Publication detail

Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

KUČERA, R. ŠÁTEK, V. HASLINGER, J. FIALOVÁ, S. POCHYLÝ, F.

Original Title

Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions

Type

journal article in Web of Science

Language

English

Original Abstract

Unlike the Navier boundary condition, the present paper deals with the case when the slip of a fluid along the wall may occur only when the shear stress attains certain bound which is given a-priori and does not depend on the solution itself. The mathematical model of the velocity-pressure formulation with this type of the threshold slip boundary condition is given by the so-called variational inequality of the second kind. For its discretization we use P1-bubble/P1 mixed finite elements. The resulting algebraic problem leads to the minimization of a non-differentiable energy function subject to linear equality constraints representing the discrete impermeability and incompressibility condition. To release the former one and to regularize the non-smooth term characterizing the stick-slip behavior of the algebraic formulation, two additional vectors of Lagrange multipliers are introduced. Further, the velocity vector is eliminated and the resulting minimization problem for a quadratic function depending on the dual variables (the discrete pressure, the normal and shear stress) is solved by the interior point type method which is briefly described. To justify the threshhold model and to illustrate the efficiency of the proposed approach, three physically realistic problems are solved and the results are compared with the ones solving the Stokes problem with the Navier boundary condition.

Keywords

Stokes problem, Navier boundary condition, hydrophobia, fluid slip, algebraic formulation

Authors

KUČERA, R.; ŠÁTEK, V.; HASLINGER, J.; FIALOVÁ, S.; POCHYLÝ, F.

Released

2. 1. 2017

Publisher

The American Society of Mechanical Engineers

Location

New York

ISBN

0098-2202

Periodical

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME

Year of study

139

Number

1

State

United States of America

Pages from

0112021

Pages to

0112029

Pages count

9

URL

http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532

BibTex

@article{BUT126870,
  author="Radek {Kučera} and Václav {Šátek} and Jaroslav {Haslinger} and Simona {Fialová} and František {Pochylý}",
  title="Modelling of Hydrophobic Surfaces by the Stokes Problem with the Stick-Slip Boundary Conditions",
  journal="JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME",
  year="2017",
  volume="139",
  number="1",
  pages="0112021--0112029",
  doi="10.1115/1.4034199",
  issn="0098-2202",
  url="http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532"
}