Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell

Abstract

We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.

42 pages, 5 figures, added references, minor changes, to appear in Int. J. Mod. Phys. B (1998)

References in corpus (1)

• Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

Cited by in corpus (10)

• Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis
• Hydrodynamic instabilities in miscible fluids
• Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows
• The Saffman-Taylor problem on a sphere
• Mode-coupling approach to non-Newtonian Hele-Shaw flow
• Computational Analysis of Interfacial Dynamics in Angled Hele-Shaw Cells: Instability Regimes
• Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell
• Viscous fingering patterns in ferrofluids
• Hamiltonian formulation towards minimization of viscous fluid fingering
• On the displacement of two immiscible Oldroyd-B fluids in a Hele-Shaw cell