Abstract
The covering surfaces of a Hele-Shaw cell may be roughened mechanically, or modified by random chemical patches which change the wetting properties. We discuss first the quasi-static injection of a single fluid (with a finite contact angle θe) in an imperfect cell. The shape of the injected region depends critically on a dimensionless number i (ratio of the boundary energy τ over the capillary energy fluctuations in one patch). At τ