Direct numerical simulation of the sedimentation of a particle pair in a shear-thinning fluid

By combining the momentum exchange method and a unified interpolation bounce-back scheme, a multiple-relaxation-time lattice Boltzmann method is developed to simulate the particle dynamics in a power-law fluid. With this method, the sedimentation of a particle pair in a shear-thinning power-law fluid for the generalized Archimedes number (Ar*) varying from 100 to 400 is studied. Depending on the value of Ar* and initial geometrical configuration, the particle pair is found to experience several different movement states, namely, the steady oblique doublet, periodic oscillation, period-doubling bifurcation, steady horizontal doublet, and chaos. Distinct from two groups of multiple stable states in the Newtonian system, three groups of multiple stable states are clearly identified in the present shear-thinning system: the steady oblique coexists with the periodic oscillation, the steady horizontal doublet coexists with the period-doubling bifurcation, and the steady horizontal doublet coexists with the chaos state. Moreover, the drafting, kissing, and tumbling (DKT) behavior of a particle pair observed in the Newtonian system is absent in the present shear-thinning system. It is attributed to the high-viscosity region between the particles, which can increase the viscous drag acting on the particle, thus preventing the particles from approaching each other and reducing particle aggregation. In addition, a critical value of the power-law index is obtained, below which the DKT state would not happen regardless of Ar*.