Regular and complex singularities of the generalized thin film equation in two dimensions

Dallaston, Michael C.; Fontelos, Marco A.; Herrada, Miguel A.; López-Herrera, José M.; Eggers, Jens

doi:10.1017/jfm.2021.286

J. Fluid Mech.

2021

DOI: 10.1017/jfm.2021.286

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Regular and complex singularities of the generalized thin film equation in two dimensions

Michael C. Dallaston

Marco A. Fontelos

Miguel A. Herrada

et al.

Abstract: Abstract

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Cited by 4 publications

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Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox

Durastanti,

Giacomelli

2023

J Nonlinear Sci

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In the regime of lubrication approximation, we look at spreading phenomena under the action of singular potentials of the form $$P(h)\approx h^{1-m}$$ P ( h ) ≈ h 1 - m as $$h\rightarrow 0^+$$ h → 0 + with $$m>1$$ m > 1 , modeling repulsion between the liquid–gas interface and the substrate. We assume zero slippage at the contact line. Based on formal analysis arguments, we report that for any $$m>1$$ m > 1 and any value of the speed (both positive and negative) there exists a three-parameter, hence generic, family of fronts (i.e., traveling-wave solutions with a contact line). A two-parameter family of advancing “linear-log” fronts also exists, having a logarithmically corrected linear behavior in the liquid bulk. All these fronts have finite rate of dissipation, indicating that singular potentials stand as an alternative solution to the contact-line paradox. In agreement with steady states, fronts have microscopic contact angle equal to $$\pi /2$$ π / 2 for all $$m>1$$ m > 1 and finite energy for all $$m<3$$ m < 3 . We also propose a selection criterion for the fronts, based on thermodynamically consistent contact-line conditions modeling friction at the contact line. So as contact-angle conditions do in the case of slippage models, this criterion selects a unique (up to translation) linear-log front for each positive speed. Numerical evidence suggests that, fixed the speed and the frictional coefficient, its shape depends on the spreading coefficient, with steeper fronts in partial wetting and a more prominent precursor region in dry complete wetting.

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Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox

Durastanti,

Giacomelli

2023

J Nonlinear Sci

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Condensation dynamics on inclined heterogeneous substrates

Vrionis,

Demou,

Savva

2024

International Journal of Thermofluids

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The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics

Chapman¹,

Dallaston

Kalliadasis

et al. 2023

Physica D: Nonlinear Phenomena

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Regular and complex singularities of the generalized thin film equation in two dimensions

Abstract: Abstract

Cited by 4 publications

References 58 publications

Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox

Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox

Condensation dynamics on inclined heterogeneous substrates

The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics

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