Selection rules for the tip-splitting instability

Fjords in viscous fingering: selection of width and opening angle

Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths lambda(c)/2, where lambda(c) is the most unstable wavelength from a linear stability analysis. Further, fjords open at an angle of 8.0 degrees +/- 1.0 degree. These selection rules hold for a wide range of pumping rates and fjord lengths, widths, and directions.