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We consider here a discrete system of spheres interacting through alubrication force. This force is dissipative, and singular near contact: itbehaves like the reciprocal of interparticle distance. We propose a macroscopicconstitutive equation which is built as the natural continuous counterpart ofthis microscopic lubrication model. This model, which is of the newtonian type,relies on an elongational viscosity, which is proportional to the reciprocal ofthe local fluid fraction. We then establish the convergence in a weak sense ofsolutions to the discrete problem towards the solution to the partialdifferential equation which we identified as the macroscopic constitutiveequation.

Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces