QUARTERLY OF APPLIED MATHEMATICS VOLUME LVI, NUMBER 3 SEPTEMBER 1998, PAGES 413-429 EFFECTS OF AN EXTERNAL PERIODIC BODY FORCE ON THE INTERFACIAL STABILITY OF A NEMATIC LAYER By GALAL M. MOATIMID and YUSRY O. EL-DIB Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt 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 first- order 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. 1. Introduction. Liquid crystals are a state of matter intermediate between that of a crystalline solid and an isotropic liquid. They possess many of the mechanical proper- ties of a liquid, e.g., high fluidity, inability to support shear, formation, and coalescence of droplets. At the same time they are similar to crystals in that they exhibit anisotropy in their optical, electrical, and magnetic properties. They are considered subjects of great interest for both fundamental and practical reasons [1]—[3]. Fundamentally, many mesophases in which liquid crystals exist and their corresponding phase transition char- acteristics offer a good testing ground for statistical mechanics. Nematic liquid crystals [1] are anisotropic liquids in which the constituting molecules are, on average, aligned with their unique axis parallel to a preferred direction in space. This direction is labeled by the director n. Though a nematic liquid flows as easily as an isotropic liquid consisting of similar molecules, an analysis of the viscosities turns out Received November 10, 1994. 1991 Mathematics Subject Classification. Primary 82B24, 82D25. ©1998 Brown University 413