Effect of the inverse Langevin approximation on the solution of the Fokker-Planck equation of non-linear dilute polymer
Article dans une revue avec comité de lecture
Date
2016Journal
Journal of Non-Newtonian Fluid MechanicsAbstract
The Langevin function is defined by L (x ) = coth (x ) −1 /x . Its inverse is useful for many applications and especially for polymer science. As the inverse exact expression has no analytic representation, many ap- proximations have been established. The most famous approximation is the one traditionally used for the finitely extensible non-linear elastic (FENE) dumbbell model in which the inverse is approximated by L −1 (y ) = 3 y/ (1 −y 2 ) . Recently Martin Kröger has published a paper entitled ‘Simple, admissible and accurate approximations of the inverse Langevin and Brillouin functions, relevant for strong polymer de- formation and flows’ (Kröger, 2015) in which he proposed approximations with very reduced error in relation to the numeric inverse of the Langevin function. The question we aim to analyze in this short communication is: when one uses the traditional approximation rather than the more accurate one pro- posed by Kröger is that really significant regarding the value of the probability distribution function (PDF) in the frame work of a kinetic theory simulation? If yes when we move to the upper scale by evaluating the value of the stress, can we observe a significant difference? By making some simple 1D simulations in homogeneous extensional flow it is demonstrated in this short communication that the PDF prediction within kinetic theory framework as well as the macroscopic stress value are both affected by the quality of the approximation.
Files in this item
Related items
Showing items related by title, author, creator and subject.
-
Communication avec acteA design process is a sequence of design phases, starting with the design requirement and leading to a definition of one or several system architectures. For every design phase, various support tools and resolution methods ...
-
Communication sans actenone
-
Article dans une revue avec comité de lectureThe aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model ...
-
Article dans une revue avec comité de lectureThe use of cohesive zone models is an efficient way to treat the damage, especially when the crack path is known a priori. This is the case in the modeling of delamination in composite laminates. However, the simulations ...
-
Article dans une revue avec comité de lectureThis study proposes to simulate the deep drawing on carbon woven composites in order to reduce the manufacturing cost and waste of composite material during the stamping process, The multi-scale anisotropic approach of ...