# An integral formulation for some slow viscous flows with free surfaces

## Abstract

For some viscous incompressible flows at low Reynolds numbers we deduce a system of nonlinear integral equations for stream function and vorticity. A coating flow problem and a capillary free boundary problem are considered in details.

## Authors

Mirela Kohr Ile
Babes-Bolyai University, Faculty of Mathematics

Calin-Ioan Gheorghiu
Institute of Mathematics

## Keywords

slow viscous flow; free surface; stream function; vorticity; integral equation; nonlinear; coating flow; capillary flow;

### References

See the expanding block below.

## Paper coordinates

C.I. Gheorghiu, M. Kohr-Ile, An integral formulation for some slow viscous flows with free surfaces, Mathematica, 36 (59) (1994), pp. 43-54.

?

Mathematica

?

?

?

## References

[1] E Chifu, C.I. Gheorghiu, I. Stan, Surface Mobility of Surfacant Solutions XI. Numerical Analysis for the Marangoni and the Gravity Flow in a This Liquid Layer of Triangular Section,  Rev. Roumaine Chim., 29, 1 (1984) 31-42.

[2] C. Cuvelier, On e Computation of Free Boundaries, Research in Numerical Gluid Mechanics, (Delft 1986), 18-29, Notes Numer. Fluid Mech., 17, Vieweg, Braunschweig, 1987.

[3] M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, 1964.

[4] T.M. Fischer, G.C. Hsiao, W. I., Wendland, Singular Perturbations for the exterior Three-Dimensional Slow Viscous Flow Problem, J. Math. Anal. Appl. 110 (1985) 583-603.

[5] M.A. Kelmanson, A Direct Boundary Integral Formulation for the Oseen Flow Past a Two-Dimensional Cylinder for Arbitrary Cross-Section, Acta-Mechanica, 68 (1987), 99-119.

[6] M.A. Kelmanson, An Integral  Equation Method for the Solution of Singular Stow Flows Problems, Journal Comp. Physics, 51 (1983), 139-158.

[7] M.E. O’Neil, F. Chorlton, Ideal and incompressibile fluid dynamics, Ellis Horwood, Chichester, West Sussox, 1986.

[8] T. Petrila, C.I. Gheorghiu, Finite Element Methods and Applications, Ed. Academiei București, 1987, (in Romanian)

[9] T. Petrila, M. Kohr,  Some boundary techniques for viscous flows,  Rev. D’Analyse Numerique et de Theorie de l’Approx., 21, 2 (1992) 167-182.

[10] H. Saito, I. E. Scriven,  Study of Coating Flow by the finite Element Method, Journal of  Comp. Physics, 42 (1981), 53-76.

[11] M. Van Den Tempel, Damping of Waves by Surface-Active Materials,  The Journal of Chem. Physics, 42, 8 (1965), 2769-2777.