• français
    • English
    français
  • Login
Help
View Item 
  •   Home
  • Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM)
  • View Item
  • Home
  • Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology

Type
Articles dans des revues avec comité de lecture
Author
CRUZ, Camilo
86289 Procédés et Ingénierie en Mécanique et Matériaux [Paris] [PIMM]
CHINESTA, Francisco
REGNIER, Gilles
86289 Procédés et Ingénierie en Mécanique et Matériaux [Paris] [PIMM]

URI
http://hdl.handle.net/10985/9991
DOI
10.1007/s11831-012-9072-2
Date
2012
Journal
Archives of Computational Methods in Engineering

Abstract

Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks.

Files in this item

Name:
PIMM - ACME - CRUZ - 2012.pdf
Size:
4.033Mb
Format:
PDF
View/Open

Collections

  • Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM)

Related items

Showing items related by title, author, creator and subject.

  • Shear-strain step response in linear regime of dilute suspensions of naturally bent carbon nanotubes 
    CRUZ, Camilo; ILLOUL, Lounès; CHINESTA, Francisco; REGNIER, Gilles (Wiley, 2012)
    Impressive enhancements of the storage modulus have been documented when low volume fractions of single wall carbon nanotubes (SWNTs) are added to a Newtonian solvent for obtaining dilute suspensions. The intrinsic bending ...
  • Thermoforming of a PMMA transparency near glass transition temperature 
    GILORMINI, Pierre; CHEVALIER, Luc; REGNIER, Gilles (Wiley, 2010)
    In order to simulate the thermoforming of a transparency, constitutive equations are proposed for the nonlinear viscoelastic behaviour of poly(methyl methacrylate) near glass transition temperature, which include large ...
  • Legitimate domain of a Newtonian behavior for thermal nanoimprint lithography 
    TEYSSEDRE, Hubert; GILORMINI, Pierre; LANDIS, Stefan; REGNIER, Gilles (Elsevier, 2013)
    Nanoimprint lithography is an efficient way to reproduce nanostructures down to 20 nanometers in sub-micrometer polymeric films. To optimize this process, simulation using a Newtonian behavior is a cheap and efficient way ...
  • Simulation of the stretch blow moulding process: from the modelling of the microstructure evolution to the end-use elastic properties of polyethylene terephthalate bottles 
    COSSON, Benoit; CHEVALIER, Luc; REGNIER, Gilles (Springer, 2012)
    The whole stretch blow-moulding process of PET bottles is simulated at the usual process temperature in order to predict the elastic end-use properties of the bottles. An anisotropic viscoplastic constitutive law, coupled ...
  • Forced assembly by multilayer coextrusion to create oriented graphene reinforced polymer nanocomposites 
    LI, Xiguang; MCKENNA, Gregory; MIQUELARD-GARNIER, Guillaume; GUINAULT, Alain; SOLLOGOUB, Cyrille; REGNIER, Gilles; ROZANSKI, Artur (ELSEVIER, 2013)
    A potential advantage of platelet-like nanofillers as nanocomposite reinforcements is the possibility of achieving two-dimensional stiffening through planar orientation of the platelets. The ability to achieve improved ...

Browse

All SAMCommunities & CollectionsAuthorsIssue DateCenter / InstitutionThis CollectionAuthorsIssue DateCenter / Institution

Newsletter

Latest newsletterPrevious newsletters

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales