  The flow of emulsions in confined microfluidic channels is affected by
surface roughness. Directional roughness effects have recently been reported in
channels with asymmetric boundary conditions featuring a flat wall, and a wall
textured with a directional roughness, the latter promoting a change in the
velocity profiles when the flow direction of emulsions is inverted [D. Filippi
et al., Adv. Mater. Technol. 8, 2201748 (2023)]. An operative protocol is
needed to reconstruct the stress profile inside the channel from velocity data
to shed light on the trigger of the directional response. To this aim, we
performed lattice Boltzmann numerical simulations of the flow of model
emulsions with a minimalist model of directional roughness in two dimensions: a
confined microfluidic channel with one flat wall and the other patterned by
right-angle triangular-shaped posts. Simulations are essential to develop the
protocol based on mechanical arguments to reconstruct stress profiles. Hence,
one can analyze data to relate directional effects in velocity profiles to
different rheological responses close to the rough walls associated with
opposite flow directions. We finally show the universality of this protocol by
applying it to other realizations of directional roughness by considering
experimental data on emulsions in a microfluidic channel featured with a flat
wall and a wall textured by herringbone-shaped roughness.
