  The kinetic roughening of a stable oil--air interface, moving in a Hele--Shaw
cell which contains a quenched columnar disorder (tracks) has been studied. A
capillary effect is responsible for the dynamic evolution of the resulting
rough interface, which exhibits anomalous scaling. The three independent
exponents needed to characterize the anomalous scaling are determined
experimentally. The anomalous scaling is explained in terms of the initial
acceleration and subsequent deceleration of the interface tips in the tracks
coupled by mass conservation. A phenomenological model that reproduces the
measured global and local exponents has been introduced.
