Weak solutions to thin-film equations with contact-line friction

2017 ◽  
Vol 19 (2) ◽  
pp. 243-271 ◽  
Author(s):  
Maria Chiricotto ◽  
Lorenzo Giacomelli
Keyword(s):  
Thin Film ◽  
Contact Line ◽  
Weak Solutions ◽  
Thin Film Equations ◽  
Contact Line Friction

Thin-film equations with “partial wetting” energy: Existence of weak solutions

2005 ◽  
Vol 209 (1-4) ◽  
pp. 17-27 ◽  
Author(s):  
Michiel Bertsch ◽  
Lorenzo Giacomelli ◽  
Georgia Karali
Keyword(s):  
Thin Film ◽  
Weak Solutions ◽  
Existence Of Weak Solutions ◽  
Partial Wetting ◽  
Thin Film Equations

scholarly journals Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

2021 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Benjamin Gess ◽  
Manuel V. Gnann ◽  
Günther Grün
Keyword(s):  
Thin Film ◽  
Energy Estimates ◽  
Approximation Procedure ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Scalar Conservation Law ◽  
Thin Film Equation ◽  
Degenerate Parabolic ◽  
Scalar Conservation ◽  
Martingale Solutions

AbstractWe prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.

scholarly journals Experimental study of the contact line friction coefficient

2020 ◽  
Vol 1677 ◽  
pp. 012156
Author(s):  
N Sibiryakov ◽  
W Zheng ◽  
O Kabov ◽  
B Bai
Keyword(s):  
Experimental Study ◽  
Friction Coefficient ◽  
Contact Line ◽  
Contact Line Friction

Use of Scanning Microphotometer to Determine the Evaporative Heat Transfer Characteristics of the Contact Line Region

1981 ◽  
Vol 103 (2) ◽  
pp. 325-330 ◽  
Author(s):  
R. Cook ◽  
C. Y. Tung ◽  
P. C. Wayner
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Contact Line ◽  
Heat Transfer Characteristics ◽  
Thin Film Thickness ◽  
Thickness Profile ◽  
Line Region ◽  
Evaporative Heat Transfer

A scanning microphotometer was used to measure in situ the profile of an evaporating decane meniscus in the contact line region on a smooth inclined silicon substrate as a function of the evaporative heat flux. The use of this new experimental design to determine the effect of heat flux on the profile in the contact line region is discussed. The results support the hypothesis that fluid flow in the contact line region of an evaporating thin film results from a change in the thin film thickness profile.

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