Title: Non-universal behavior in the bubble model: it's a drag.

Author (Talk): Craig Maloney, Northeastern

Abstract:

We study several variants of Durian's bubble model above the random close packing volume fraction. We show that the flow curves follow the Herschel-Bulkley (HB) law with an exponent which depends on the drag mechanism. The HB exponent is approximately 1/3 when the dissipative forces are proportional to the velocity of particles with respect to the imposed flow and 1/2 when the dissipative forces are proportional to the velocity of the particles with respect to their neighbors. These results are in agreement with several recent experiments on pastes, emulsions, and foams in various flow geometries. We argue that the HB exponent is directly related to the spatial correlations in the velocity and finite-time-displacement fields. The instantaneous velocities are anisotropic and show long-ranged correlations which decay like 1/r^2. These correlations can be understood to be the result of elastic displacements in response to local slip events. These correlations are cut off beyond a length which scales the same way with shearing rate as the stress (1/3 for flow-damping, 1/2 for local-damping). The displacements decay much more slowly in space, like 1/r, but display the same anisotropy and are cut off with rate in the same way as the velocities. The diffusion coefficient shows the same dependence on rate as the velocity/displacement correlations. These results strongly suggest that it is the spatial correlations in the velocities/displacements which govern the rheology rather than the precise details of the viscous drag at the particle interfaces/contacts.