Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

Green, Micah J.; Brown, Robert A.; Armstrong, Robert C.

doi:10.1016/j.jnnfm.2008.09.004

Cited by 6 publications

(4 citation statements)

References 43 publications

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“…[24]. The constitutive equations (16), (17), and (18) can be rewritten in terms of s = (W xy , W xx , W yy ) as…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…The fluid starts in an equilibrium state at t = 0, and is subjected to a step xy shear stress of magnitude Σ 0 . The homogeneous shear rate that arises in response to this stress, γ0 (t), can be calculated by numerical solution of the ordinary differential equations (16,17,18) (setting D = 0) and substituting for γ using…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…Textures in the orientation of the director (e.g. [16]), including a banded structure in the velocity direction have been predicted using models of rod-like LCPs, and some of these have included spatial variation in the shear rate [17]. However, the corresponding models have not been developed for flow-aligning semiflexible LCPs.…”

Section: Introductionmentioning

confidence: 99%

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Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

Adams

Corbett

2018

Phys. Rev. E

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In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semiflexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs, it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly nonuniform spatial velocity profiles have been observed in experiments. We analyze the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behavior of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.

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“…[24]. The constitutive equations (16), (17), and (18) can be rewritten in terms of s = (W xy , W xx , W yy ) as…”

Section: Linear Stability Analysismentioning

confidence: 99%

Section: Linear Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

Adams

Corbett

2018

Phys. Rev. E

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“…This formulation is similar to the development of [19][20][21]. A solution of rigid rods can be described by the distribution function f (r, u, t), which describes the probability that a rod will have location r and orientation u at time t. Integrating f over all orientations u gives the local number density n(r, t).…”

Section: Formulationmentioning

confidence: 99%

Spinodal decomposition and nematic coarsening in a rigid-rod solution

Green

Brown

Armstrong

2009

Journal of Non-Newtonian Fluid Mechanics

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Stochastic semi-Lagrangian micro–macro calculations of liquid crystalline solutions in complex flows

Prieto

Ilg

Bermejo

et al. 2010

Journal of Non-Newtonian Fluid Mechanics

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Keywords:Liquid crystal Stochastic simulation Semi-Lagrangian scheme Micro-macro Finite element Richardson Euler-Maruyama A general method for the simulation of complex flows of liquid crystalline polymers (LCPs) using a stochastic semi-Lagrangian micro-macro method is introduced. The macroscopic part uses a spatialtemporal second order accurate semi-Lagrangian algorithm, where ideas from the finite element and natural element methods are mixed in order to compute average quantities. The microscopic part employs a stochastic interpretation of the Doi-Hess LCP model, which is discretized with a second order Richardson extrapolated Euler-Maruyama scheme.The new method is validated and tested using the benchmark problem of flow between rotating eccentric cylinders. In a decoupled analysis, a discussion on the sensibility of the scalar order parameter to the macroscopic flow is offered. For the coupled situation, the proposed method predicts disclinations at certain regions of the geometry, as well as an accentuated abatement of the flow as the strength of the micro-macro interaction increases. Further examples are provided at different Peclet and concentration numbers to gain insight on the behavior of complex flows of LCPs in the eccentric cylinder geometry.The generality and robustness of the method, as well as its accurate prediction of LCP behavior under complex flows are main features of the implementation.

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Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

Cited by 6 publications

References 43 publications

Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

Spinodal decomposition and nematic coarsening in a rigid-rod solution

Stochastic semi-Lagrangian micro–macro calculations of liquid crystalline solutions in complex flows

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