Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows

Forest, M. Gregory; Wang, Qi

doi:10.1007/s00397-002-0252-0

Cited by 78 publications

(94 citation statements)

References 125 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These simple closure approximations respect the traceless property of the orientational dynamic equation, and have been shown to yield a good approximation of kinetic theory in the dynamics of monodomains at the nematic concentrations of interest here [10,15,16]. These closures are exact when the molecules are aligned perfectly.…”

Section: Continuity Equationmentioning

confidence: 85%

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles (with Z. Cui, M.G. Forest and Q. Wang), SIAM J. Appl. Math. , 66 (4), 2006 Abstract. Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in the rod or platelet ensemble translate to nonuniform composite properties and to residual stresses in the material. These issues motivate our analysis of two prototypes for planar shear processing: drag-driven Couette and pressure-driven Poiseuille flows. Hydrodynamic theories for high aspect ratio rod and platelet macromolecules in viscous solvents are well developed, which we apply in this paper to model the coupling between short-range excluded volume interactions, anisotropic distortional elasticity (unequal elasticity constants), wall anchoring conditions, and hydrodynamics. The goal of this paper is to generalize scaling properties of steady flow molecular structures in slow Couette flows with equal elasticity constants [M. G. Forest et al., J. Rheol., 48 (2004), pp. 175-192] in several ways: to contrast isotropic and anisotropic elasticity; to compare Couette versus Poiseuille flow; and to consider dynamics and stability of these steady states within the asymptotic model equations.

show abstract

Section: Continuity Equationmentioning

confidence: 85%

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Certain descriptions of the rheology of non-Newtonian complex fluids containing liquid crystalline polymers combine macroscopic partial differential equations with microscopic stochastic differential equations ( [9], [11], [14], [12], [7]). A simple model of nematic liquid crystalline polymers -the rigid rod model -using the Maier-Saupe potential, gives rise to a Smoluchowski equation for the single particle distribution function on the unit sphere ( [2], [10], [4], [13], [5]). In spite of its simplicity, this equation exhibits nontrivial nonlinear dynamical features, in contrast with classical Fokker-Planck equations for noninteracting particles ( [8]).…”

mentioning

confidence: 99%

Remarks on a Smoluchowski equation

Constantin¹,

Kevrekidis²,

Titi³

2004

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

Abstract.We study the long time dynamics of a Smoluchowski equation arising in the modeling of nematic liquid crystalline polymers. We prove uniform bounds for the long time average of gradients of the distribution function in terms of the nondimensional parameter characterizing the intensity of the potential. In the two dimensional case we obtain lower and upper bounds for the number of steady states. We prove that the system is dissipative and that the potential serves as unique determining mode of the system.

show abstract

“…An asymptotic formula for the critical value is established in terms of the other material parameters and compared with direct numerical computations. The rigorous as well as asymptotic results for the equilibria of the Smoluchowski equation will provide valuable insights into the governing system of pdes which is prototypical in kinetic theories for solution of polymers and dispersions [13,18,23,24,14]. …”

Section: Discussionmentioning

confidence: 99%

Nonparallel solutions of extended nematic polymers under an external field

Zhou¹,

Wang²,

Wang³

2007

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

View full text Add to dashboard Cite

Abstract. We continue the study on equilibria of the Smoluchowski equation for dilute solutions of rigid extended (dipolar) nematics and dispersions under an imposed electric or magnetic field [25]. We first provide an alternative proof for the theorem that all equilibria are dipolar with the polarity vector parallel to the external field direction if the strength of the permanent dipole (µ) is larger than or equal to the product of the external field (E) and the anisotropy parameter (α 0 ) (i.e. µ ≥ |α 0 |E). Then, we show that when µ < |α 0 |E, there is a critical value α * ≥ 1 for the intermolecular dipole-dipole interaction strength (α) such that all equilibria are either isotropic or parallel to the external field if α ≤ α * ; but nonparallel dipolar equilibria emerge when α > α * . The nonparallel equilibria are analyzed and the asymptotic behavior of α * is studied. Finally, the asymptotic results are validated by direct numerical simulations.

show abstract

Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows

Cited by 78 publications

References 125 publications

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Remarks on a Smoluchowski equation

Nonparallel solutions of extended nematic polymers under an external field

Contact Info

Product

Resources

About