Using an immersed boundary-lattice Boltzmann method, we investigated the response of dense granular suspensions to time-varying shear rates and flow reversals. The evolution of the relative apparent viscosity and particle structures was analysed. The concentration of solids (φ v ) and particle Reynolds numbers (Re p ) were varied over the ranges 6% ≤ φ v ≤ 47% and 0.105 ≤ Re p ≤ 0.529. The simulations included sub-grid scale corrections for unresolved lubrication forces and torques (normal and

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... angential). When φ v surpasses 30%, the contribution of the tangential lubrication corrections to the shear stress is dominant. While for intermediate solids fractions we find weak shear-thinning, we see weak shear-thickening for φ v > 40%. We show how the structure and apparent viscosity of a suspension evolves after a reversal of the shear direction. For 47% solids, simulations with step changes in the shear rate show the effects of the previous shear history on the viscosity of the suspension. J o u r n a l P r e -p r o o f Journal Pre-proof sions is typical practice in many processes, such as wastewater treatment, drilling operations, and ore refining plants, operating such transport lines frequently results in significant disruptions. Improved understanding of the complicated dynamics of particle-particle and fluid-particle interactions is thus highly desirable. Specifically, changes in the rheology and structure that occur due to the effects of flow reversals and abrupt shifts in the shear rate are of particular interest to us, as the transport of slurry involves such phenomena in bends, fittings, and valves. In our previous study (Srinivasan et al., 2020), we explored the effects of steady shear rate on rheology by implementing a spring-like force to handle particle collisions. In this paper, we improve the modelling of interparticle interactions by applying explicit lubrication corrections over sub-grid scale distances, so that the resulting simulation can provide a better understanding of both the steady-state and transient rheological behaviour of granular suspensions. We restrict ourselves to suspensions of particles typically some 300 micron in diameter, with solids volume fractions φ v between 6 and 47%, and particle Reynolds numbers Re p between 0.105 and 0.529. Over the last few decades, research on the rheology of suspensions has advanced through both experimental and computational studies. Brady and Bossis (1985) used Stokesian dynamics to investigate the apparent viscosity (the ratio of the effective viscosity over the viscosity of the suspending fluid) of concentrated suspensions. Jogun and Zukoski (1996) conducted experiments with plate-like particles suspended inside a basic solution to study its rheological behaviour (the yielding type of response). A review article by Stickel and Powell (2005) also discusses the rheology of dense suspensions with more emphasis on microstructure and total fluid stresses. The non-Newtonian behaviour of dense suspensions, such as normal-stress differences and shearinduced migration, has been discussed by Guazzelli (2017) and co-workers (Simon et al., 2015). By coupling the Lattice Boltzmann Method (LBM) with a hybrid Immersed Boundary Method (IBM) and a bounce-back scheme, Lorenz et al. (2018) demonstrated the continuous and dis-2 J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof Reynolds number typically of O(10 −1 ), and the flow is laminar. The carrier liquid phase is Newtonian with kinematic viscosity ν. We model the suspensions as consisting of monodisperse rigid spheres that are 300 micron in diameter, which is typical for the slurries we are interested in. 5 J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof c for φ v = 10, 33, 40, and 47%. With an increase in φ v , for a fixed h * c the average cluster size 27 J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J Bergenholtz, J F Brady, and M Vicic. The non-Newtonian rheology of dilute colloidal suspensions. . Local transient rheological behavior of concentrated suspensions. Journal of Rheology, 55(4):835-854, 2011. J F Brady and G Bossis. The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. Journal of Fluid Mechanics, 155:105-129, 1985. E Brown and H M Jaeger. Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Reports on Progress in Physics, 77(4):046602, 2014. 36 J o u r n a l P r e -p r o o f Journal Pre-proof S Chen and G D Doolen. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30(1):329-364, 1998. T Dbouk, L Lobry, and E Lemaire. Normal stresses in concentrated non-Brownian suspensions. Journal of Fluid Mechanics, 715:239-272, 2013. J J Derksen and S Sundaresan. Direct numerical simulations of dense suspensions: wave instabilities in liquid-fluidized beds. V G Kolli, E J Pollauf, and F Gadala-Maria. Transient normal stress response in a concentrated suspension of spherical particles. Journal of Rheology, 46(1):321-334, 2002. I M Krieger and T J Dougherty. A mechanism for non-Newtonian flow in suspensions of rigid spheres. Transactions of the Society of Rheology, 3(1):137-152, 1959. 37 J o u r n a l P r e -p r o o f Journal Pre-proof T Krüger, F Varnik, and D Raabe. Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method. Computers & Mathematics with Applications, 61(12):3485-3505, 2011. T Krüger, H Kusumaatmaja, A Kuzmin, O Shardt, G Silva, and E M Viggen. The lattice Boltzmann method: Principles and practice. Springer, 2017. P M Kulkarni and J F Morris. Suspension properties at finite Reynolds number from simulated shear flow. Physics of Fluids, 20(4):040602, 2008. A J C Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. Journal of Fluid Mechanics, 271:285-309, 1994a. A J C Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. Journal of Fluid Mechanics, 271:311-339, 1994b. E Lorenz, V Sivadasan, D Bonn, and A G Hoekstra. Combined lattice-Boltzmann and rigid-body method for simulations of shear-thickening dense suspensions of hard particles. Computers & Fluids, 172:474-482, 2018. N Q Nguyen and A J C Ladd. Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Physical Review E, 66(4):046708, 2002. M E O'Neill and R Majumdar. Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part 1. The determination of exact solutions for any values of the ratio of radii and separation parameters. of non-Brownian 38 J o u r n a l P r e -p r o o f Journal Pre-proof suspensions of rough frictional particles under shear reversal: A numerical study. Journal of Rheology, 60(4):715-732, 2016. X Shan and H Chen. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47(3):1815, 1993. A Sierou and J F Brady. Rheology and microstructure in concentrated noncolloidal suspensions. of dense suspensions of noncolloidal spheres in yield-stress fluids. Journal of Fluid Mechanics, 776, 2015. S Srinivasan, H.E.A Van den Akker, and O Shardt. Shear thickening and history-dependent rheology of monodisperse suspensions with finite inertia via an immersed boundary lattice Boltzmann method. A Ten Cate, J J Derksen, L M Portela, and H E A Van den Akker. Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. Journal of Fluid Mechanics, 519:233-271, 2004. Y Thorimbert, F Marson, A Parmigiani, B Chopard, and J Lätt. Lattice Boltzmann simulation of dense rigid spherical particle suspensions using immersed boundary method. Computers & Fluids, 166:286-294, 2018. 39 J o u r n a l P r e -p r o o f Journal Pre-proof Highlights:  Numerical simulations of granular suspensions exhibit weak shear-thickening.  The contribution of tangential lubrication stress to the total stress of the suspension is substantial.  Temporal evolution of the suspension viscosity and particle structures follow similar dynamics.  Memory effects of both the interstitial liquid and particle structures affect the suspension viscosity. J o u r n a l P r e -p r o o f Journal Pre-proof