Micro-Macro Simulation of Viscoelastic Flows at High Weissenberg Number

Mohit Bajaj^a, Matteo Pasquali^b and J. Ravi Prakash^a

^aDepartment of Chemical Engineering, Monash University,

Melbourne, VIC 3800, Australia,

^bDepartment of Chemical Engineering, MS 362, Rice University,

Houston, TX 77005, USA

We present here a micro-macro approach based on combining the Brownian configuration fields (BCF) method (van den Brule et al, JNNFM 1997) with the Galerkin finite element method, to compute both a viscoelastic flow around a cylinder and a slot coating flow (free surface flow). A distinct advantage of the BCF method is its ability to treat models for which no exact closed-form constitutive equations exist, such as FENE dumbbells or models with hydrodynamic and excluded volume interactions.

Most of the studies in literature on viscoelastic flow around a cylinder are limited to the use of an Oldroyd-B constitutive equation, which is a poor constitutive model compared to other more sophisticated constitutive models such as FENE-P, FENE etc. Here, we show numerical results for different constitutive models with both linear and non-linear dumbbells using BCF. We are able to obtain solutions beyond the limiting Weissenberg numbers (Wi) typically encountered in macroscopic schemes. In particular, we show that the FENE and FENE-P models produce mesh converged results with relatively coarse meshes at high Wi number compared to the meshes used to solve an Oldroyd-B constitutive model.

Computations were also found to be stable at much higher Wi number using the BCF method for a slot coating flow. We observe that the slot coating flow behaviour of dilute polymer solutions is dramatically different from that of ultra-dilute solutions (studied previously by Pasquali and Scriven, JNNFM, 2002) in terms of the failure of flow computations at high Wi.