The interface dynamics of a surfactant drop on a thin viscous film

被引：3

作者：

Chugunova, Marina ^{[1
]}

King, John R. ^{[2
]}

Taranets, Roman M. ^{[3
,4
]}

机构：

[1] Claremont Grad Univ, Inst Math Sci, 150 E 10th St, Claremont, CA 91711 USA

[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

[3] Natl Acad Sci Ukraine, Inst Appl Math & Mech, UA-83114 Donetsk, Ukraine

[4] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2017年 / 28卷 / 04期

关键词：

System of parabolic equations; thin liquid films; surfactant spreading; free boundary; fluid interface; waiting-time phenomenon; finite speed of support propagation; WEAK SLIPPAGE; INSOLUBLE SURFACTANT; WAITING-TIMES; LOWER BOUNDS; EQUATION; BEHAVIOR; PROPAGATION; EXISTENCE; SUPPORT;

D O I：

10.1017/S0956792516000474

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a system of two coupled parabolic equations that models the spreading of a drop of an insoluble surfactant on a thin liquid film. Unlike the previously known results, the surface diffusion coefficient is not assumed constant and depends on the surfactant concentration. We obtain sufficient conditions for finite speed of support propagation and for waiting-time phenomenon by application of an extension of Stampacchia's lemma for a system of functional equations.

引用

页码：656 / 686

页数：31

共 44 条

[1] [Anonymous], UKR MATH B
[2] HIGHER-ORDER NONLINEAR DEGENERATE PARABOLIC EQUATIONS
BERNIS, F
FRIEDMAN, A
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) : 179 - 206
[3] Bernis F., 1996, Adv. Differential Equations, V3, P337
[4] Bertozzi AL, 1998, COMMUN PUR APPL MATH, V51, P625, DOI 10.1002/(SICI)1097-0312(199806)51:6<625::AID-CPA3>3.0.CO
[5] 2-9
[6] Bertozzi AL, 2000, INDIANA U MATH J, V49, P1323
[7] Small- and waiting-time behavior of the thin-film equation
Blowey, James F.
King, John R.
Langdon, Stephen
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 67 (06) : 1776 - 1807
[8] MONOLAYER FLOW ON A THIN-FILM
BORGAS, MS
GROTBERG, JB
[J]. JOURNAL OF FLUID MECHANICS, 1988, 193 : 151 - 170
[9] Surfactant-assisted spreading of a liquid drop on a smooth solid surface
Chan, KY
Borhan, A
[J]. JOURNAL OF COLLOID AND INTERFACE SCIENCE, 2005, 287 (01) : 233 - 248
[10] Nonnegative Weak Solutions for a Degenerate System Modeling the Spreading of Surfactant on Thin Films
Chugunova, Marina
Taranets, Roman M.
[J]. APPLIED MATHEMATICS RESEARCH EXPRESS, 2013, (01) : 102 - 126

← 1 2 3 4 5 →