Numerical investigation of particle migration in rheometric flows of suspensions

The rheological characterization of noncolloidal suspensions is quite a challenging task, since they may exhibit different behaviors, such as shear thickening, shear thinning and yield stress. During rheometric tests, problems such as slip, sedimentation, and particle migration might contribute to scatter the data. Particle migration for concentrated suspension has been studied under neutral buoyancy (Acrivos and Leighton 1987; Phillips et al. 1992; Chow et al. 1994; Ramachandran and Leighton 2008; Rebouças et al. 2018) but not much has been found for dilute or semi-dilute suspensions in literature. Some authors have reported that for low Reynolds number the particle migration across streamlines is shear induced in concentrated suspensions. Although several studies have reported that particle migration occurs from high to low shear regions, experimental evidence verified in the current work shows that particle may also migrate from low to high shear regions. The aim of the current work is to investigate numerically particle migration taking place in rheometric flows between parallel plates. The proposed model is based on a two-fluid model that considers averaged mass and momentum equations for each phase and includes constitutive equations for drag, virtual mass and lift forces to account for interphase interactions between solid and liquid phases. The equations are solved by using the Finite Volume ANSYS ® CFX ® software. The studied geometry consists of a 35 mm parallel-disk geometry separated by 1 mm gap. A 3D solution domain is assumed, the disks are modeled as no-slip walls, with one rotating and the other static. The lateral interface between the sample and the environment is modeled as a free-slip surface. Buoyancy is considered, the flow is assumed as isothermal and laminar, and the phases are treated as Newtonian incompressible fluids. The sample is initially assumed to be static and the solid particles is homogeneously dispersed inside the liquid phase at a known volume fraction. A transient calculation is run until the dispersion settles inside the domain and a steady state flow is reached. The suspension solvent is a mineral oil with a viscosity of 0.025 [Pa s] and density of 869.7 [kg/m]. Several simulations were run by changing the disk rotating speeds from 5 to 100 [rad s], the particle sizes from 10 to 100 [m], the solid phase densities from 600 to 2300 [kg/m] and the particle volume fractions from 10 to 30%. The numerical results were corroborated with analytical solutions for liquid single-phase flows. As observed in prior works (Batchelor and College 1951; Mellor et al. 1968; McCoy and Denn 1971; Dewey 1984), the single-phase flow solutions revealed that the secondary radial flow generated between the disks starts to influence the calculated torque at a given rotating Reynolds number. The secondary radial flow orientation, however, depends on which disk is rotating. The fluid flows outwards near the rotating disk and then return inwards near the static disk. The two phase-flow simulations revealed that this secondary flow orientation affects significantly particle migration. Induced by the secondary flow, heavy particles tend to migrate outwards when the lower disk rotates and inwards when the upper disk rotates. Particles lighter than the liquid experience a reverse mechanism since they float to the upper disk due to buoyancy. These different trends ultimately cause particular effects on the apparent viscosity, for which numerical results showed good agreement with measured values.