填隙二阶流体下圆球平行于壁平移的粘性阻力

离散元法是分析散体力学行为的数值方法。存在填隙流体时，颗粒之间或颗粒与壁之间产生的法向挤压力和切向阻力、阻力矩，是湿颗粒离散元法的理论基础。二阶流体是以微小偏离牛顿流体本构而考虑时间影响的一种流体。它具有常粘度，并且第一和第二法向应力差正比于剪切率的平方。根据Reynolds润滑理论，采用小参数法，导出了存在填隙二阶流体时，圆球沿平行于平壁缓慢移动时流体的速度场和压力方程，进而求出切向阻力和阻力矩的解析解。有趣的是在推导时所得的速度场和压力方程形式比牛顿流体要复杂得多，但最终结果表明圆球沿平行于平壁移动时因填隙二阶流体引起的切向阻力和阻力矩与牛顿流体时的结果相同。

Viscous Resistance of a Sphere Translational Move Parallel to a Wall with Interstitial Second Order Fluid

The Discrete Element Method is a powerful tool in analyzing granular assembly. Due to the interstitial fluid between the partials or the partial and the wall, the solutions of the pressure, tangential force and torque between the two granules are the theoretical foundation of the wet granular discrete element method. The so called second order fluid is a fluid model whose constitutive relation deviates slightly from a Newtonian fluid while the time effects are considered, normally it has a constant viscosity, and both the first and second normal stress differences are proportional to the square of shear ratio. Based on the Reynolds' lubrication approximation and utilizing the Perturbation method, the velocity and the pressure equations for a sphere translating parallel to a wall with an interstitial second order fluid was derived for modeling wet granular assembles using Discrete Element Method. As a result, an analytical solution for the tangential force and the torque was obtained. It is interesting to find that, although the equations for the velocity and the pressure are more complicated in their form than a Newtonian fluid, however the final results are simple and the same as those for a Newtonian fluid.