Periodic forcing in viscous fingering of a nematic liquid crystal.

Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell is studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers are observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.