论文标题
在简单的剪切流下,非弹性粗糙球的惯性悬浮液中的非牛顿流变学
Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow
论文作者
论文摘要
在简单的剪切流下,非弹性粗糙硬球的惯性悬浮液的非牛顿运输特性取决于Boltzmann动力学方程。间质气体对粗糙球体的影响是通过Fokker-Planck广义方程建模的,用于旋转球体,该方程考虑了晶粒自由度的转化和旋转自由度与背景粘性气体的耦合。广义的fokker-planck术语是线性$ \ mathbf {v} $和angular $ \boldsymbolΩ$速度空间中两个普通的fokker-planck差异操作员的总和。与往常一样,每个fokker-planck运算符由阻力术语(与$ \ Mathbf {v} $和/或$ \boldsymbolΩ$)加上一个随机langevin术语,该术语由后台温度$ t_ \ text {ex} $构成。 Boltzmann方程是通过两种不同但互补的方法来求解的:(i)通过Grad的力矩方法,以及(ii)使用Bhatnagar-Gross-Krook(BGK)型动力学模型,适用于无弹性的粗糙硬球。如\ emph {平滑}非弹性硬球的情况,我们的结果表明,温度和非牛顿粘度都大大增加,随着剪切速率的增加(不连续的剪切增厚效果),而四度速度速度矩也表现出$ s $ shape。特别是,虽然与光滑的情况相比,高水平的粗糙度可能会略微减弱粘度的跳跃,但旋转温度的情况恰恰相反。作为这些结果的应用,还进行了稳定的简单剪切流解的线性稳定性分析,表明存在参数空间的区域,其中稳定的解决方案变得线性不稳定。
Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokker-Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker-Planck term is the sum of two ordinary Fokker-Planck differential operators in linear $\mathbf{v}$ and angular $\boldsymbolω$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $\mathbf{v}$ and/or $\boldsymbolω$) plus a stochastic Langevin term defined in terms of the background temperature $T_\text{ex}$. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grad's moment method, and (ii) by using a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As occurs in the case of \emph{smooth} inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with increasing the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an $S$-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable.