Dynamics of viscous fingers in Hele-Shaw cells of liquid crystals Theory and experiment

The theoretical and experimental developments in the interfacial dynamics and the formation of viscous fingering patterns in Hele-Shaw cells of liquid crystal-air systems are summarized and discussed. These include radial and linear cells with or without grooves engraved on the cell plates. Instabilities of fingers, the role of intrinsic and extrinsic anisotropies, etc., are emphasized. In a linear cell, when the injected air is kept at constant pressure, a whole sequence of successive instabilities of fingers (hump, tip-splitting, sidewrinkling, sidebranching and DLA-like structure) is observed in a single run of the experiment. In our theory, the equations of motion of nematic flows in Hele-Shaw cells are derived from the Ericksen-Leslie equations. In the linear approximation, the equations resemble those of isotropic liquids with the presence of effective viscosities and anisotropic surface tension. Experimental observations are interpreted with the introduction of an effective control parameter which may be time dependent. Special features of viscous fingers in liquid crystals in contrast to those in isotropic liquids, such as asymmetric dendritics, displacement of the finger from the central axis of the linear cell, and reentrant sequence of patterns, are pointed out. Plausible explanations of these phenomena are given. In this newly developed field, a large number of interesting problems remain to be solved.