Details
| Original language | English |
|---|---|
| Pages (from-to) | 1229-1246 |
| Number of pages | 18 |
| Journal | Applicable Analysis |
| Volume | 100 |
| Issue number | 6 |
| Publication status | Published - 9 Jul 2019 |
Abstract
Given any positive speed, we prove the existence of a travelling wave solution for a viscous incompressible thin dilatant liquid film coated with an insoluble surfactant. Relying on first principles of fluid mechanics, lubrication theory leads to a coupled system of second-order partial differential equations for the film's height and the surfactant's concentration where a second-order approximation of the viscosity function is used. The travelling wave solution is (Formula presented.) -regular and generates a heteroclinic orbit which connects two distinct equilibrium points of the associated plane dynamical system.
Keywords
- A. Constantin, dilatant fluid, heteroclinic orbit, surfactant, thin film, Travelling wave
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Applicable Analysis, Vol. 100, No. 6, 09.07.2019, p. 1229-1246.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Travelling wave solutions in dilatant non-Newtonian thin films with second-order viscosity
AU - Zhuang, Yuehong
AU - Escher, Joachim
N1 - Funding information: This work is sponsored by China Scholarship Council and partially supported by National Natural Science Foundation of China under the grant number 11571381. The first author would like to express his sincere thanks to Institut für Angewandte Mathematik, Leibniz Universität Hannover for the support from October 2018 to September 2019 as a joint PhD student.
PY - 2019/7/9
Y1 - 2019/7/9
N2 - Given any positive speed, we prove the existence of a travelling wave solution for a viscous incompressible thin dilatant liquid film coated with an insoluble surfactant. Relying on first principles of fluid mechanics, lubrication theory leads to a coupled system of second-order partial differential equations for the film's height and the surfactant's concentration where a second-order approximation of the viscosity function is used. The travelling wave solution is (Formula presented.) -regular and generates a heteroclinic orbit which connects two distinct equilibrium points of the associated plane dynamical system.
AB - Given any positive speed, we prove the existence of a travelling wave solution for a viscous incompressible thin dilatant liquid film coated with an insoluble surfactant. Relying on first principles of fluid mechanics, lubrication theory leads to a coupled system of second-order partial differential equations for the film's height and the surfactant's concentration where a second-order approximation of the viscosity function is used. The travelling wave solution is (Formula presented.) -regular and generates a heteroclinic orbit which connects two distinct equilibrium points of the associated plane dynamical system.
KW - A. Constantin
KW - dilatant fluid
KW - heteroclinic orbit
KW - surfactant
KW - thin film
KW - Travelling wave
UR - http://www.scopus.com/inward/record.url?scp=85068686558&partnerID=8YFLogxK
U2 - 10.1080/00036811.2019.1636973
DO - 10.1080/00036811.2019.1636973
M3 - Article
AN - SCOPUS:85068686558
VL - 100
SP - 1229
EP - 1246
JO - Applicable Analysis
JF - Applicable Analysis
SN - 0003-6811
IS - 6
ER -