Effect of geometric base roughness on size segregation

¹ Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
² Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong
³ Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, 70910-900, Brasília, DF, Brazil

^* e-mail: fiona.kwok@hku.hk

Published online: 30 June 2017

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 R_a, which combines both factors for any arbitrary bumpy base comprising equally-sized spheres. It is shown in mono-disperse flows that as R_a increases, a transition occurs from slip (R_a < 0.51) to non-slip (R_a > 0.62) conditions. This work focuses on such a phase transition in bi-disperse flows, in which R_a 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 R_a evolves with the progress of segregation. Consistent with the slip/non-slip transition in mono-disperse flows, basal sliding arises at low values of R_a and the development of segregation might be affected; when R_a increases to a certain level (R_a > 0.62), non-slip condition is respected. This work extends the validity of R_a to bi-disperse flows, which can be used to understand the geometric boundary effect during segregation.