Flow and Slippage of a Soft-Material by Controlled Surface Roughness Shape

An assembly of soft jammed particles (“soft-material”) usually exhibits a complex rheology with a yield stress, i.e. a threshold value below which the material responds elastically to external perturbations. When flowing in a confined microfluidic channel, the material exhibits an effective slippage at the walls, which becomes the dominant contribution to the flow below or close to yield. Wall roughness is commonly accepted to decrease wall slippage, however quantitative assessments of the impact of surface roughness shape on wall slippage are scarce in literature. With the help of numerical simulations, in this work we systematically assess the impact of surface roughness shape on the scaling-laws that relate the wall slippage to wall stress. Both linear and quadratic scaling laws are observed for small and large values of wall stress respectively, provided that surfaces are flat/weakly rough. At moderate/large roughness, the linear scaling is suppressed, while the quadratic one persists. In all cases, the scaling observations are accompanied by a systematic analysis of the micro-mechanics in the rough boundary layer.