Author:
Degregoria A. J.,Schwartz L. W.
Abstract
We develop a time-dependent numerical algorithm, using a boundary-integral approach, to investigate fingering in Hele-Shaw cells. Starting from a sinusoidal variation in the initial interface, stable fingers quickly form for a wide range of the dimensionless surface-tension parameter. For very low values of the parameter, the incipient finger bifurcates. The stable fingers are clearly the same as those obtained by McLean & Saffman (1981) using a steady-state algorithm. These steady-state solutions were found to be linearly unstable. We resolve this apparent discrepancy regarding stability by tracing the fate of small disturbances placed on and about the finger tip. We show that some small disturbances do, indeed, grow initially; however, they reach a maximum amplitude and decay as they convect backward from the tip of the finger to regions where stabilizing surface tension is the major physical force. Relatively large imposed disturbances, on the other hand, cause a finger to bifurcate; the critical disturbance amplitude decreases as the surface tension is reduced
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference22 articles.
1. Taylor, G. I. & Saffman, P. G. 1959 A note on the motion of bubbles in a Hele-Shaw cell and porous medium.Q. J. Mech. Appl. Maths 12,265–279.
2. Botha, J. F. & Pinder, G. F. 1983 Fundamental Concepts in the Numerical Solution of Differential Equations. Wiley.
3. McLean, J. W. & Saffman, P. G. 1981 The effect of surface tension on the shape of fingers in a Hele-Shaw cell.J. Fluid Mech. 102,455–469.
4. Chouke, R. L. , van Meurs, P. & van Der Poel, C. 1959 The instability of slow, immiscible, viscous, liquid—liquid displacements in permeable media.Trans. AIME 216,188–194.
5. Nittmann, J. , Daccord, G. & Stanley, H. E. 1985 Fractal growth of viscous fingers: quantitative characterization of a fluid instability phenomenon.Nature 314,141–144.
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