BIAXIAL STEADY-STATES AND THEIR STABILITY IN SHEAR FLOWS OF LIQUID-CRYSTAL POLYMERS

The biaxiality of the steady state solutions and their stability to ou t-of-plane disturbances in shear flows of spatially homogeneous liquid crystal polymers using two approximate models, BMAB-Doi and BMAB-HL1, which are derived from the kinetic theory developed by Bhave et al. ( 1993) (BMAB) using the Doi and the first Hinch-Leal closure approximat ion, respectively, are studied. By casting the models in a novel biaxi al representation of the orientation tensor with two built-in order pa rameters and a triad of directors, we show explicitly that the steady states of the BMAB models exhibit biaxial symmetry except for some uni axial degeneracy at isolated Peclet numbers and polymer concentration values. Moreover, we obtain all the steady states in which two directo rs are confined to the shearing plane and analyze their stability with respect to both in-plane and out-of-plane disturbances. We find that (1) flow-aligning family is the unique stable solution family in the B MAB-Doi model, where two order parameters are of opposite signs; (2) t he flow-aligning family in the BMAB-HL1 model is stable only in a fini te range of polymer concentration 0 < N less than or equal to 10, the log-rolling family is born unstable and attains stability through an i nstability to stability transition at a sufficiently high polymer conc entration value, N > 10, which grows with respect to the Peclet number ; (3) The loss-of-stability in the flow-aligning family at N = 10 is c aused by a one-dimensional director rotational instability pertinent t o the existence of the maximum allowable degree of orientation with re spect to the how-aligning major director, 5/6, and is coincident with the change-of-sign behavior of the first normal stress difference and the smaller order parameter as well. (C) 1997 The Society of Rheology.