Rheology and particle migration in suspensions of hard to soft particles

Understanding and predicting the flow of dense suspensions of solid particles dispersed in a liquid is important for many industrial processes as well as for natural phenomena. The description and the prediction of flows of suspensions require expressions for the stress tensor with respect to the volume fraction (and shear rate, when relevant), and a description of particle migration, which sets the spatial and temporal volume fraction field.

The project aims at studying numerically the rheological properties of suspensions of hard to soft spheres, dispersed in a Newtonian fluid. Using a DEM approach, and a recently developed model of lubricated contact, we will study the role of particle deformability, an essential ingredient which is usually overlooked in existing simulations. Deformability is crucial to regularise the divergence of the lubrication forces at contact, but its effects on the suspension rheology remain to be investigated in depth.

Our recently developed model of lubricated contacts produced new results related to the role of contact friction and led to a complete set of constitutive relations for dense suspensions¹. We are now able to tackle efficiently the case of slightly deformable particles, for which there exists very few dedicated studies in the literature. Lubrication, friction and deformability are strongly coupled. Under contact, deformation leads to a decrease of the friction coefficient, but also induces rolling friction by creating a flat interface. However, deformation under lubrication forces can also prevent contact formation. At a macroscopic level, these effects are ignored by the established “𝜇( 𝐼𝑣)” constitutive model of hard sphere suspensions, as there is a new dimensionless number characterizing the competition between shear forces and particle elasticity, the capillary number Ca. We will study the stress tensor in homogenous shear. We will deduce from the numerical results phenomenological expressions based on systematic variations of the particle deformability, in a large range of volume fraction and shear rates, effectively extending the 𝜇( 𝐼𝑣) rheology to a 𝜇( 𝐼𝑣,Ca) rheology. We will also focus on viscous resuspension, which occurs when an external force field (typically gravity) is exerted on a flowing buoyant suspension, leading to gradients of volume fraction. This phenomenon is closely related to particle migration and the study of the transient regime from a homogenous (non flowing) suspension to the re-suspended steady state will lead to improve existing continuum models by determining expansional viscosity.

¹ See Chevremont et al. 2019, 2020