In multiphase flows, accurately modeling the interaction between the liquid phase of complex fluids and a porous medium of solid spheres poses a fundamental challenge. The dynamics of moderately dense non-colloidal suspensions constituted by static random arrays of mono-disperse spherical particles in non-linear viscoelastic fluids is studied numerically. This numerical study consists of about 9000 different systems, in which the volume fraction of the dispersed solid phase, the Reynolds number Re , the solvent viscosity ratio β , the Weissenberg number Wi , and the mobility parameter of the Giesekus model α were varied to understand the particle's interactions with the viscoelastic suspending fluid. We aim to investigate the relationship between the volume fraction of the dispersed solid phase and the non-linear rheology of shear-thinning viscoelastic fluids with the normalized average drag force . In addition, by assessing the flow patterns predicted numerically, we were able to provide a characterization of the velocity and stress fields as a function of the simulation parameters.
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