When a less viscous fluid displaces a more viscous fluid in a narrow gap — a Hele-Shaw cell — the interface destabilizes into branching, fractal-like patterns called viscous fingers. The Saffman-Taylor instability creates these fingers because small perturbations at the interface grow: where the less viscous fluid advances slightly, it encounters less resistance and advances further. The positive feedback produces progressively thinner, more branched structures.
The instability is suppressed by oscillating the cell walls. If the gap width periodically narrows and widens — the confining plates vibrate perpendicular to the flow — the fingering pattern stabilizes. The interface becomes smoother and advances more uniformly.
The oscillation works because it modifies the effective mobility of the fluids. During the narrowing phase, the increased confinement raises the viscous resistance for both fluids but preferentially decelerates the advancing finger tips, where the interface curvature is highest. During the widening phase, the interface relaxes. The alternation between damping and relaxation suppresses the fastest-growing perturbation modes.
The counterintuitive element is that adding disturbance (vibration) suppresses disturbance (fingering). A static system that is unstable becomes stable when the boundary itself becomes dynamic. The shaking doesn't overpower the instability — it changes the growth rates of the competing perturbation modes, selectively suppressing the ones that would dominate in the static case.
Noise in the boundary suppresses noise in the flow. The system is more orderly when its container is less still. Stability is not the absence of perturbation but the right kind of perturbation applied at the right boundary.