Droplet motion with contact-line friction: long-time asymptotics in complete wetting

被引：1

作者：

Giacomelli, Lorenzo ^{[1
]}

Gnann, Manuel V. ^{[2
]}

Peschka, Dirk ^{[3
]}

机构：

[1] Sapienza Univ Rome, SBAI Dept, Via A Scarpa 16, I-00161 Rome, Italy

[2] Delft Univ Technol, Delft Inst Appl Math, Fac Elect Engn Math & Comp Sci, Mekelweg 4, NL-2628 CD Delft, Netherlands

[3] Weierstrass Inst, Mohrenstr 39, D-10117 Berlin, Germany

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2023年 / 479卷 / 2274期

关键词：

self-similar solutions; thin films; dynamic contact angle; THIN-FILM EQUATION; TRAVELING-WAVE SOLUTIONS; WELL-POSEDNESS; LUBRICATION APPROXIMATION; WEAK SLIPPAGE; BOUNDARY-PROBLEMS; WAITING-TIMES; FINITE SPEED; FLOW; BEHAVIOR;

D O I：

10.1098/rspa.2023.0090

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the spreading rate of solutions depending on the strength of friction at the contact line, as well as their (global or local) corrections, which are due to the dynamical nature of the free boundary conditions. These results are complemented with full transient numerical solutions of the free boundary problem.

引用

页数：23

共 50 条

[1] Universality in dynamic wetting dominated by contact-line friction
Carlson, Andreas
Bellani, Gabriele
Amberg, Gustav
PHYSICAL REVIEW E, 2012, 85 (04):
[2] Contact-line fluctuations and dynamic wetting
Fernandez-Toledano, J-C.
Blake, T. D.
De Coninck, J.
JOURNAL OF COLLOID AND INTERFACE SCIENCE, 2019, 540 : 322 - 329
[3] DISSIPATION AND CONTACT-LINE MOTION
HALEY, PJ
MIKSIS, MJ
PHYSICS OF FLUIDS A-FLUID DYNAMICS, 1991, 3 (03): : 487 - 489
[4] Critical dynamics of contact-line motion
Kumar, S
Reich, DH
Robbins, MO
PHYSICAL REVIEW E, 1995, 52 (06) : R5776 - R5779
[5] EFFECT OF THE CONTACT-LINE DYNAMICS ON THE OSCILLATIONS OF A COMPRESSED DROPLET
Alabuzhev, A. A.
Lyubimov, D. V.
JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS, 2012, 53 (01) : 9 - 19
[6] Effect of the contact-line dynamics on the oscillations of a compressed droplet
A. A. Alabuzhev
D. V. Lyubimov
Journal of Applied Mechanics and Technical Physics, 2012, 53 : 9 - 19
[7] Long-time asymptotics of the Hunter-Saxton equation on the line
Ju, Luman
Xu, Kai
Fan, Engui
JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 390 : 451 - 493
[8] Long-time asymptotics for the Hirota equation on the half-line
Guo, Boling
Liu, Nan
Wang, Yufeng
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 174 : 118 - 140
[9] Long-time asymptotics of the Camassa-Holm equation on the line
de Monvel, Anne Boutet
Shepelsky, Dmitry
INTEGRABLE SYSTEMS AND RANDOM MATRICES: IN HONOR OF PERCY DEIFT, 2008, 458 : 99 - 116
[10] Effect of the contact-line dynamics on the natural oscillations of a cylindrical droplet
A. A. Alabuzhev
D. V. Lyubimov
Journal of Applied Mechanics and Technical Physics, 2007, 48 : 686 - 693

← 1 2 3 4 5 →