SUPERCRITICAL BIFURCATIONS IN SIMPLE SHEAR-FLOW OF A NON-ALIGNING NEMATIC - REACTIVE PARAMETER AND DIRECTOR ANCHORING EFFECTS

Non-linear numerical analysis of the Leslie-Ericksen (L-E) equations f or transient and steady rectilinear simple shear flows is presented fo r a typical non-aligning rigid-rod low molecular weight nematic (8CBP (4-noctyl-4'-cyanobiphenyl)). Instead of the fixed torque balance used by previous investigators, a computationally efficient and accurate f orm of the torque balance, gyroscopic torque balance, is formulated an d implemented. A series of experimentally measured material constant s ets is used to investigate the effect of the reactive parameter lambda on the three-dimensional orientation field. Stable steady state solut ions for both parallel and homeotropic orientation anchorings are obta ined. Dynamic simulations show the stability properties of the steady state solutions and the routes to the stable steady states. The exchan ge of stability in the orientation and velocity fields is described as a supercritical bifurcation. Two families of stable steady state solu tions are found: in-shear-plane (IP) solutions and out-of-shear-plane (OP) solutions; the former are characterized by the confinement of the director within the shear plane while the latter are characterized by three-dimensional orientation. It is found that the stability of the steady states is controlled by the magnitude of the Ericksen number (E ). Orientational transitions from IP to OP are shown to occur when E e xceeds a certain critical value E(co), that depends on the magnitude o f the reactive parameter and the director wall anchoring. The non-line ar stability theory of Landau was used to describe these transition ph enomena. The calculated apparent viscosity and first normal stress dif ference for the OP solutions are shown to be smooth functions of the E ricksen number E.