4,864 research outputs found
Viscous fingering patterns in ferrofluids
Viscous fingering occurs in the flow of two immiscible, viscous fluids
between the plates of a Hele-Shaw cell. Due to pressure gradients or gravity,
the initially planar interface separating the two fluids undergoes a
Saffman-Taylor instability and develops finger-like structures. When one of the
fluids is a ferrofluid and a perpendicular magnetic field is applied, the
labyrinthine instability supplements the usual viscous fingering instability,
resulting in visually striking, complex patterns. We consider this problem in a
rectangular flow geometry using a perturbative mode-coupling analysis. We
deduce two general results: viscosity contrast between the fluids drives
interface asymmetry, with no contribution from magnetic forces; magnetic
repulsion within the ferrofluid generates finger tip-splitting, which is absent
in the rectangular geometry for ordinary fluids.Comment: 29 pages, 5 figures, Late
Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell
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.Comment: 42 pages, 5 figures, added references, minor changes, to appear in
Int. J. Mod. Phys. B (1998
Gravity-driven instability in a spherical Hele-Shaw cell
A pair of concentric spheres separated by a small gap form a spherical
Hele-Shaw cell. In this cell an interfacial instability arises when two
immiscible fluids flow. We derive the equation of motion for the interface
perturbation amplitudes, including both pressure and gravity drivings, using a
mode coupling approach. Linear stability analysis shows that mode growth rates
depend upon interface perimeter and gravitational force. Mode coupling analysis
reveals the formation of fingering structures presenting a tendency toward
finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review
Development of Knife-Edge Ridges on Ion-Bombarded Surfaces
We demonstrate in both laboratory and numerical experiments that ion
bombardment of a modestly sloped surface can create knife-edge like ridges with
extremely high slopes. Small pre-fabricated pits expand under ion bombardment,
and the collision of two such pits creates knife-edge ridges. Both laboratory
and numerical experiments show that the pit propagation speed and the precise
shape of the knife edge ridges are universal, independent of initial
conditions, as has been predicted theoretically. These observations suggest a
novel method of fabrication in which a surface is pre-patterned so that it
dynamically evolves to a desired target pattern made of knife-edge ridges.Comment: 5 pages, 4 figure
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