Contact Friction and Normal Stresses in Particle Suspensions

Starting with the Smoluchowski equation for the two-particle configuration space, where particles interact via lubrication and Coulomb friction forces, we derive a continuum model for the particle suspension microstructure and stress. The model predicts, that contact friction induces an inter-particle pull in the flow direction and an inter-particle push in the gradient direction, i.e., a positive first normal stress difference. These results rationalise experimental observations in shear thickening suspensions, reported in the literature.