# Thickening of viscoelastic flow in a model porous medium

## TL;DR

This study numerically investigates viscoelastic flow through a model porous medium, revealing mechanisms behind flow thickening as the Weissenberg number increases, with implications for understanding polymer solution flow behavior.

## Contribution

It identifies two distinct mechanisms of flow thickening in porous media and explores how porosity influences these effects using numerical simulations.

## Key findings

- Flow exhibits initial mild decrease then dramatic thickening with increasing Weissenberg number.
- Two mechanisms of thickening are identified depending on obstacle spacing.
- Flow remains steady across all Weissenberg numbers in a linear array configuration.

## Abstract

We study numerically two-dimensional creeping viscoelastic flow past a biperiodic square array of cylinders within the Oldroyd B, FENE-CR and FENE-P constitutive models of dilute polymer solutions. Our results capture the initial mild decrease then dramatic upturn ('thickening') seen experimentally in the drag coefficient as a function of increasing Weissenberg number. By systematically varying the porosity of the flow geometry, we demonstrate two qualitatively different mechanisms underpinning this thickening effect: one that operates in the highly porous case of widely spaced obstacles, and another for more densely packed obstacles, with a crossover between these two mechanisms at intermediate porosities. We also briefly consider 2D creeping viscoelastic flow past a linear array of cylinders confined to a channel, where we find that the flow is steady for all Weissenberg numbers explored.