A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in Newtonian fluids

Abstract

SynopsisWe propose a new, minimal tensorial model attempting to clearly represent the role of microstructure on the viscosity of non-colloidal suspensions of rigid particles. Qualitatively, this model proves capable of reproducing several of the main rheological trends exhibited by concentrated suspensions: anisotropic and fore-aft asymmetric microstructure in simple shear and transient relaxation of the microstructure towards its stationary state. The model includes only few constitutive parameters, with clear physical meaning, that can be identified from comparisons with experimental data. Hence, quantitative predictions of the complex transient evolution of apparent viscosity observed after shear reversals are reproduced for a large range of volume fractions. Comparisons with microstructural data shows that not only the depletion angle, but the pair distribution function, are well predicted. To our knowledge, it is the first time that a microstructure-based rheological model is successfully compared to such a wide experimental dataset.

Tensorial rheological model for concentrated non-colloidal suspensions: normal stress differences

“…While this latter model involves thirteen free parameters, it failed to provide quantitative comparisons with shear-reversal experiments: an unexpected sharp spike in both apparent viscosity and normal stress differences was obtained at the time of the reversal. Using a much simpler model, involving only four free parameters and a linear evolution evolution for the conformation tensor, Ozenda et al (2018) recently obtained a good quantitative agreement with the shear-reversal measurements of Blanc et al (2011) for a wide range of volume fraction φ. Furthermore, at the micro-structural scale, the model successfully reproduced both the pair distribution function and the depletion angles measured by Blanc et al (2013).…”

A Continuum Model for Complex Flows of Shear Thickening Colloidal Solutions

“…In particular, if we neglect the c 9 term, which we will do throughout much of this paper, it may be possible to extract k 4 and c 7 from experimental SAOS data. Neglecting c 9 , the model, in essence, only has three adjustable parameters, now on the same order as the model by [31].…”

“…Such a constitutive model would need to take into account the underlying mechanisms of shear and extensional thickening, as well as the construction and destruction of microstructure by flow [24]. To tackle this challenge, recent work has focused on developing constitutive models that describe the evolution of the microstructure of particle suspensions coupled with general equations for fluid flow [25][26][27][28][29][30][31][32][33] In early models [25][26][27][28], particle stress is made explicitly dependent on the microstructure through the consideration of a local conformation tensor that is inspired from the orientation distribution tensor defined for dilute fiber suspensions [34]. Hand [35] formulated a general representation theorem for the total Cauchy stress tensor in terms of the conformation tensor and the deformation rate tensor.…”

“…More recent theories have focused on deriving constitutive models that reduce the number of free parameters and provide a more direct connection with the microstructure of non-colloidal suspensions [31,33]. Ozenda et al [31] proposed a new, minimal tensorial model representing the role of microstructure on the viscosity of non-colloidal suspensions of rigid particles.…”

“…More recent theories have focused on deriving constitutive models that reduce the number of free parameters and provide a more direct connection with the microstructure of non-colloidal suspensions [31,33]. Ozenda et al [31] proposed a new, minimal tensorial model representing the role of microstructure on the viscosity of non-colloidal suspensions of rigid particles. Their model qualitatively reproduces several of the main rheological trends exhibited by concentrated suspensions: anisotropic and fore-aft asymmetric microstructure in simple shear and transient relaxation of the microstructure toward its stationary state.…”