Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2025-01-03T23:21:34.672Z Has data issue: false hasContentIssue false
  • English
  • Français

An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow

Published online by Cambridge University Press:  20 April 2006

Poul Bach  and
Ole Hassager
Poul Bach
Affiliation:
Instituttet for Kemiteknik, Danmarks Tekniske Højskole, Lyngby, Denmark
Ole Hassager
Affiliation:
Instituttet for Kemiteknik, Danmarks Tekniske Højskole, Lyngby, Denmark
Get access Rights & Permissions [Opens in a new window]

Abstract

An algorithm is constructed for the use of the Lagrangian kinematic specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 173 - 190
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bach, P. & Hassager, O. 1984 A Lagrangian finite element method for the simulation of flow of Newtonian liquids. AIChE J. 30, 508.Google Scholar
Bach, P. & Villadsen, J. 1984 Simulation of the vertical flow of a thin wavy film using a finite element method. Intl J. Heat and Mass Transfer 27, 815.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1977 Dynamics of Polymeric Liquids, Vol. I; Fluid Dynamics. Wiley.
Chung, T. J. 1978 Finite Element Analysis in Fluid Dynamics. McGraw-Hill.
Cook, R. D. 1974 Concepts and Applications of Finite Element Analysis. Wiley.
Crochet, M. J. & Walters, K. 1983 Computational Techniques for Visco-elastic Fluid Flow. In Computational Analysis of Polymer Processing (eds. J. R. A. Pearson & S. M. Richardson), New York: Applied Science Publishers.
Hassager, O. & Bisgaard, C. 1983 A Lagrangian finite element method for the simulation of flow of non-Newtonian liquids. J. Non-Newtonian Fluid Mech. 12, 153.Google Scholar
Hirt, C. W., Cook, J. L. & Butler, T. D. 1970 A Lagrangian method for calculation of the dynamics of an incompressible fluid with free surface. J. Comp. Phys. 5, 103.Google Scholar
Hocking, L. M. 1981 Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Maths 34, 37.Google Scholar
Huh, C. & Mason, S. G. 1977 The steady movement of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401.Google Scholar
Kistler, S. F. & Scriven, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (eds J. R. A. Pearson & S. M. Richardson). New York: Applied Science Publishers.
Landau, L. D. & Lifshitz, E. M. 1958 Statistical Physics. Pergamon.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lowndes, J. 1980 The numerical simulation of the steady movement of a fluid meniscus in a capillary tube. J. Fluid Mech. 101, 631.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1.Google Scholar
Ngan, C. G. & Dussan V., E. B. 1982 On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech. 118, 27.Google Scholar
Roach, P. J. 1976 Computational Fluid Dynamics. Albuquerque: Hermosa Publishers.
Ruschak, K. J. 1980 A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Intl J. Numer. Meth. Engng 15, 639.Google Scholar
Sani, R. L., Gresho, P. M., Lee, R. L. & Griffiths, D. F. 1981 The cause and cure (?) of the spurious pressure generated by certain FEM solutions of the incompressible Navier-Stokes equations: Part 1. Intl J. Numer. Meth. Fluids 1, 17.Google Scholar
Sokolnikoff, I. S. & Redheffer, R. M. 1966 Mathematics of Physics and Modern Engineering. McGraw-Hill.
Tanner, R. I. 1983 Extrudate swell. In Computational Analysis of Polymer Processing (eds J. R. A. Pearson & S. M. Richardson). New York: Applied Science Publishers.