We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discreteelement simulations whose results we also present.

While there has been much success in modeling the linear and nonlinear rheology of monodisperse entangled linear polymers, progress in the constitutive modeling of polymeric materials continues to lag behind the needs of industry. Industrially sourced polymers are typically polydisperse (comprising a broad distribution of molecular weights), making their rheology more suitable for processing but also more difficult to predict. To date, there are no molecular-based constitutive models that are practically suitable for describing industrially relevant polymers in industrially relevant flows. In this article, we extend but strongly simplify the model of Read et al. [J. Rheol. 56, 823-873 (2012)], which is able to predict the linear and nonlinear rheology of bidisperse blends but is prohibitively complex for industrial use. We propose a pair of simplified tube models for polydisperse melts of entangled linear polymers that combine the success of the double reptation approximation [des Cloizeaux, Europhys. Lett. 5, 437-442 (1988)] in the linear regime with the success of the Rolie-Poly constitutive equation [Likhtman et al., J. Non Newtonian Fluid Mech. 114, 1-12 (2003)] in the nonlinear regime. We first review the key concepts of the double reptation approximation and the original (monodisperse) Rolie-Poly constitutive model. Subsequently, we provide the details of our approximate models for the particular case of a bidisperse blend and show that these models naturally identify the effects from couplings between constraint release and chain retraction (i.e., the so-called "enhanced stretch relaxation time"). Finally, we generalize to a multicomponent (polydisperse) model, based on the same underlying principles. Along the way, we also show that both of our models are in qualitative, and largely quantitative, agreement with experimental data for bidisperse and polydisperse melts of entangled linear polymers.

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We recently developed a tensorial constitutive model for dense, shear-thickening particle suspensions that combines rate-independent microstructural evolution with a stress-dependent jamming threshold. This gives a good qualitative account for reversing flows, although it quantitatively overestimates structural anisotropy [J. J. J. Gillissen et al., Phys. Rev. Lett. 123 (21), 214504 (2019)]. Here we use the model to predict the unjamming effect of superposed transverse oscillations on a steady shear flow in the thickened regime [N. Y. C. Lin et al., Proc. Nat. Acad. Sci. USA 113, 10774]. The model successfully reproduces the oscillation-mediated viscosity drop observed experimentally. We compare the time-dependent components of the stress and microstructure tensors to discrete-element simulations. Although the model correctly captures the main qualitative behaviour, it generally over-predicts the microstructural anisotropy in steady shear, and it under-predicts the number of particle contacts in oscillating shear. It also does not fully capture the correct variation in phase angle between the transverse component of the microstructure and the shear rate oscillations, as the amplitude of the latter is increased. These discrepancies suggest avenues for future improvements to the model. arXiv:1911.00280v2 [physics.flu-dyn]

We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both unentangled systems (Rouse-like motion) and well entangled systems (reptation, contour length fluctuations, chain retraction, and constraint release). Special attention is given to the solutions that emerge when the 'breaking time' of the chain becomes fast compared to various stress relaxation processes. In these 'fast breaking' limits, we reproduce previously known results (with some corrections) and also present new results for nonlinear stress relaxation dynamics. Our analysis culminates with a fully developed constitutive model for the fast breaking regime in which stress relaxation is dominated by contour length fluctuations. Linear and nonlinear rheology predictions of the model are presented and discussed.