Effect of particle size ratio on shear-induced onset of particle motion at low particle Reynolds numbers: From high shielding to roughness

We study incipient motion of single beads on regular substrates made of spherical particles of a different size in steady shear flow at small particle Reynolds numbers. We cover a large range of sizes: from small beads that are highly shielded from the shear flow by the substrate spheres, and hence, are susceptible to the flow through the interstices of the substrate, to beads fully exposed to the flow, where the substrate rather acts like roughness of an otherwise flat surface. Numerical and experimental studies agree within measurement uncertainty. To describe the findings, we extend a recently derived model for particles of equal size which was validated over a wide range of substrates [Agudo et al., Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers, J. Fluid Mech. 825, 284-314 (2017)]. The extended model covers the entire spectrum of size ratios, where the critical Shields number varies from about zero to infinity. The model properly describes the numerical and experimental data. For well exposed beads, we find a scaling law between the critical Shields number and the size ratio between mobile bead and substrate spheres with an exponent of -1.