Development of radial fingering patterns

Abstract

Measurements of radial fingering patterns have been performed over a range of dimensionless force parameter 1.1\ensuremath{\le}C\ensuremath{\le}35. All observed flows show a power law dependence of radius of gyration on area with exponent (1/1.79). Local curvatures provide the best characterization of pattern ramification. The power spectra of these curvatures are used to define an average wave number K\ifmmode\bar\else\textasciimacron\fi{}. A scaling is observed to collapse dimensionless average wave number (K\ifmmode\bar\else\textasciimacron\fi{}') versus dimensionless area of the mixing zone onto one function which rises early in the flows and then coarsens as the flows become more developed.