Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress

Abstract

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Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

“…E ngineers use large-amplitude oscillatory shear (LAOS) flow experiments to investigate the physics of complex liquids (Giacomin and Dealy, [1] Chapter 11 of Cho, [2] Equation (2.42) of Carreau and De Kee [3] ). Since its conception in 1935, [4,5] (mindful of the erratum following Reference 4 of Saengow et al [6,7] ) oscillatory shear flow has become by far the most popular laboratory method for exploring the physics of polymeric liquids.…”

“…We generate oscillatory shear flow by confining the fluid to a simple shear apparatus and then by displacing one solid-liquid boundary sinusoidally in its own plane (see Figure 1 of Saengow et al [6] ). The corresponding cosinusoidal shear rate is given by:…”

“…Specifically, we choose the Oldroyd 8-constant framework. We choose this framework for its rich diversity of important and popular special cases (Table 4 of Saengow et al [6] lists 14 of these). The Oldroyd 8-constant framework is not just a constitutive model with 8 constants.…”

“…19-20 of Bird et al [40] ). [6] Case III in Jones [14] ), for corrugated wire coated through a corrugated die (see Section 3 of Jones and Jones [15] and Section 2 of Jones [16] ), and for plastic pipe extrusion for elliptical pipe, [17,18] and also for extrusion from an eccentric annular pipe die (Case II in Jones, [14] Saengow et al [19,20,21,22] ). The Oldroyd 8-constant framework is given by (see Equation (8.1-2) of Bird et al [23] and Oldroyd [24] ):…”

2017 winner of The Canadian Journal of Chemical Engineering award for best graduate student paper

“…Chai focused on oscillatory shear performed at large amplitudes (LA), where the molecules are grossly distorted from their shapes at rest. Chai arrived at the first exact mathematical equations for interpreting the stresses associated with these gross distortions in LAOS …”