Orientational order induced mode switching at coupled interfaces of a nematic-isotropic free bilayer

Instabilities at the coupled deformable interfaces of a nematic-isotropic free bilayer can engender rich morphological patterns governed by an intricate interplay of nematic elasticity, surface and interfacial energetics, gravitational forces, and intermolecular forces. This work presents a theoretical investigation of the instability in a bilayer composed of a liquid crystal film resting on a water layer having a free deformable nematic-air surface and a confined nematic-isotropic interface. Utilizing a long-wave hydrodynamic model, the formulation couples the Ericksen-Leslie equations with the Navier-Stokes equations to quantify growth rates of the instability across NLC thickness and director orientations. The formulation examines the competing roles of gravitational, van der Waals, and elastic forces in governing the deformations at the bilayer interfaces. For micro-thick films, density contrast between the layers initiates classical Rayleigh-Taylor instabilities (RTIs), while in nano-thin regimes, disjoining pressure drives mode dynamics. In both scenarios, we identify a pair of primary instability modes-the confined interfacial mode (CIM) and the free surface mode (FSM)-whose relative dominance is dictated by film thickness, anchoring configuration, and the spreading coefficients at the surface or interface. Systematic variation of director orientations and three canonical surface anchoring arrangements reveals critical transitions and instability mode responses, especially under asymmetrical spreading conditions. The results uncover mode switching controlled by NLC orientation and interfacial energetics, offering fundamental insights into the spatiotemporal structuring of layered soft materials. The framework provides an elementary direction for designing reconfigurable morphologies in NLC-based bilayer systems relevant to wetting, templating, and self-patterning applications.