A fully deterministic micro-macro simulation of complex flows involving reversible network fluid models

Micro-macro models associate the coarse-grained molecular scale of the kinetic theory to the macroscopic scale of continuum mechanics. The conservation equations are solved along with the microscopic equation or the so-called Fokker-Planck equation. In this paper, a micro-macro approach based on the separated representation introduced in [2,3] with the Stream-Tube method [10-12,21,22] is implemented to study the main features of fiber and polymer networks solutions in complex flows. The Fokker-Planck equation, that defines the fluid microstructure, is solved using a separated representation strategy and is coupled to the macroscopic equations through the macroscopic extra-stress tensor evaluated at the microscopic level. Then, the flow kinematics is solved by applying the Stream-Tube method.

[1]  Fumihiko Tanaka,et al.  Viscoelastic properties of physically crosslinked networks. 1. Transient network theory , 1992 .

[2]  B. Mokdad,et al.  On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach , 2007 .

[3]  Octavio Manero,et al.  Rheological modelling of complex fluids: A transient network model with microstates , 2005 .

[4]  L. Gary Leal,et al.  Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems: Part 2. The effect of flow perturbations on the simple shear behavior of LCPs , 1999 .

[5]  Cédric Chauvière,et al.  A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations , 2003 .

[6]  Ahmad Mahmoud,et al.  Finite element and stream-tube formulations for flow computations - two-dimensional applications , 2002, Math. Comput. Simul..

[7]  Francisco Chinesta,et al.  A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids - Part II: Transient simulation using space-time separated representations , 2007 .

[8]  Kenneth D. Knudsen,et al.  Brownian dynamics simulation of reversible polymer networks using a non-interacting bead-and-spring chain model , 2007 .

[9]  Jean-Robert Clermont,et al.  Numerical simulation of complex flows of non‐Newtonian fluids using the stream tube method and memory integral constitutive equations , 1995 .

[10]  Dana Grecov Radu.  Formulations theoriques et simulations numeriques d'ecoulements de fluides viscoelastiques entre cylindres excentriques et en conduites , 2000 .

[11]  Manuel Laso,et al.  “SMART” POLYMERS IN FINITE-ELEMENT CALCULATIONS , 1992 .

[12]  J. Clermont.  Analysis of incompressible three-dimensional flows using the concept of stream tubes in relation with a transformation of the physical domain , 1988 .

[13]  Francisco Chinesta,et al.  Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers , 2009 .

[14]  R. Keunings.  MICRO-MACRO METHODS FOR THE MULTISCALE SIMULATION OF VISCOELASTIC FLOW USING MOLECULAR MODELS OF KINETIC THEORY , 2004 .

[15]  Catalin R. Picu,et al.  Network model for the viscoelastic behavior of polymer nanocomposites , 2004 .

[16]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[17]  Jean-Robert Clermont,et al.  Numerical study of flows of complex fluids between eccentric cylinders using transformation functions , 2002 .

[18]  Jay D. Schieber,et al.  Brownian dynamics simulation of reversible polymer networks under shear using a non-interacting dumbbell model , 2003 .

[19]  Stuart L. Cooper,et al.  Models of shear-thickening behavior in physically cross-linked networks , 1993 .

[20]  Magdeleine Normandin,et al.  A numerical approach for computing flows by local transformations and domain decomposition using an optimization algorithm , 2002 .

[21]  Cédric Chauvière,et al.  Simulation of dilute polymer solutions using a Fokker–Planck equation , 2004 .

[22]  Jean-Robert Clermont,et al.  Numerical simulations of non-stationary flows of non-Newtonian fluids between concentric and eccentric cylinders by stream-tube method and domain decomposition , 2008 .

[23]  Francisco Chinesta,et al.  A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids , 2006 .

[24]  Jan Mewis,et al.  Evaluation of a transient network model for telechelic associative polymers , 2004 .

[25]  J. Clermont,et al.  Three-dimensional extrudate swell experimental and numerical study of a polyethylene melt obeying a memory-integral equation , 1999 .

[26]  Ashok Srinivasan,et al.  Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems Part 1: Method , 1997 .