The understanding of the rheological behaviour of suspensions in aqueous electrolytes is necessary for the optimal design of hydraulic transport lines. In these applications, particle size is at least 10 micron, and the particle Reynolds number, Rep, is finite: O(10−1). Although there are some experimental and numerical data on the rheology of such suspensions, the number of detailed analyses is limited. Therefore, 3-D direct numerical simulations of dense suspensions in aqueous electrolytes are conducted to assess the dynamics of the relative apparent viscosity and particle structures. The solid–liquid interfaces are resolved, and the flow is simulated, employing an in-house immersed boundary-lattice Boltzmann method code. In addition to the hydrodynamics resolved in the computational grid, our simulations include unresolved sub-grid scale lubrication corrections and non-contact electric double layer (EDL) and Van der Waals forces for a wide range of particle volume fractions, ϕv, at a single Rep=0.1. Under these conditions, the contribution of the Van der Waals force was found to be weak. With an increase in ϕv, the effect of EDL forces decreased the relative apparent viscosity. Particle layering and structural arrangements were analysed for ϕv=43 and 52%. As the Debye length (i.e., the thickness of EDL) decreases, the particle layers near the walls weakened. The analyses reveal how at these high volume fractions, chain-like assemblies are transformed into hexagonal arrangements.@en

We carried out 3D simulations of monodisperse particle suspensions subjected to a constant shear rate with the view to investigate the effect of electrical double layers around the particles on apparent suspension viscosities. To this end, expressions for Debye length, zeta potential, and ionic strength (pH) of the liquid were incorporated into our in-house lattice Boltzmann code that uses the immersed boundary method and includes subgrid lubrication models. We varied the solids concentration and particle radius, keeping the particle Reynolds number equal to 0.1. We report on results with respect to the effect of pH in the range 9 through 12 and of Debye length on apparent viscosity and spatial suspension structures, particularly at higher solids volume fractions, and on the effect of flow reversals.@en

Three-dimensional direct numerical simulations of dense suspensions of monodisperse spherical particles in simple shear flow have been performed at particle Reynolds numbers between 0.1 and 0.6. The particles translate and rotate under the influence of the applied shear. The lattice Boltzmann method was used to solve the flow of the interstitial Newtonian liquid, and an immersed boundary method was used to enforce the no-slip boundary condition at the surface of each particle. Short range spring forces were applied between colliding particles over sub-grid scale distances to prevent overlap. We computed the relative apparent viscosity for solids volume fractions up to 38% for several shear rates and particle concentrations and discuss the effects of these variables on particle rotation and cluster formations. The apparent viscosities increase with increasing particle Reynolds number (shear thickening) and solids fraction. As long as the particle Reynolds number is low (0.1), the computed viscosities are in good agreement with experimental measurements, as well as theoretical and empirical equations. For higher Reynolds numbers, we find much higher viscosities, which we relate to slower particle rotation and clustering. Simulations with a sudden change in shear rate also reveal a history (or hysteresis) effect due to the formation of clusters. We quantify the changes in particle rotation and clustering as a function of the Reynolds number and volume fraction.@en

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 (ϕv) and particle Reynolds numbers (Rep) were varied over the ranges 6%≤ϕv≤47% and 0.105≤Rep≤0.529. The simulations included sub-grid scale corrections for unresolved lubrication forces and torques (normal and tangential). When ϕv 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 ϕv>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.@en