Modelling of concentrated suspensions using a continuum constitutive equation

Abstract

We simulate the behaviour of suspensions of large-particle, non-Brownian, neutrally-buoyant spheres in a Newtonian liquid with a Galerkin, finite element, Navier–Stokes solver into which is incorporated a continuum constitutive relationship described by Phillips et al. (1992). This constitutive description couples a Newtonian stress/shear-rate relationship (where the local viscosity of the suspension is dependent on the local volume fraction of solids) with a shear-induced migration model of the suspended particles. The two-dimensional and three-dimensional (axisymmetric) model is benchmarked with a variety of single-phase and two-phase analytic solutions and experimental results. We describe new experimental results using nuclear magnetic resonance imaging to determine non-invasively the evolution of the solids-concentration profiles of initially well-mixed suspensions as they separate when subjected to slow flow between counter-rotating eccentric cylinders and to piston-driven flow in a pipe. We show good qualitative and quantitative agreement of the numerical predictions and the experimental measurements. These flows result in complex final distributions of the solids, causing rheological behaviour that cannot be accurately described with typical single-phase constitutive equations.

Three‐dimensional free surface flow simulation of segregating dense suspensions

“…The solid fraction decreases in front of the piston pushing the suspension and is higher in the second half of the domain along the pipe axis. This is in agreement with experimental observation [9]. The mean solid fraction on sections normal to the pipe axis was computed and plotted along the pipe axis in Figure 9.…”

“…The uniformity of the suspension downstream of the piston will then affect the distribution of particles inside the molded part. An experimental study of this problem was performed by Subia et al [9]. The piston radius is 2.54 cm and the pipe was filled with material on a length of 30 cm.…”

“…Phillips et al [8] introduced the diffusive flux model based on the concept of particle concentration 453 diffusion. Experimental validation of the model for simple 1D or 2D problems is shown in References [9,10]. The suspension balance model was first introduced by Nott and Brady [11], who introduced the concept of suspension 'temperature'.…”

“…The solution algorithm and the finite element approach are described in Section 3. In Section 4, the approach is validated for flow problems for which experimental data are available: circular Couette flow, piston-driven flow and sudden contractionexpansion flow [9,13,17]. The ALE formulation is first compared with an Eulerian solution for the case of the piston-driven flow problem and used to solve the sudden contraction-expansion flow.…”

Synergy between shear-induced migration and secondary flows on red blood cells transport in arteries: considerations on oxygen transport

“…The used benchmark corresponds to the pipe flow studied in [43]: it consists of a pressure-driven axial flow of a monomodal suspension through a 122 cm long pipe with radius 2.54 cm. A uniformly mixed suspension of spherical particles of 3178 mm in diameter with initial volume fraction of 0.50 was set in motion under an inlet mass flow rate of 0.3 kg s 21 with a constant inlet volume fraction of 0.5.…”