Dynamics of Free Surface and Pure Elongational Flows of Liquid Crystalline Polymers

The performance properties of many polymers are dom inated by the molecular alignment induced during pro cessing by the elongational ow component that is the diagonal component of the velocity gradient tensor Here we discuss two idealizations of this ow microstructure in teraction We rst summarize our recent studies of biaxial nematic patterns and phase transitions Forest andWang a of lyotropic liquid crystalline polymers LCPs in response to imposed elongational ows We show radi ally symmetric biaxial nematic patterns coexist with ho mogeneous biaxial patterns characterized by Rey Rey All biaxial patterns in unidirectional stretching ows are unstable whereas planar stretching induces can didate stable biaxial nematic patterns Non homogeneous biaxial patterns have potential core defects and two spe cial director alignments are selected by imposing a nite pressure condition along the axis of ow symmetry The role of director dynamics in response to ow perturbations is described and in particular new elongation induced director instabilities are revealed extending seminal sta bility and phase transition results Khokhlov and Se menov See et al Bhave et al Rey Hu and Ryskin We then examine two spe cial solution families of the governing equations for free surface radially symmetric cylindrical LCP ber ows following analogous Newtonian results of Segur et al Se gur et al The cylindrical free surface only accom modates uniaxial orientation and from these ideal tran sient solutions we analyze the linearized stability of the coupled ow and microstructure in the LCP thin lament approximation Forest et al