  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.
