Journal of Fluid Mechanics

The effect of surface tension on the shape of fingers in a Hele Shaw cell

J. W.  McLean a1 and P. G.  Saffman a1
a1 Applied Mathematics, California Institute of Teclmology, Pasadena, California 91125

Article author query
mclean jw   [Google Scholar] 
saffman pg   [Google Scholar] 


The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.

(Published Online April 20 2006)
(Received June 24 1980)