# Balancing size and density segregation in bidisperse dense granular flows

Deepak R. Tunuguntla, Anthony R. Thornton

Several experimental studies have illustrated a balance between the segregation forces arising due to size- and density-differences. However, no detailed studies have been carried out to quantify this balance. In 2014, by utilising discrete particle simulations, we presented a simple relationship between the particle size- and density-ratio, $s^a = \hat \rho$, where 'a' determines whether the partial pressure scales with the diameter, surface area or volume of the particle. For a 50:50 mix (in volume) of bidisperse granular mixtures, we found the partial pressure to scale with the volume of the particle, i.e. a = 3. Moreover, there also exists a range of size- and density-ratios that satisfy the relation $s^3 = \hat \rho$, where the bidisperse mixture remains homogeneously mixed. However, in this proceeding, we deviate from the conventional 50:50 mixes and consider a slightly extreme case of mixes, such as the 10:90 (in volume) mixes, which are often found in nature and industries. By doing so we observe that the partial pressure does not scale with the particle volume and, more importantly, the zero-segregation relation is not as simple as $s^a = \hat \rho$. However, there does exist a range of size- and density-ratios for which the mixture weakly segregates.