Surprises in viscous fingering

In this paper, we review some aspects of viscous fingering in a Hele-Shaw c ell that at first sight appear to defy intuition. These include singular ef fects of surface tension relative to the corresponding zero-surface-tension problem both for the steady and unsteady problem. They also include a disp roportionately large influence of small effects like local inhomogeneity of the flow field near the finger tip, or of the leakage term in boundary con ditions that incorporate realistic thin-film effects. Through simple explic it model problems, we demonstrate how such properties are not unexpected fo r a system approaching structural instability or ill-posedness.