Abstract
The motion of a two-dimensional bubble which is moving between two parallel plates under the influence of a constant pressure has been investigated using the Boundary Element Method. A free surface location algorithm has been developed so that the profile of the bubble may be predicted over a large range of values of the surface tension. The numerically predicted results are compared with existing experimental data and the results are encouraging.
Similar content being viewed by others
References
Fairbrother, F. and Stubbs, A. E.,Studies in electro-endosmosis Part VI. The “Bubble-tube” Method of Measurement. J. Chem. Soc.,1, 527–529 (1935).
Taylor, G. I.,Deposition of a viscous fluid on the wall of a tube. J.F.M.,10, 161–165 (1961).
Bretherton, F. P.,The motion of long bubbles in tubes. J.F.M.,10, 166–188 (1961).
Cos, B. G.,On driving a viscous fluid out of a tube. J.F.M.,14, 81–96 (1962).
Novotny, M. and Bartle, K. D., Blomberg, L.,Dependence of film thickness on column radius and coating rate in preparation of capillary columns for gas chromatography. J. Chromat.,45, 469–476 (1969).
Novotny, M. and Bartle, K. D.,Preparation of thick-film glass capillary columns by the dynamic coating procedure. J. Chromat.,93, 405–412 (1974).
Blomberg, L.,Measurement of the average thickness of the film of stationary phase in dynamically coated glass capillary columns for gas chromatography. J. Chromat.,138, 7–18 (1977).
Saffman, P. G. and Taylor. G. I.,The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy. Soc.,A245, 312–329 (1958).
Pitts, E.,Penetration of fluid into a Hele-Shaw cell: the Saffman-Taylor experiment. J.F.M.,97, part 1, 53–64 (1980).
McLean, J. W. and Saffman, P. G.,The effect of surface tension on the shape of fingers in a Hele-Shaw cell. J.F.M.,102, 455–469 (1981).
Shen, E. I. and Udell, K. S.,A finite element study of low Reynolds number two-phase flow in cylindrical tubes. J. of Appl. Mech.,52, 253–256 (1985).
Saffman, P. G.,Viscous fingering in Hele-Shaw cells. J.F.M.,173, 73–94 (1986).
Schwartz, L. W., Princen, H. M. and Kiss, A. D.,On the motion of bubbles in capillary tubes. J.F.M.,172, 259–275 (1986).
Coyne, J. C. and Elrod, H. G.,Conditions for the rupture of a lubricating film. Part 1:Theoretical model. Trans. A.S.M.E., J. Lub. Tech.,92, 451–456 (1970).
Ingham, D. B. and Kelmanson, M. A.,Boundary Integral Equation Analyses of Singular, Potential and Biharmonic Problems. Springer-Verlag, Berlin/New York 1984.
Saito, H. and Scriven, L. E.,A study of coating flows by the finite element method. J. Comp. Phys.,42, 53–76 (1981).
Carter, G. C.,The Modelling and Analysis of Coating Processes. PhD Thesis, Leeds University 1985.
Reinelt, D. A. and Saffman, P. G.,The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Stat. Comp.,6, 542–561.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ingham, D.B., Ritchie, J.A. & Taylor, C.M. The motion of a semi-infinite bubble between parallel plates. Z. angew. Math. Phys. 43, 191–206 (1992). https://doi.org/10.1007/BF00944746
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00944746