Labyrinthine instability in thin liquid films

When a thin liquid film on a solid surface has a thickness corresponding to a particular part the spinodal region of the disjoining pressure versus thickness isotherm, the film breaks down. One of the patterns that emerges on the breakdown has been referred to as wavy instability. It is compared here to the labyrinthine instability seen in magnetic films. The system is modeled following the procedure used in magnetic systems, and the pattern of wavy instability is broken down into a curved thick-thin film in equilibrium with a flat thin-thin film of constant thickness. Minimization of free energy leads to expressions for various length scales that characterize the system. Comparisons with published experimental results on nematic liquid crystals for a number of very different features are satisfactory. They include film thicknesses in the bulk at equilibrium where the capillary pressure is not zero, and is determined as a part of the solution, as well as film thicknesses in the ledge where the capillary pressure is zero. Stability analysis shows that the system is unstable in both directions with some qualifiers. A model is proposed in the form of a tiled structure to explain the labyrinthine form.