Abstract
The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_{1}$ , whereas positive values of $N_{1}$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.
Highlights
Steady-shear rheology provides a fundamental framework for the investigation and description of the properties of incompressible non-Newtonian fluids
These are commonly identified with the shear stress σ ≡ σxy, through which the viscosity η ≡ σ /γis defined, and the first and second normal stress differences, N1 ≡ σxx − σyy and N2 ≡ σyy − σzz, respectively. (We set x as the flow direction, y as the gradient direction and z as the vorticity direction of the simple shear flow.) Newtonian fluids are characterized by a constant value of η, while N1 and N2 are zero
It is only at volume fractions approaching the jamming conditions that we can observe positive values of N1 and our results indicate that, for a computational model that aims at simulating hard-sphere suspensions, these ought to be regarded as artefacts of the numerical approximation
Summary
Steady-shear rheology provides a fundamental framework for the investigation and description of the properties of incompressible non-Newtonian fluids. Upon increasing the volume fraction φ in the high-Péclet-number limit, there is a transition from a regime in which the negative values of N1 are essentially determined by hydrodynamic interactions to a regime in which synergies between hydrodynamic and contact interactions produce even more evident negative values of N1 It is only at volume fractions approaching the jamming conditions that we can observe positive values of N1 and our results indicate that, for a computational model that aims at simulating hard-sphere suspensions, these ought to be regarded as artefacts of the numerical approximation. This fact suggests that experimental measurements of positive values of N1 may indicate the presence of elastic interactions, such as soft elastic layers at particle surfaces or some cohesive bonding between particles, that cannot be captured by simple hard-sphere models Another possible explanation for these observations traces them back to boundary effects, due to the presence of walls that cannot be avoided in a standard rheometer (Yeo & Maxey 2010; Gallier et al 2016). N0 is more informative than N2, as appears from its use in presenting experimental measurements (see, for instance, Boyer, Pouliquen & Guazzelli 2011b)
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