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

Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

“…This expression for p couples the evolution of f to the continuity equation (∇ · v = 0) and momentum equation [9,34,33]. For our computations, the momentum equation is written in the inertialess DEVSS-G formulation [39] as…”

“…For simple shear flow, variations of f, v, and G are restricted to the y-dimension [33], and flow are in the x-direction. The channel has length bL in the y-dimension.…”

“…Zhou et al [31,32] used a numerical scheme that coupled a finite difference discretization in physical space with spherical harmonics in orientation space in order to simulate the Doi diffusion equation with Marrucci-Greco elasticity in planar Couette flow. Yu and Zhang [33] followed this work by simulating the full nonhomogeneous Doi diffusion equation with the Onsager potential; their simulations invoked the simplifying constraint that rod orientations be restricted to the plane of shear with no logrolling or kayaking states allowed. This constraint is similar to the planar constraint invoked by Marrucci and Maffettone and effectively reduces orientation space to a single dimension Â.…”

Numerical Simulation of Emergence of Textures in Flows of Liquid Crystalline Polymers using a Constitutive Model with Long-Range Elasticity

“…[17][18][19][20][21][22][23][24] Constitutive equations including long-range elastic interactions in the nematic potential were successfully applied to describe defect textures. 17,18) Tsuji and Rey 19) have numerically analyzed the shear flow of LC materials using a nonlinear and nonequilibrium theory including the short-and long-range order elasticity and viscous effects.…”

Solução numérica de escoamentos de cristais líquidos nemáticos

“…Essa teoria tem sido utilizada por vários investigadores (ver por exemplo [56,55,144,145]) mas a aplicação dessa teoria a escoamentos em duas dimensões utilizando as equações completas de Doi e Edwards ainda não foi considerada. Mais detalhes sobre a teoria de Doi e Edwards [41] podem ser encontrados em [111,112].…”