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 (Re 1). Two different non-Newtonian fluids are considered -a simplified Phan-Thien-Tanner (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 pressurecontrolled 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 ) 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 (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 fluid). To conclude, this study aims to afford to the experimentalist a system of knowledge to apriori delineate the peeling characteristics of a certain class of complex fluids.