Viscous fingering as an archetype for growth patterns (Q2708426)

This review article describes the instability of a moving fluid-fluid interface, the so-called Saffman-Taylor instability, and considers its nonlinear evolution. Even at small amplitude, this instability can have deleterious influence on the coating flows relevant to oil recovery, whereby attempts are made to force more oil from an aging reservoir by injecting a displacing fluid. At large amplitude, the instability causes the interface to form complex shapes, and is a paradigm for many pattern-forming systems both within fluid mechanics and beyond (e.g. diffusion-limited aggregation or solidification instability). The author gives a detailed survey of the phenomenon, and draws some important conclusions concerning Laplacian, quasi-Laplacian and diffusive growth patterns.NEWLINENEWLINENEWLINEContents: 1. Introduction; 2. The basis of Saffman-Taylor viscous fingering instability; 3. The basis of the instability of other physical systems; 4. The existence of stable curved fronts; 5. Fractal structures; 6. Directional growth; 7. Conclusions.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00020].