Rheology of Granular Mixtures Differing in Size and/or Density

Rheology of mono-dispersed granular materials is well understood and it is well known that these materials follow a friction law where the shear stress to pressure ratio is determined by the Inertial number $I$. However, rheology of the general and more common case of granular mixtures of different size and/or different density particles has not received attention of researchers. We study the rheology of binary mixtures flowing over an inclined plane under the influence of gravity by means of DEM simulations. We show that the friction law for single component granular material with appropriate modification in the inertial number expression captures the rheology of the mixtures as well and can predict the viscosity of both, same-size different-density particle mixtures and different-size same-density particle mixtures. For the case of mixture of particles differing in size and density both, we obtain a well-mixed or a segregated state depending upon the over-all composition of the mixture. The modified friction law is able to predict the viscosity for this case as well for both well-mixed and segregated state. Thus we show that friction law with a generalized definition of Inertial number can predict the rheology of granular mixtures differing in size and/or density.