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

## TL;DR

This study investigates how different geometrical wall roughness shapes affect the flow behavior of soft materials in microchannels, revealing that roughness suppresses flow and alters the flow-stress relationship.

## Contribution

It provides a quantitative analysis of the influence of roughness shape and value on flow initiation and behavior in soft-material microchannel flows, using numerical simulations.

## Key findings

- Roughness suppresses flow and introduces a characteristic stress threshold.
- Flow rate dependence on wall stress is linear for smooth walls.
- Steeper flow-stress relationships emerge with increased roughness and shape variation.

## Abstract

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 $\Phi$ 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 $\Phi$ 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.