Modeling and Simulation of Inhomogeneous Time-Dependent Poiseuille Pipe Flow of Aggregating Concentrated Suspensions

The development of appropriate models and an efficient methodology for the effective numerical simulation of transient pipe flows of aggregating suspensions fluids, exhibiting thixotropic and viscoelastic effects, is discussed. A pseudo-spectral method based on Chebyshev orthogonal polynomial spatial approximations is used. This numerical method has been validated against the analytical solution of Newtonian and upper-convected Maxwell fluids in oscillatory Poiseuille flows.

To model the viscoelastic and thixotropic characteristics of the aggregating suspension rheology, we use a multiscale approach, where a reduced (zero-moment-based) model of the aggregation based on a microscopic population balance approach is coupled with a phenomenological macroscopic extended White-Metzner-type viscoelastic model for the stress. We also describe the effect of stress and wall-induced migration through a variant of the Phillips et al. [Phys. Fluids 4 (1992) 30-40] model. We show the development of concentration gradients depending on both the steady and oscillatory pressure gradient characteristics. A potentially important result for applications is that the superposition of oscillatory gradient to the steady one can potentially increase the average fluid throughput.