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

Shear-induced migration in concentrated suspensions: Particle mass conservation, contact pressure and jamming

“…Inclusion of a true yield stress in jammed zones through, e.g., frictional effects Saramito [see, e.g., 55], would also be necessary to avoid the use of a regularised apparent viscosity and predict more realistic particle stress values in these regions. Finally, the development of anisotropic micro-structures in both jammed and sheared regions could also be considered through specific tensorial constitutive relations [13]. Once these more realistic constitutive models will be implemented and tested, future work shall also consider the extension of the numerical algorithm in order to efficiently address more complex geometries such as 3D channel flows, flows around obstacles [56,57], or re-suspension experiments [58].…”

“…Contacts and friction can also lead to shear-thickening effects, and influence the value of the critical particle volume fraction φ m above which the suspension is jammed and behaves as a solid [5,6]. Various constitutive models have been proposed to describe these properties, either through phenomenological expressions of the particle stresses [7,8,6], inclusion of auxiliary conformation tensors related to micro structure evolution [9,10,11,12,13], or by explicitly accounting for granular processes [14,15].…”

“…Since the study is primarily devoted to the formulation and numerical solution of the system of conservation laws, particle stress is modelled using the classical phenomenological constitutive relation proposed by Morris and Boulay [7]. Inter-particle friction or effects of micro structure are not directly taken into account at this stage, although they might be included in further versions of the model by using more sophisticated constitutive models [10,15,13]. As explained below, we do however introduce an additional pressure term that can be interpreted as a jamming pressure, to properly deal with the complementarity condition.…”

The physics of dense suspensions

“…This limits the number of free parameters but involves (often uncontrolled) approximations, in particular the closure of higher moments of n, such as nnnn in terms of nn (130,125). While phenomenological models can achieve quantitative agreement with experimental data regarding the transient behavior of the shear stress in simple shear (126), their predictions for normal stresses (when tested) are usually poorer (131,125) (although some aspects of the steady state behavior can be captured (132)).…”