DYNAMIC SIMULATIONS OF SHEAR-FLOW-INDUCED CHIRALITY AND TWISTED-TEXTURE TRANSITIONS OF A LIQUID-CRYSTALLINE POLYMER

An alternative computational adaptive method to solve the Leslie-Erick sen equations of nematic hydrodynamics is presented. The method uses a daptive torque balances and is able to accurately compute arbitrary th ree-dimensional orientation fields. The method is applied, in conjunct ion with computational bifurcation methods, to solve the governing equ ations for a model rigid-rod, non-aligning, nematic polymer, in steady and transient rectilinear simple shear flows, using fixed parallel di rector anchoring. The five-component solution vector consists of the p rimary and secondary velocity components and the three-dimensional dir ector field n. The parameter space is the line representing the magnit udes of the Ericksen number (epsilon). According to the magnitude of e psilon, seven types of stable steady-state solutions are found and ful ly characterized. The seven types of solutions are classified as in-pl ane solutions if the director remains within the shear plane, defined by the how direction and the velocity gradient, and as out-of-plane (O P) solutions if the director field is out of the shear plane (three-di mensional orientation). The six OP solutions are-three pairs of mirror -image solutions that differ from each other by their rotation number (Lambda). Two pairs of out-of-plane solution branches are achiral (Lam bda = 0) and display one-way twisting from the shear plane. One pair o f out-of-shear-plane solution branches is chiral (Lambda = +/-1) and d isplays a full 2 pi director rotation when going from the bottom plate to the top plate. The nucleation mechanisms of these chiral branches are identified using a torque analysis. The main bifurcation phenomena and the local stability of the branches are summarized in a bifurcati on diagram. The main structural changes, as the parameter epsilon incr eases, are captured by visualization of the transient director field. The main features of the velocity field are captured by particle track ing visualization, which yields three-dimensional particle motions dri ven by the combined primary and secondary flows. The main mechanical r esponses, captured by the transient theological functions (apparent vi scosity and the first normal stress differences) exhibit, at low shear rates, non-Newtonian responses that are usually found in isotropic, v iscous, or viscoelastic liquids, at large shear rates. Dynamic simulat ion in conjunction with the bifurcation diagram is used to construct t he stability phase diagram, which yields the adopted stable steady-sta te solution that results from shearing a monodomain sample with fixed parallel director anchoring. Finally, the strain history is shown to c ontrol,the finally adopted steady state, thus invalidating linear supe rposition which is usually valid at small shear rates.