Peeling of linearly elastic sheets using complex fluids at low Reynolds numbers

TL;DR

This study explores how complex non-Newtonian fluids influence the peeling dynamics of elastic sheets at low Reynolds numbers, revealing different propagation behaviors and providing scaling laws for various regimes.

Contribution

It introduces a detailed analysis of fluid-structure interaction with non-Newtonian fluids, including scaling laws and similarity solutions for peeling regimes.

Findings

Shear thinning fluids cause sub-diffusive peeling fronts.

Peeling speed is faster with shear thinning fluids despite sub-diffusive propagation.

Scaling laws delineate regimes based on elasticity and fluid properties.

Abstract

We investigate the transient, fluid structure interaction (FSI) of a non-Newtonian fluid peeling two linearly elastic sheets at low Reynolds numbers. Two different non-Newtonian fluids are considered; a simplified sPTT model, and an inelastic fluid with shear thinning viscosity (generalized Newtonian fluid). In the limit of small gap between the sheets, we invoke a lubrication approximation and numerically solve for the gap height between the two sheets during the start-up of a pressure-controlled flow. What we observe is that for an impulse pressure applied to the sheet inlet, the peeling front moves diffusively toward the end of the sheet when the fluid is Newtonian. However, when one examines a complex fluid with shear thinning, the propagation front moves sub-diffusively in time , but ultimately reaches the end faster due to an order of magnitude larger pre-factor for the propagation speed. We provide scaling analyses and similarity solutions to delineate several regimes of peeling based on the sheet elasticity, Wi number (for sPTT fluid), and shear thinning exponent (for generalized Newtonian fluid). To conclude, this study aims to afford to the experimentalist a system of knowledge to delineate the peeling characteristics of a certain class of complex fluids.