Effects of an External Periodic Body Force on the Interfacial Stability of a Nematic Layer

On using the Ericksen-Leslie continuum theory, the interfacial hydrodynamic stability of a nematic layer has been investigated. The layer is assumed to be influenced by an external vertical periodic body force. A general form of the deformations of the interface is considered. The normal modes technique has been utilized. The coupling between hydrodynamic motion and internal degrees of freedom (molecular orientation) includes some changes in the structure and dispersion of the surface modes. The problem contains nontraditional boundary-value equations that lead to a transcendental equation in the zero-order perturbation. The method of multiple time scales is used to analyze firstorder perturbation equations. The solvability condition is obtained. It is found that a resonance mode may appear due to the periodicity of the external periodic body force. The transition curves are obtained. The analytical results are numerically confirmed taking into account the natural physical parameters of the MBBA and PAA nematics. It is found that the amplitude of the external periodic body force plays a destabilizing influence on the system. It is also found that the increase of the periodicity of the external force leads to a contraction in the instability of the system. It is also observed that the mechanism of the instability of MBBA differs from that of PAA.