Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

Saxton, Matthew; Vella, Dominic; Whiteley, Jonathan; Oliver, James M.

doi:10.1007/s10665-016-9892-4

Cited by 12 publications

(12 citation statements)

References 58 publications

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“…The interfacial kinetic resistance does not lead to the singularity relaxation (this was first shown in ref. [30]). Another microscopic phenomenon thus needs to be introduced into the modeling of such a phenomenon to relax the singularity.…”

Section: Discussionmentioning

confidence: 99%

“…Note that the interfacial kinetic resistance alone does not relax the singularity in the hydrodynamic problem. Saxton et al [30] showed that regularization can be achieved by considering both interfacial resistance and hydrodynamic slip. In the present study, similarly to the moving contact line problem considered in our preceding work [26], the Kelvin effect is used to relax the contact line singularity.…”

Section: Hydrodynamic Contact Line Singularity Related To the Mass Exmentioning

confidence: 99%

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Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere

2018

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Evaporation or condensation in the vicinity of the immobile (pinned) contact line in an atmosphere of some inert (noncondensable) gas is considered here in a partial wetting configuration. Such a problem is relevant to many situations, in particular to a drop or a liquid film drying in open air. The thermal effects are not important and the mass exchange rate is controlled by the vapor dynamics in the gas. By following previous works, we account for the weak coupling between the diffusion in the gas and flow in the liquid through the Kelvin effect. Such a problem is nonlocal because of the diffusion in the gas. For generality, we consider a geometry of a liquid wedge posed on a flat and homogeneous substrate surrounded by a gas phase with a diffusion boundary layer of uniform thickness Λ. Similarly to the moving contact line problem, the phase change leads to the hydrodynamic contact line singularity. The asymptotic analysis of this problem is carried out for the liquid wedge of the length L ≫ Λ. Three asymptotic regions are identified: the microscopic one (in which the singularity is relaxed, in the present case with the Kelvin effect) and two intermediate regions. The Kelvin effect alone turns to be sufficient to relax the singularity. The scaling laws for the interface slope and mass evaporation/condensation flux in each region are discussed. It is found that the difference of the apparent contact angle (i.e. interface slope in the second intermediate region) and the equilibrium contact angle is inversely proportional to the square root of Λ and square root of the microscopic length, whatever is the singularity relaxation mechanism.

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Section: Discussionmentioning

confidence: 99%

Section: Hydrodynamic Contact Line Singularity Related To the Mass Exmentioning

confidence: 99%

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere

2018

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“…Although having q vanish at x = a ± may be too restrictive in some cases, e.g. when we have mass loss through evaporation, as q is maximized there [49][50][51], it is appropriate for cases where mass flux is localized somewhere within the droplet's footprint [42,48]. Thus, setting q ± = 0 in Eq.…”

Section: Matchingmentioning

confidence: 99%

“…Noteworthy also is the related 2D numerical study within the framework of the computationally more demanding diffuse interface Cahn-Hilliard formalism [48], which investigates similar dynamics for localized fluxes. Studies which are pertinent to the present work also include a numerical study of imbibition in permeable substrates [28], as well as works on evaporative dynamics, which may model diffusion-dominated evaporation with a spatially dependent mass flux that is weakly singular at the contact line [49,50]; or evaporation in a pure-vapour atmosphere on homogeneous [36,51] and rough surfaces [37,38], where the mass flux is expressed as a function of the droplet thickness.…”

Section: Introductionmentioning

confidence: 99%

Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics

Groves,

Savva

2020

Preprint

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We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting longwave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasi-static dynamics and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simulations of the full model for a number of representative cases within the domain of applicability of the analysis. Specifically, we focus on situations where the mass of the drop changes periodically to highlight a number of interesting features of the dynamics, which include stick-slip, hysteresislike effects, as well as the possibility for the droplet to alternate between the constant-radius and constant-angle stages which have been previously reported in related works. These features of the dynamics are further scrutinized by investigating how the bifurcation structure of droplet equilibria evolves as the mass of the droplet varies.

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“…Similar results are obtained in Saxton et al (2016), where the effect of evaporation on the evolution of the contact-set radius is studied. In Saxton et al (2017), vapour transport and kinetic effects are used to regularize the mass-flux singularity at the contact line in an evaporating spreading droplet.…”

Section: Introductionmentioning

confidence: 99%

Surface-tension- and injection-driven spreading of a thin viscous film

2018

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We consider the spreading of a thin viscous droplet, injected through a finite region of a substrate, under the influence of surface tension. We neglect gravity and assume that there is a precursor layer covering the whole substrate and that the rate of injection is constant. We analyse the evolution of the film profile for early and late time, and obtain power-law dependencies for the maximum film thickness at the centre of the injection region and the position of an apparent contact line, which compare well with numerical solutions of the full problem. We relax the conditions on the injection rate to consider more general time-dependent and spatially varying forms. In the case of power-law injection of the form$t^{k}$, we observe a switch in the behaviour of the evolution of the film thickness for late time from increasing to decreasing at a critical value of$k$. We show that point-source injection can be treated as a limiting case of a finite-injection slot and the solutions exhibit identical behaviours for late time. Finally, we formulate the problem with thickness-dependent injection rate, discuss the behaviour of the maximum film thickness and the position of the apparent contact line and give power-law dependencies for these.

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Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

Cited by 12 publications

References 58 publications

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere

Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere

Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics

Surface-tension- and injection-driven spreading of a thin viscous film

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