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

Abstract

We investigate the transient, fluid–structure interaction (FSI) of a non-Newtonian fluid peeling two Hookean sheets at low Reynolds numbers ( R e ≪ 1 ). Two different non-Newtonian fluids are considered – a simplified Phan–Thien–Tanner (sPTT) model fluid, 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 ( x f ∼ t 1 / 2 ) towards 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 ( x f ∼ t α , α < 0 . 5 ), but ultimately reaches the end faster due to an order of magnitude larger prefactor for the propagation speed. We provide scaling analyses and similarity solutions to delineate several regimes of peeling based on the sheet elasticity, flow Weissenberg number (for sPTT fluid), and shear-thinning exponent (for generalized Newtonian fluids). To conclude, this study aims to afford to the experimentalist a system of knowledge to a priori delineate the peeling characteristics of a certain class of complex fluids. • Modeled fluid–structure interaction of a complex fluid peeling two Hookean sheets. • Examined two different fluid constitutive rheological models. • Developed simulations and similarity solutions for the peeling front during start-up. • Quantified peeling time effects due to shear thinning. • Peeling time for a shear-thinning fluid is smaller than a Newtonian fluid.