  The Hele-Shaw experiment is performed with a circular invasion to study the
scaling and dynamic behavior of the interface. We did not find any universal
power law. The time exponent varies with the range of scale, as has been
reported in the literature but not captured by existing models. We ascribe this
distinct difference from the planar injection to the fact that our interface
size grows with time. This renders the old geometries being constantly pushed
apart to leave rooms for new features. As a result, the amplitude of the
interface spectrum will decrease with the angular momentum, different from that
of a white noise commonly assumed for the planar injection. Due to the moving
boundary, the existing Kardar-Parisi-Zhang and Edwards-Wilkinson (EW) equations
can no longer be applied. We propose a modified EW equation that not only
conserves the fluid volume, but is also capable of predicting all the above
features. Two phenomenological coefficients are introduced to represent the
competing trend of instability and smoothness. Their dependence on the
microscopic parameters are determined from dimensional arguments, and their
estimated values conform with the experiments.
