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http://hdl.handle.net/10985/9991
Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology
CRUZ, Camilo; CHINESTA, Francisco; REGNIER, Gilles
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/99912012-01-01T00:00:00ZCRUZ, CamiloCHINESTA, FranciscoREGNIER, GillesKinetic 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.Shear-strain step response in linear regime of dilute suspensions of naturally bent carbon nanotubes
http://hdl.handle.net/10985/6800
Shear-strain step response in linear regime of dilute suspensions of naturally bent carbon nanotubes
CRUZ, Camilo; ILLOUL, Lounès; CHINESTA, Francisco; REGNIER, Gilles
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 dynamics of carbon nanotubes (CNTs) has been proposed to explain such elasticity. CNTs contain topological defects inducing naturally bent structures in absence of external forces and, hence, a semiflexible filament with a bent configuration at minimal internal-bending-energy is used for mimicking the structure of SWNTs in suspension. Previous continuous model is discretized as a non-freely jointed bead-rod chain with a naturally bent configuration for simulating the rheological behaviour after a shear-strain step in linear regime of SWNT dilute suspension by using a Brownian dynamics (BD) approach. In general, bead-rod chains exhibit an instantaneous relaxation after a high shear-strain step. Bending rigidity and number of constitutive rods are found to be determinant parameters in the internal-energy relaxation behaviour of non-freely jointed bead-rod chains in dilute solution. Proper comparisons between the BD simulation results and the experimental data for treated SWNT dilute suspensions confirm the consistency of the physical model mimicking the structure of a SWNT.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/68002012-01-01T00:00:00ZCRUZ, CamiloILLOUL, LounèsCHINESTA, FranciscoREGNIER, GillesImpressive 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 dynamics of carbon nanotubes (CNTs) has been proposed to explain such elasticity. CNTs contain topological defects inducing naturally bent structures in absence of external forces and, hence, a semiflexible filament with a bent configuration at minimal internal-bending-energy is used for mimicking the structure of SWNTs in suspension. Previous continuous model is discretized as a non-freely jointed bead-rod chain with a naturally bent configuration for simulating the rheological behaviour after a shear-strain step in linear regime of SWNT dilute suspension by using a Brownian dynamics (BD) approach. In general, bead-rod chains exhibit an instantaneous relaxation after a high shear-strain step. Bending rigidity and number of constitutive rods are found to be determinant parameters in the internal-energy relaxation behaviour of non-freely jointed bead-rod chains in dilute solution. Proper comparisons between the BD simulation results and the experimental data for treated SWNT dilute suspensions confirm the consistency of the physical model mimicking the structure of a SWNT.Mechanical and microstructural characterization of flowing weld lines in injection-molded short fiber-reinforced PBT
http://hdl.handle.net/10985/14636
Mechanical and microstructural characterization of flowing weld lines in injection-molded short fiber-reinforced PBT
BARADI, Mohamed Besher; CRUZ, Camilo; RIEDEL, Thomas; REGNIER, Gilles
The aim of this work is an extensive experimental mechanical and microstructural characterization of flowing weld lines (WLs) in injection-molded short glass fiber-reinforced polybutylenterephthalate (PBT) using X-ray computed tomography and digital image correlation (DIC). It was found that the induced fiber orientation (FO) in a flowing WL is similar to that induced by flow along a wall. In this test case, the impact of the flowing WL on the FO did not vanish after a flow length of 70 mm. The shape of the inserts, which originated the flowing WLs, only had a marginal effect on the induced FO gradient. By reducing part thickness, the erasing of the FO gradient induced by the WL is reached at shorter flow distances. At the WLs, there is a reduction of the fiber volume fraction in comparison to the regions far from the WL plane. DIC results show a pronounced strain localization at the WL, which can be explained by the FO gradient induced by the WL.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/146362019-01-01T00:00:00ZBARADI, Mohamed BesherCRUZ, CamiloRIEDEL, ThomasREGNIER, GillesThe aim of this work is an extensive experimental mechanical and microstructural characterization of flowing weld lines (WLs) in injection-molded short glass fiber-reinforced polybutylenterephthalate (PBT) using X-ray computed tomography and digital image correlation (DIC). It was found that the induced fiber orientation (FO) in a flowing WL is similar to that induced by flow along a wall. In this test case, the impact of the flowing WL on the FO did not vanish after a flow length of 70 mm. The shape of the inserts, which originated the flowing WLs, only had a marginal effect on the induced FO gradient. By reducing part thickness, the erasing of the FO gradient induced by the WL is reached at shorter flow distances. At the WLs, there is a reduction of the fiber volume fraction in comparison to the regions far from the WL plane. DIC results show a pronounced strain localization at the WL, which can be explained by the FO gradient induced by the WL.