Towards a Fokker-Planck Rheometer

Francisco Chinesta,A Jeffrey Giacomin,Roland Keunings,Ralph H Colby,Gary L Leal,Amine Ammar,Albert Co

doi:10.1063/1.2964618

Abstract

Models of kinetic theory provide a coarse‐grained description of molecular configurations wherein atomistic processes are ignored. Kinetic theory models can be very complicated mathematical objects sometimes defined in highly multidimensional spaces including the physical space, the time and the conformational space. In the past, stochastic based simulations were preferred to circumvent or at least alleviate the curse of dimensionality that many kinetic theory models exhibit. Recently, we proposed alternative solution strategies of the kinetic theory models based on the use of model reduction and separated representations for solving generic Fokker‐Planck descriptions. These strategies have been successfully applied to solve a large variety of models.

Highlights

Many natural and synthetic fluids are viscoelastic materials, in the sense that the stress endured by a macroscopic fluid element depends upon the history of the deformation experienced by that element
Theoretical modelling and methods of computational rheology have an important role to play in elucidating this coupling
The traditional approach has been to derive from a particular kinetic theory model a macroscopic constitutive equation that relates the viscoelastic stress to the deformation history

Summary

Introduction

Many natural and synthetic fluids are viscoelastic materials, in the sense that the stress endured by a macroscopic fluid element depends upon the history of the deformation experienced by that element. Models of kinetic theory provide a coarse-grained description of molecular configurations wherein atomistic processes are ignored. The traditional approach has been to derive from a particular kinetic theory model a macroscopic constitutive equation that relates the viscoelastic stress to the deformation history.

Results

Conclusion