Stress communication and filtering of viscoelastic layers in oscillatory shear

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We revisit a classical topic: response functions of viscoelastic layers in large amplitude oscillatory shear. Motivated by questions concerning protective biological layers, we focus on boundary stresses in a parallel plate geometry with imposed oscillatory strain or stress. These features are gleaned from resolution and analysis of coupled standing waves of deformation and stress. We identify a robust non-monotone variation in boundary stress signals with respect to all experimental controls: viscoelastic moduli of the layer, layer thickness, and driving frequency. This structure of peaks and valleys in boundary values of shear and normal stress indicates redundant mechanisms for stress communication (by tuning to the peaks) and stress filtering (by tuning to the valleys). In this paper, we first restrict to a single-mode non-linear Maxwell model for the viscoelastic layer, where analysis renders a transparent explanation of the phenomena. We then consider a Giesekus constitutive model of the layer, where analysis is supplanted by numerical simulations of coupled non-linear partial differential equations. Parametric studies of wall stress values from standing waves confirm persistence of the Maxwell model phenomena. The analysis and simulations rely on and extend our recent studies of shear waves in a micro parallel plate rheometer [S.M. Mitran, M.G. Forest, L. Yao, B. Lindley, D. Hill, Extenstions of the Ferry shear wave model for active linear and nonlinear microrheology, J. Non-Newtonian Fluid Mech. 154 (2008) 120–135; D.B. Hill, B. Lindley, M.G. Forest, S.M. Mitran, R. Superfine, Experimental and modeling protocols from a micro-parallel plate rheometer, UNC Preprint, 2008].