Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods

In the present work, a numerical algorithm based on a combination of the lattice Boltzmann method (LBM) and the improved smoothed profile method (iSPM) has been proposed to study the motion of one, two and many circular particles in a non-Newtonian fluid. At first, the velocity profile of the non-Newtonian fluid at various power law indexes ( n ) was analyzed and the findings were compared with the numerical results of the previous works. Then, the motion of one circular cylinder and the hydrodynamic interactions between two particles in a shear flow were investigated. It was observed that Re shear, p had no important impact on the rotation of a single cylinder. In the two particles interaction, increasing the shear rate caused the particles to tumble on each other more closely and during a longer time. Therefore, the effective viscosity of a particulate suspension was considered for different Reynolds numbers and solid volume fractions, showing a satisfactory agreement with the previously published data. The results, therefore, showed that inertia increased the particles contribution to the effective viscosity of the suspension.