Convection driven by centrifugal buoyancy in nematics

The onset of thermal convection in a nematic contained in a vertical rotating cylindrical annulus heated from the outside is studied as a function of the planar alignment of the liquid crystal director n. When n is horizontal, the results confirm data on gravitational buoyancy. An original first order like convection mode is obtained when n is parallel to the cylinder axis. Thermal convection in uniformly-aligned nematic liquid crystals is strongly modified both qualitatively and quantitatively with respect to the isotropic case [1] due to the coupling between the flow and molecular orientation [2]. In the planar configuration, considered here, the orientation characterized by a unit vector n the director and induced at the bounding surfaces is parallel to the plates. In gravity induced convection, the convective rolls are orientated perpendicular to n and the instability threshold is typically 500 times smaller than for an isotropic fluid of similar mean properties. In this note, we study the case for which gravity (g) is replaced by the centrifugal force (W2 r) acting on a planar nematic contained between two concentric cylinders in solid body rotation about a vertical axis z. The destabilizing temperature gradient is applied radially so that the outer temperature To is larger than the inner one Ti, AT = To T ;. For isotropic fluids, it has been established both theoretically and experimentally [3] that the effect of centrifugal buoyancy is equivalent to that of gravitational buoyancy in the corresponding Rayleigh Benard problem (g +-+ W2 r) when the effect of viscosity in the Ekman boundary layers can be neglected (the kine(*) Supported in part by NSF grants GA 31247 (C.R.C.) and GA 38867 (E.G.). (**) Also Laboratoire de Physique des Solides associe au C.N.R.S., 91405 Orsay, France. matic viscosity v ~ 1 cgs and the Ekman number E = v/wr2 satisfies the inequality ~ ~ (l/d )4 ; the height of the cell I 2.25 cm, its width d = 750 ~ and the mean radius r = 2 cm). However, the axes of the convection rolls have a preferred alignment along the axis of rotation when the Coriolis force is important. This alignment effect is a consequence of the Taylor-Proudman theorem. The theorem follows from the balance between the Coriolis force and the pressure gradient, in the hydrodynamic equations of motion. When this basic balance exists, the flow field must be independent of the coordinate along the axis of rotation. When the convection rolls are aligned along z, the flow is essentially independent of z. In this letter, we compare the aligning effects due to rotation and to the molecular orientation in the liquid crystalline state. We use MBBA (methoxy p.n. benzilidene bubyl anilin) which is nematic at room temperature. The film is contained between two concentric lucite cylinders treated by polishing to provide the planar molecular alignment at the facing surfaces. The alignment in the upper half (u) is horizontal (along the azimuthal 0 axis, see Fig. 1). In the lower half (1), it is vertical (along z). The temperature difference across thefilm, AT, is obtained by circulating water at different and controlled temperatures on the outer walls of the annular cell. The AT values indicated here have been corrected to account for the finite thermal resistance of the cylinder walls. Stroboscopic and Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01975003605014500