On the impact of controlled wall roughness shape on the flow of a soft-material

We explore the impact of geometrical corrugations on the near-wall flow properties of a soft-material driven in a confined rough microchannel. By means of numerical simulations, we perform a quantitative analysis of the relation between the flow rate $\mathrm{\Phi }$ and the wall stress ${\sigma }_w$ for a number of setups, by changing both the roughness values as well as the roughness shape. Roughness suppresses the flow, with the existence of a characteristic value of ${\sigma }_w$ at which flow sets in. Just above the onset of flow, we quantitatively analyze the relation between $\mathrm{\Phi }$ and ${\sigma }_w$. While for smooth walls a linear dependency is observed, steeper behaviours are found to set in by increasing wall roughness. The variation of the steepness, in turn, depends on the shape of the wall roughness, wherein gentle steepness changes are promoted by a variable space localization of the roughness.