Toward a microscopic description of flow near the jamming threshold

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that i) the viscosity eta diverges with the coordination number z as eta similar to (z(c) - z)(-( 3+theta)/( 1+theta)), ii) the operator which governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency omega(min) similar to (z(c) - z)((3+theta)/(2+2 theta)), and iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/ < f > similar to(z(c) - z)(1/(1+theta)) where theta characterizes the distribution of contact forces P(f) similar to f(theta) at jamming, and where z(c) is the Maxwell threshold for rigidity.