Capturing the dynamics of a two orifice silo with the μ(I) model and extensions

Granular material in a silo with two openings can display a `flow rate dip’, where a non-monotonic relationship between flow rate and orifice separation occurs. In this paper we study continuum modelling of the silo with two openings. We find that the $\mu (I)$ rheology can capture the flow rate dip if physically relevant friction parameters are used. We also extend the model by accounting for wall friction, dilatancy, and non-local effects. We find that accounting for the wall friction using a Hele-Shaw model better replicates the qualitative characteristics of the flow rate dip seen in experimental data, while dilatancy and non-local effects have very little effect on the qualitative characteristics of the mass flow rate dip. However, we find that all three of these factors have a significant impact on the mass flow rate, indicating that a continuum model which accurately predicts flow rate will need to account for these effects.