Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain.
Phys Rev E. 2017 Jun;95(6-1):062906. doi: 10.1103/PhysRevE.95.062906. Epub 2017 Jun 28.
A recent model for monodisperse granular suspensions is used to analyze transport properties in spatially inhomogeneous states close to the simple (or uniform) shear flow. The kinetic equation is based on the inelastic Boltzmann (for low-density gases) with the presence of a viscous drag force that models the influence of the interstitial gas phase on the dynamics of grains. A normal solution is obtained via a Chapman-Enskog-like expansion around a (local) shear flow distribution which retains all the hydrodynamic orders in the shear rate. To first order in the expansion, the transport coefficients characterizing momentum and heat transport around shear flow are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. To simplify the analysis, the steady-state conditions when viscous heating is compensated by the cooling terms arising from viscous friction and collisional dissipation are considered to get the explicit forms of the set of generalized transport coefficients. The shear-rate dependence of some of the transport coefficients of the set is illustrated for several values of the coefficient of restitution.
最近提出的单分散颗粒悬浮体模型被用于分析接近简单（或均匀）剪切流的空间非均匀状态下的输运性质。动力学方程基于弹性玻尔兹曼方程（适用于低密度气体），其中存在粘性阻力项，用以模拟中间气相对颗粒动力学的影响。通过在局部剪切流分布周围进行类似于Chapman-Enskog 的展开，得到正常解，该展开保留了剪切率中的所有流体力学阶数。在展开的一阶，描述剪切流周围动量和热输运的输运系数以一组耦合线性积分方程的解的形式给出，这些方程可以通过使用玻尔兹曼方程的动力学模型进行近似求解。为了简化分析，当粘性加热由粘性摩擦和碰撞耗散引起的冷却项补偿时，考虑稳态条件，以得到广义输运系数集的显式形式。对于恢复系数的几个值，说明了该组输运系数中的一些系数随剪切速率的变化关系。
