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Understanding the behaviour of multiphase flows of solid in viscoelastic fluids is essential in several industrial applications, such as oil sands mining and polymer processing. For this aim, a novel numerical algorithm was implemented on an open-source finite-volume fluid flow solver coupled with an immersed boundary method, to allow the use of viscoelastic constitutive equations on the fluid (continuous) phase. To avoid numerical issues related to high Weissenberg number flows the log-conformation tensor approach can be employed on the newly developed algorithm. The accuracy of the algorithm was evaluated by studying several benchmark flows, namely: (i) the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluids; (ii) rotation of a sphere in a homogeneous shear viscoelastic fluid flow; (iii) the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, considering both Newtonian and viscoelastic suspending fluids. All the results obtained, on the referred case studies, allowed either to replicate the ones available on the published literature, or to describe additional effects promoted by the assumption of viscoelastic behaviour on the continuous phase. To illustrate the potential of the developed code, a newly case study of the shear-induced solid particle alignment in wall-bounded Newtonian and viscoelastic fluids was studied. The role of the fluid rheology and finite gap size on both the approach rate and pathways of the solid particles are described., This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013. The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF).

This study reports the development of a direct simulation code for solid spheres moving through viscoelastic fluids with a range of different Theological behaviors. The numerical algorithm was implemented on an open source finite-volume solver coupled with an immersed boundary method, and is able to perform fully-resolved simulations, wherein all flow scales associated with the particle motion are resolved. The formulation employed exploits the log-conformation tensor to avoid high Weissenberg number issues when calculating the polymeric extra stress. A number of benchmark flows were simulated using this method, to assess the accuracy of the newly developed solver. First, the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluid was computed, and the numerical results were verified by comparison with experimental and computational data from the literature. Additionally, the spatial and temporal accuracies of the algorithm were evaluated, and different transient and advection discretization schemes were investigated. Second, the rotation of a sphere in a homogeneous shear flow was studied, and again the numerical results obtained were compared to those from the literature. Good agreement is obtained for the variation in the particle rotation rate as a function of Weissenberg number, using both the newly implemented algorithm and an alternative fixed-mesh approach. Finally, the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, consisting of either a Newtonian or viscoelastic suspending fluid was investigated. For the Newtonian fluid good agreement was obtained for the particle equilibrium position when compared to the well known Segre-Silberberg effect, and for the viscoelastic fluid the effect of the retardation ratio on the final particle equilibrium position was studied. Additionally, the newly-developed solver capabilities were tested to study the shear-induced particle alignment in wall-bounded Newtonian and viscoelastic fluids. The r, This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013 as well as by the MIT Portugal Program (MPP). The authors would like to acknowledge the Minho University cluster under the project Search-ON2: Revitalization of HPC infrastructure of UMinho (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2-0 Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF). Additionally, the authors would like to acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. http://www.tacc.utexas.edu Finally, the authors thank Bruno Santos from FSD blueCAPE Lda for insightful comments regarding the usage of the TACC resources.