Effect of long range order on sheared liquid crystalline materials: Flow regimes, transitions, and rheological phase diagrams

Abstract

A generalized theory that includes short-range elasticity, long-range elasticity, and flow effects is used to simulate and characterize the shear flow of liquid crystalline materials as a function of the Deborah (De) and Ericksen (Er) numbers in the presence of fixed planar director boundary conditions; the results are also interpreted as a function of the ratio R between short-range and long-range elasticity. The results are effectively summarized into rheological phase diagrams spanned by De and Er, and also by R and Er, where the stability region of four distinct flow regimes are indicated. The four regimes for planar (two-dimensional orientation) shear flow are (1) the elastic-driven steady state, (2) the composite tumbling-wagging periodic state, (3) the wagging periodic state, and (4) the viscous-driven steady state. The coexistence of the four regimes at a quacritical point is shown to be due to the emergence of a defect structure. The origin, the significant steady and dynamical features, and the transitions between these regimes are thoroughly characterized and analyzed. Quantitative and qualitative comparisons between the present complete model predictions and those obtained from the classical theories of nematodynamics (Leslie-Ericksen and Doi theories) are presented and the main physical mechanisms that drive the observed deviations between the predictions of these models are identified. The presented results fill the previously existing gap between the classical Leslie-Ericksen theory and the Doi theory, and present a unified description of nematodynamics.

Robustness of pulsating jet-like layers in sheared nano-rod dispersions

“…These long-time transient responses have been identified in experiments [4,[6][7][8] and confirmed through theoretical descriptions [9][10][11][12][13][14][15].…”

“…We note that the formation of composite tumbling-wagging 1D heterogeneous attractors have been observed previously, including studies of Tsuji and Rey [13] and the authors [31], where in-plane symmetry was imposed and pure shear was also imposed. The present simulations do not enforce in-plane symmetry, and solve for the fully coupled flow, yet we find the space-time attractor is in-plane; the out-of-plane degrees of freedom in the tensor and full kinetic distribution function simply decay to zero.…”

Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

“…In equilibrium studies,˚w all induces an oblate layer of rods near the wall for low values of N and a nematic layer of rods near the wall for high values of N. However, there is no particular nematic director that is preferred. Previous, tensor-based rheological studies used anchoring boundary conditions on S to force the nematic director to lie in a particular orientation [28,30]. Yu and Zhang approximated the wall by replacing the wall potential with an excluded-volume potential associated with a region with a high density of stationary rods (we term this technique as the "frozen-rod" potential).…”

“…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.…”

Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals

“…When | λ | > 1, strain overcomes vorticity effects, and the average orientation is close to the velocity for rods and the velocity gradient for disks, respectively, while for | λ | < 1 complex periodic and steady three -dimensional (3D) orientation modes arise (Tsuji and Rey, 2000 ). A general expression for the tumbling parameter is given by the product of a shape function ‫ޒ‬ ( p ) and a thermorheological function g T S T , , ( , , ) ϕ ϕ γ ( ) (Rey, 2010 ):…”