Effect of geometric base roughness on size segregation

Abstract

The geometric roughness at boundaries has a profound impact on the dynamics of granular flows. For a bumpy base made of fixed particles, two major factors have been separately studied in the literature, namely, the size and spatial distribution of base particles. A recent work (Jing et al. 2016) has proposed a roughness indicator Ra, which combines both factors for any arbitrary bumpy base comprising equally-sized spheres. It is shown in mono-disperse flows that as Ra increases, a transition occurs from slip (Ra < 0.51) to non-slip (Ra > 0.62) conditions. This work focuses on such a phase transition in bi-disperse flows, in which Ra can be a function of time. As size segregation takes place, large particles migrate away from the bottom, leading to a variation of size ratio between flow- and base-particles. As a result, base roughness Ra evolves with the progress of segregation. Consistent with the slip/non-slip transition in mono-disperse flows, basal sliding arises at low values of Ra and the development of segregation might be affected; when Ra increases to a certain level (Ra > 0.62), non-slip condition is respected. This work extends the validity of Ra to bi-disperse flows, which can be used to understand the geometric boundary effect during segregation.