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 $\left(\mathrm{A}{\mathrm{r}}^{*}\right)$ varying from 100 to 400 is studied. Depending on the value of $\mathrm{A}{\mathrm{r}}^{*}$ 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 $\mathrm{A}{\mathrm{r}}^{*}$.

中文翻译：

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剪切稀化流体中颗粒对沉降的直接数值模拟

通过将动量交换方法与统一的插值反跳方案相结合，开发了一种多重弛豫时间晶格玻尔兹曼方法来模拟幂律流体中的粒子动力学。使用此方法，对于广义阿基米德数，在剪切稀化幂律流体中颗粒对的沉降$（\mathrm{一种}{\mathrm{[R}}^{*}）$研究范围从100到400不等。根据值$\mathrm{一种}{\mathrm{[R}}^{*}$在初始几何构型下，发现该粒子对经历了几种不同的运动状态，即稳定的斜双峰，周期振荡，周期倍增分叉，稳定的水平双峰和混沌。与牛顿系统中的两组多个稳态不同，在当前的剪切稀疏系统中清楚地识别出三组多个稳态：稳态斜向与周期振动并存，稳态水平双峰与周期倍增分叉并存。 ，并且稳定的水平双峰与混沌状态共存。此外，在本剪切稀化系统中不存在在牛顿系统中观察到的颗粒对的牵伸，亲吻和翻滚（DKT）行为。这归因于颗粒之间的高粘度区域，这会增加作用在颗粒上的粘性阻力，从而防止颗粒彼此靠近并减少颗粒聚集。另外，获得了幂律指数的临界值，在该临界值以下，无论如何，DKT状态都不会发生$\mathrm{一种}{\mathrm{[R}}^{*}$。