Rolie-Poly fluid flowing through constrictions: Two distinct instabilities

Reis, Timothy; Wilson, H.J.

doi:10.1016/j.jnnfm.2013.01.002

Cited by 14 publications

(4 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The original intended use for this model was for computationally demanding calculations such as complex flow geometries. Indeed the model's computational simplicity has been exploited in numerical studies of polymer processing [4][5][6][7][8][9], flow instabilities [10,11], and shear banding [12][13][14][15][16]. However, the relative simplicity of the Rolie-Poly model also makes it amenable to analytic calculation.…”

Section: Introductionmentioning

confidence: 99%

Analytic solutions of the Rolie Poly model in time-dependent shear

Holroyd

Martin

Graham

2017

Journal of Rheology

View full text Add to dashboard Cite

We consider shear flows that comprise of step changes in the shear rate. For these flows, we derive analytic solutions of the Rolie-Poly constitutive equation. Our method involves piecing together solutions for constant rate shear in a variety of flow rate regimes. We obtain solutions for interrupted shear, recoverable strain and non-linear relaxation following cessation of flow. Whenever strong flow is present we neglect reptation, as other mechanisms dominate and for interrupted shear our solution is approximate as we neglect convective constraint release. Our analytic solutions provide new insight in several ways. These include revealing the mechanism of some experimental features of these flows; suggesting a method to extract the polymer contribution to the normal stress in the velocity gradient direction (σyy) from shear stress measurements alone; and a method to isolate the influence of convective constraint release (CCR) from damping function measurements. We also run complementary GLaMM model calculations to verify that insight from our analytic approach translates to this more detailed model.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytic solutions of the Rolie Poly model in time-dependent shear

Holroyd

Martin

Graham

2017

Journal of Rheology

View full text Add to dashboard Cite

show abstract

“…The non‐dimensional form of the Rolie‐Poly constitutive equation is given by 32

\begin{matrix} lefttrue \\ We [\frac{\partial σ}{\partial t} + u \cdot \nabla σ - (\nabla u) σ - σ {(\nabla boldu)}^{normalT}] \\ = \begin{array}{l} (1 goodbreak- β) (\nabla boldu goodbreak+ {(\nabla u)}^{T}) goodbreak- \frac{2 (1 goodbreak- β)}{{italicWe}_{R}} boldI (1 goodbreak- \sqrt{3 / τ}) \\ goodbreak- boldσ (1 goodbreak+ \frac{2 italicWe}{{italicWe}_{R}}) goodbreak+ \frac{2 italicWe \sqrt{3 / τ}}{{italicWe}_{R}} boldσ (1 goodbreak- β^{*}) goodbreak+ \frac{6 italicWe β^{*}}{{We}_{R} τ} boldσ, \end{array} \end{matrix}

Where

italicWe = τ_{d} U / L

and

{We}_{R} = τ_{R} U / L

are orientation Weissenberg number and stretch Weissenberg number respectively; and

τ = \frac{We}{1 - β} italictr boldσ + italictr boldI

.…”

Section: Mathematical Modelmentioning

confidence: 99%

Macroscopic and mesoscopic simulation of polystyrene melt in the filling process of injection molding

Liu

Jiang

2023

J of Applied Polymer Sci

View full text Add to dashboard Cite

In this article, a fluid flow and heat transfer model which consist of the mass, momentum, and energy conservation equations together with the level set equation and Rolie‐Poly constitution equation is proposed and applied to simulate the rheological behaviors of viscoelastic polystyrene melt in the filling process of injection molding. The macroscopic velocity, pressure, temperature, stress, and mesoscopic molecular conformation of polystyrene melt are shown and analyzed detailedly during the mold filling process. The single‐mode Rolie‐Poly model is employed to describe the stress–strain relationship of polystyrene melt, and the level set method is used to capture the evolution of melt front interface. The governing equations for polymer melt are discretized by the finite volume method on collocated mesh, and solved by the SIMPLE algorithm. Numerical simulations have been implemented based on rectangular cavities with different gate locations, and rectangular and circular inserts. Numerical results indicate that the gate locations, gate numbers, insert size and shape are major factors that affect the rheological behaviors of polystyrene melt in the filling stage of injection molding, and polymer chains experienced higher shear and extension effects in the regions near to mold walls and obstacle. In addition, the length and position of weld lines are discussed in the current study.

show abstract

“…These experimental results were verified using the Rolie-Poly model, and the mechanism between viscoelastic instability and molecular polymer dynamics was discussed by the authors. The model was also used by Reis and Wilson (2013) to investigate the connection between the molecular dynamics and the elastic instabilities of the entangled polymer melts.…”

Section: Introductionmentioning

confidence: 99%

“…One is called "FLOWSOLVE" which was used by and Hassell et al (2008a, b) to simulate the complex flow behavior, and the other is called "EUFLOW" which was used by Lord et al (2010) to investigate the flow behavior of polymer fluid. These two kinds of solvers are based on the finite element method, while Reis and Wilson (2013) employed the semi-staggered dilation-free finite volume method to discretize the governing equations. In this paper, the continuity, the momentum, and the constitutive equations are discretized by finite volume method and solved by Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm on collocated mesh.…”

Section: Introductionmentioning

confidence: 99%

Finite volume simulations of behavior for polystyrene in a cross-slot flow based on Rolie-Poly model

et al. 2016

View full text Add to dashboard Cite

The flow behavior of polystyrenes is investigated numerically for a cross-slot geometry using Rolie-Poly model with finite extensibility, and governing equations for the polystyrene melts are solved by finite volume method with domain extension technique on the collocated grid. The effect of molecular weight, flow rate, and two kinds of Weissenberg numbers on the principal stress difference (PSD) profiles are discussed detailedly. The microstructures of polymer melts, including molecular orientation, extension, and deformation, are also investigated and presented in this paper. We found that the orientation of Weissenberg number is the major factor affecting the PSD profiles and the performance of the RoliePoly model has been improved greatly by introducing finite extensibility at high extension rate. The numerical results are consistent with the available experiment results, which demonstrate the capabilities of single-mode Rolie-Poly model with finite extensibility to simulate the flow behavior of polystyrenes and the numerical method developed in this paper.

show abstract

Rolie-Poly fluid flowing through constrictions: Two distinct instabilities

Cited by 14 publications

References 36 publications

Analytic solutions of the Rolie Poly model in time-dependent shear

Analytic solutions of the Rolie Poly model in time-dependent shear

Macroscopic and mesoscopic simulation of polystyrene melt in the filling process of injection molding

Finite volume simulations of behavior for polystyrene in a cross-slot flow based on Rolie-Poly model

Contact Info

Product

Resources

About