Theory and Simulation of Extensional Flow-Induced Biaxiality in Discotic Mesophases

(Received 22 August 1994, revised 29 May 1995, accepted 1 June 1995)

Abstract
Flow-induced biaxiality is simulated for a uniaxial discotic nematic liquid crystal subjected to a constant uniaxial, isothermal, incompressible, irrotational, extensional, three dimensional flow, using a previously presented model [Singh A.P. and Rey A.D., J. Phys. II France 4 (1994) 645]. Numerical and analytical solutions of the director triad (n, m, l), and uniaxial ( S) and biaxial ( P) alignments are given. The unit sphere description of the director triad is used to discuss and analyze the sensitivity of the director triad trajectories and the coupled alignment (uniaxial and biaxial) relaxations to the initial orientation, nematic potential ( U), and to the alignment Deborah number (dimensionless extension rate). The evolution of the director triad is given by the rotation of a moving diad (n, l) around a fixed director (m). When the poles of the orientation unit sphere are along the extension axis, and the equator lies in the compression plane of the flow, it is found that the director diad (n, l) dynamics follow geodesic flow and the trajectories belong to the same meridians (great circles through the poles). The space of stable steady state orientation of the uniaxial director n and the biaxial director m is the whole compression plane (the equator of the unit sphere), while that of the biaxial director l is the extension direction (poles). A high degree extension flow-induced biaxiality is found when the uniaxial director is away from the extension axis and when S is relatively low. The scalar order parameter couplings are captured by analyzing the trajectories in the alignment triangle. Computed scientific visualizations of biaxial molecular orientation distributions are used to correlate the director triad dynamics and the alignment's dynamics. The tensor order parameter is used to calculate the main flow-birefringences, thus providing a direct way to verify the theoretical predictions of this paper.