Nematodynamics weakly viscoelastic

The simulations in this and following sections are based on the continuum theory of weak viscoelastic nematodynamics [22, 23]. The closed set of constitutive equations... 

On the Time-Temperature Superposition in Weakly Viscoelastic Nematodynamics... 

Much research in the last few decades focused on the simulation of LCPs for various processes. Suitable rheological constitutive equations are required for this simulation. Leslie-Ericksen (LE) theory describes the flow behaviour and molecular orientation of many LCPs. LE model is limited to low shear rates and weak molecular distortions. But at high shear rate, the rate of molecular distortions is too fast. Doi and Edwards developed their model to describe the complex dynamics of macromolecules at high shear rate (Doi and Edwards 1978). Doi theory is applicable for lyotropic LCPs of small and moderate concentrations. Due to the complex nature of Doi theory, it is also challenging for simulation. Leonov s continuum theory of weak viscoelastic nematodynamics, developed on the basis of thermodynamics and constitutive relations, consider the nematic viscoelasticity, deformation of molecules as well as evolution of director. 

Leonov AI (2008b) A model of weak viscoelastic nematodynamics. Z Angew Math Phys 59 333-359... 

Leonov AI, Bassov NI, Kazankov YV (1977) The basic processing of thermosets and rubbers by injection molding (Russian). Chem Moscow 68-70 Leonov AI, Chen H (2010) Modeling and simulation in polymers. Wiley-VCH, Weinheim Leonov AI, Volkov VS (2002) A theory of viscoelastic nematodynamics. Rheol Acta Leonov AI, Volkov VS (2005) Weak viscoelastic nematodynamics Maxwell type. Condensed Matter... 

As mentioned, a lot of theoretical and experimental studies have been performed to understand physics and rheological properties of lyotropic LCPs. The molecular Doi approach with many improvements and experimental tests is well presented in the literature (e.g., see Ref. [5]). But the thermotropic LCPs were poorly understood till recently, in spite of many attempts to develop either nematodynamic or molecular description of their flow properties. The beauty of continuum approach is that it can be applied to molecular nematics ofboth different types, as well as to the nonyielding suspensions with shaped particles. Yet, general nematodynamic theories are multi-parametric. For example, the general LEP continuum LC theory contains five constitutive parameters [2]. Similarly, de Gennes potential proposed for the monodomain description of general weakly elastic behavior of LCE has also five parameters [37]. Because viscoelasticity is a combination of elastic and viscous effects, it is expected that even in easy theoretical schemes, the continuum approach to viscoelastic polymer nematodynamics should involve at least 10 constitutive parameters. 

As mentioned, there exists neither molecular nor continuum theory for describing complicated properties of thermotropic LCPs, although many experimental data for this type of LCPs have been accumulated. One of the objectives of the new continuum theory of weakly nonlinear viscoelastic nematodynamics [22, 23] is to interpret and simulate experimental data, and create models of processing for LPCs. 

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