2 research outputs found
Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
We study the singular effects of vanishingly small surface tension on the
dynamics of finger competition in the Saffman-Taylor problem, using the
asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A
343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419
(1996)] as well as direct numerical computation, following the numerical scheme
of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We
demonstrate the dramatic effects of small surface tension on the late time
evolution of two-finger configurations with respect to exact (non-singular)
zero surface tension solutions. The effect is present even when the relevant
zero surface tension solution has asymptotic behavior consistent with selection
theory.Such singular effects therefore cannot be traced back to steady state
selection theory, and imply a drastic global change in the structure of
phase-space flow. They can be interpreted in the framework of a recently
introduced dynamical solvability scenario according to which surface tension
unfolds the structually unstable flow, restoring the hyperbolicity of
multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev
Fluctuations in viscous fingering
Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels
reveal finger width fluctuations that were not observed in previous
experiments, which had lower aspect ratios and higher capillary numbers Ca.
These fluctuations intermittently narrow the finger from its expected width.
The magnitude of these fluctuations is described by a power law, Ca^{-0.64},
which holds for all aspect ratios studied up to the onset of tip instabilities.
Further, for large aspect ratios, the mean finger width exhibits a maximum as
Ca is decreased instead of the predicted monotonic increase.Comment: Revised introduction, smoothed transitions in paper body, and added a
few additional minor results. (Figures unchanged.) 4 pages, 3 figures.
Submitted to PRE Rapi