润滑力作用下球列相互作用的细观-宏观模型
Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces
摘要：
本文考虑一个球通过润滑力相互作用的离散系统。这个力是耗散的，在接触附近是奇异的：它的行为类似于粒子间距离的倒数。我们提出了一个宏观本构方程，这是建立作为自然连续对应的微观润滑模型。该模型是牛顿型的，依赖于拉伸粘度，其与局部流体分数的倒数成比例。然后，我们建立了收敛在弱意义上的解决方案的离散问题的解决方案的偏微分方程，我们确定为宏观本构方程。
英文摘要：
We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.
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