Texture evolution of sheared liquid crystalline polymers: Numerical predictions of roll-cells instability, director turbulence, and striped texture with a molecular model

Abstract

In the present work, we study the textural evolution of liquid crystal polymer ͑LCP͒ systems under planar shear at high shear rates, based on computational simulations using a recently developed molecular model with distortional elasticity ͓Feng et al. ͑2000͔͒. We concentrate our attention on the final striped texture that is observed in real LCP systems and on the secondary flow instability characterized by the formation of cross-sectional roll cells that is believed to represent the starting point of the orientational evolution. We verify that the theoretical model is capable of predicting a texture evolution that captures many of the essential features of the interplay between shear flow and LCP microstructure that are observed in experiments. We identify the mechanisms at play and the relative roles of the various forces in determining the evolution of texture at moderate shear rates and how they depend on the Deborah number, which is the characteristic parameter that defines the different regimes at moderate and high values of shear rate.

Reduced numerical modeling of flows involving liquid-crystalline polymers

“…Notable examples of mean field approaches to anisotropic particle interaction described in the kinetic theory framework are the model initially proposed by Hess in 1976 as mentioned by Doi and Edwards in [12], or the physically more realistic LC models proposed by Marrucci and coworkers [36][37][38][39] and of Beris and Edwards [3,[13][14][15]. In spite of the complexities associated with the constitutive equations resulting from solving the kinetic theory, major advances have been made in the coupled solution of the hydrodynamic field equations and the LC constitutive equation as well as in the evolution of LC structure in given velocity fields [9][10][11][17][18][19][20][21][22]26,35,42,45,48,49].…”

Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

“…(23), (18), and (26), so that (˚n j ), (f n j ), and (G n j , v n j ) are updated sequentially at each time step.…”

“…The Maier-Saupe potential can be classified as a purely "local" nematic potential, whereas the Marrucci-Greco potential contains phenomenological elastic terms similar to the first "nonlocal" contribution to the Taylor series expansion of the original Onsager potential. These tensor-based simplifications of the Doi theory [24][25][26][27] are mathematically similar to the broad class of phenomenological, tensor-based theories of LC dynamics [28][29][30], because both types of theories incorporate the same physical forces in the texture evolution equations. Both sets of theories also suffer the same drawbacks: (1) they require the assumption of constant-density, even in defects and interfaces; (2) they require closure approximations, which can be extremely imprecise; (3) they require artificial anchoring boundary conditions and (4) they lack the ability to resolve interfaces and defects on the length scale of an individual rod.…”

A kinetic–hydrodynamic simulation of microstructure of liquid crystal polymers in plane shear flow

“…Later, Forest et al gave some more detailed monodomain analysis [8][9][10][11][12]14,32]. For inhomogeneous flow, several simulations and analysis were carried out [2,4,7,17,[29][30][31]. Most of them are based on closure approximation of Doi-type kinetic theory with Onsager potential, Maier-Saupe potential or Marrucci-Greco potential.…”