(236i) Shear Rate Dependence of the Effective Viscosity and Thermal Conductivity of a Granular "Fluid"

Figueroa, I., Eli Lilly and Company

In this paper we study the effective viscosity and thermal conductivity of a granular "fluid" in a linear shear flow. To facilitate the analysis, we decompose the flow of momentum and heat into two components that act simultaneously in granular systems -- a collisional mode and a streaming mode -- and examine their dependence on shear rate and solid fraction independently. In previous studies, both viscosity and conductivity have been shown to linearly increase with the shear rate and an analog to Reynolds analogy has born fruit; however, we find that at high solid fractions this analogy breaks down and the conductivity becomes almost independent. By way of explanation we note that the transfer of collisional momentum is a rapid process that does not require long-lasting contacts, while the transfer of heat, on the other hand, is a slow process so that collisional transport is dramatically reduced by short collision times. Varying the shear rate, therefore, has competing effects on the heat flux, and the overall trend depends on the solid fraction and the absolute shear rate value.