Continuum models for the contact line problem

Weiqing Ren, Dan Hu, Weinan E

Research output: Contribution to journalArticle

Abstract

Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model and the effect of the boundary condition is investigated.

Original languageEnglish (US)
Article number102103
JournalPhysics of Fluids
Volume22
Issue number10
DOIs
StatePublished - Oct 14 2010

Fingerprint

continuums
boundary conditions
wetting
lubrication
solid surfaces
scaling laws
electric contacts
energy dissipation
molecular dynamics
thermodynamics
thin films
approximation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Continuum models for the contact line problem. / Ren, Weiqing; Hu, Dan; E, Weinan.

In: Physics of Fluids, Vol. 22, No. 10, 102103, 14.10.2010.

Research output: Contribution to journalArticle

Ren, Weiqing ; Hu, Dan ; E, Weinan. / Continuum models for the contact line problem. In: Physics of Fluids. 2010 ; Vol. 22, No. 10.
@article{5990e3d1172c47d2bb348513f1ecee20,
title = "Continuum models for the contact line problem",
abstract = "Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model and the effect of the boundary condition is investigated.",
author = "Weiqing Ren and Dan Hu and Weinan E",
year = "2010",
month = "10",
day = "14",
doi = "10.1063/1.3501317",
language = "English (US)",
volume = "22",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "10",

}

TY - JOUR

T1 - Continuum models for the contact line problem

AU - Ren, Weiqing

AU - Hu, Dan

AU - E, Weinan

PY - 2010/10/14

Y1 - 2010/10/14

N2 - Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model and the effect of the boundary condition is investigated.

AB - Continuum models are derived for the moving contact line problem through a combination of macroscopic and microscopic considerations. Macroscopic thermodynamic argument is used to place constraints on the form of the boundary conditions at the solid surface and the contact line. This information is then used to set up molecular dynamics to measure the detailed functional dependence of the boundary conditions. Long range molecular forces are taken into account in the form of a surface potential. This allows us to handle the case of complete wetting as well as the case of partial wetting. In particular, we obtain a new continuum model for both cases in a unified form. Two main parameters and different spreading regimes are identified from the analysis of the energy dissipations for the continuum model. Scaling laws in these different regimes are derived. The new continuum model also allows us to derive boundary conditions for the lubrication approximation. Numerical results are presented for the thin film model and the effect of the boundary condition is investigated.

UR - http://www.scopus.com/inward/record.url?scp=78650497180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650497180&partnerID=8YFLogxK

U2 - 10.1063/1.3501317

DO - 10.1063/1.3501317

M3 - Article

VL - 22

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 102103

ER -