncontrolled evaporation, when an inert gas is present in the atmosphere. Our work follows recent studies dedicated to the case of a liquid surrounded by its pure vapor [24][25][26], where the phase change is controlled by the latent heat effect.…”

Section: Resultsmentioning

confidence: 91%

“…. N, α and p. N equations are provided by writing equation (38) at the nodes x = x i , one more by the continuity of solution at x = L c , and the last by the mass balance (24).…”

Section: Appendix B Solution Methods For the Integro-differential Equmentioning

confidence: 99%

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Can hydrodynamic contact line paradox be solved by evaporation–condensation?

Janecek

Doumenc

Guerrier

et al. 2015

Journal of Colloid and Interface Science

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We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere above the liquid. The noslip condition is imposed at the solid-liquid interface and the system is assumed to be isothermal. The mass exchange dynamics is controlled by vapor diffusion in the inert gas and interfacial kinetic resistance. The coupling between the liquid meniscus curvature and mass exchange is provided by the Kelvin effect. The atmosphere is saturated and the substrate moves at a steady velocity with respect to the liquid wedge. A multi-scale analysis is performed. The liquid dynamics description in the phase-change-controlled microregion and visco-capillary intermediate region is based on the lubrication equations. The vapor diffusion is considered in the gas phase. It is shown that from the mathematical point of view, the phase exchange relieves the contact line singularity. The liquid mass is conserved: evaporation existing on a part of the meniscus and condensation occurring over another part compensate exactly each other. However, numerical estimations carried out for three common fluids (ethanol, water and glycerol) at the ambient conditions show that the characteristic length scales are tiny.

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Section: Mass Conservation Issuesupporting

confidence: 68%

Section: Resultsmentioning

confidence: 91%

See 1 more Smart Citation

Can hydrodynamic contact line paradox be solved by evaporation–condensation?

Janecek

Doumenc

Guerrier

et al. 2015

Journal of Colloid and Interface Science

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“…Here we consider the contact line motion of a volatile liquid in contact with an atmosphere of its pure vapor, see [20][21][22][23][24] and references therein. We show that the lubrication equation is perfectly regular when evaporation/condensation processes are taken into account.…”

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confidence: 99%

Moving contact line of a volatile fluid

et al. 2013

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Interfacial flows close to a moving contact line are inherently multi-scale. The shape of the interface and the flow at meso-and macroscopic scales inherit an apparent interface slope and a regularization length, both called after Voinov, from the dynamical processes at work at the microscopic level. Here, we solve this inner problem in the case of a volatile fluid at equilibrium with its vapor. The evaporative/condensation flux is then controlled by the dependence of the saturation temperature on interface curvature -the so-called Kelvin effect. We derive the dependencies of the Voinov angle and of the Voinov length as functions of the substrate temperature. The relevance of the predictions for experimental problems is finally discussed.The dynamics of a macroscopic solid plunging in a liquid bath [1,2] or withdrawn from it [3-5] depends sensitively on its wetting properties i.e. on the intermolecular interactions at the nanoscopic scale. The motion of the contact line separating wet from dry regions is therefore an inherently multi-scale problem. Amongst the important consequences of the coupling between inner and outer scales (Fig. 1), the speed at which a contact line can recede over a flat solid surface cannot exceed a critical value, associated to a dynamical wetting transition which leads to the formation of a dewetting ridge [6,7], of a V-shaped dewetting corner [1,[8][9][10] or to the entrainment of films [2, 10, 11] (see [12,13] for detailed reviews). In many applications, such as coating, imbibition of powders, immersion lithography or boiling-free heating, these entrainment phenomena are crucial limiting factors for industrial processes. Fig. 1 shows schematically the structure of the flow close to a moving contact line. Even for an infinitesimal velocity U , there exists a range of mesoscopic scales -roughly six decades -separating the microscopic scale from the macroscopic length L, in which the diverging viscous stress is balanced by a gradient of capillary pressure. This balance can be made quantitative in the lubrication approximation, for which the angles are assumed small, and which gives a third order differential equation for the interface profile h(x):where η is the liquid dynamic viscosity and γ the surface tension; U is positive for an advancing contact line. This equation has an exact solution [14] which reduces to the asymptotic form proposed by Voinov [15] far from the contact line, but for x ≪ L:θ V is by definition the apparent contact angle in the static case (U = 0), which can be different from the Young angle θ Y due to out of equilibrium processes taking place at a microscopic scale. The Voinov length ℓ V is also a quantity defined in the mesoscopic range of scales but inherited from the inner region, where the problem is regularized. The mesoscopic solution (2) must also be matched at the macroscopic scale L to an outer solution where viscosity can usually be neglected. Fig. 1 features the case of a spreading drop or of a growing bubble but the outer matching problem has been s...

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“…While the overall evaporation is weak, the evaporation mass flux varies sharply over the film area. The evaporation rate is especially strong near the contact line [11,12], which creates high apparent contact angles [13] in spite of the complete wetting conditions at equilibrium. The high contact angle, in its turn, causes the capillary dewetting phenomenon and a ridge-like structure along the contact line (cf.…”

Section: D Reconstructionmentioning

confidence: 99%

3D reconstruction of dynamic liquid film shape by optical grid deflection method

et al. 2018

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In this paper, we describe the optical grid deflection method used to reconstruct the 3D profile of liquid films deposited by a receding liquid meniscus. This technique uses the refractive properties of the film surface and is suitable for liquid thickness from several microns to millimeter. This method works well for strong interface slopes and changing in time film shape; it applies when the substrate and fluid media are transparent. The refraction is assumed to be locally unidirectional. The method is particularly appropriate to follow the evolution of parameters such as dynamic contact angle, triple liquid-gas-solid contact line velocity or dewetting ridge thickness.

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Contact line singularity at partial wetting during evaporation driven by substrate heating

Cited by 33 publications

References 13 publications

Can hydrodynamic contact line paradox be solved by evaporation–condensation?

Can hydrodynamic contact line paradox be solved by evaporation–condensation?

Moving contact line of a volatile fluid

3D reconstruction of dynamic liquid film shape by optical grid deflection method

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