  In this study we experimentally investigate bubbly drag reduction in a highly
turbulent flow of water with dispersed air at $5.0 \times 10^{5} \leq \text{Re}
\leq 1.7 \times 10^{6}$ over a non-wetting surface containing micro-scale
roughness. To do so, the Taylor-Couette geometry is used, allowing for both
accurate global drag and local flow measurements. The inner cylinder - coated
with a rough, hydrophobic material - is rotating, whereas the smooth outer
cylinder is kept stationary. The crucial control parameter is the air volume
fraction $\alpha$ present in the working fluid. For small volume fractions
($\alpha < {4}\,\%$), we observe that the surface roughness from the coating
increases the drag. For large volume fractions of air ($\alpha \geq 4\,\%$),
the drag decreases compared to the case with both the inner and outer cylinders
uncoated, i.e. smooth and hydrophilic, using the same volume fraction of air.
This suggests that two competing mechanisms are at place: on the one hand the
roughness invokes an extension of the log-layer - resulting in an increase in
drag - and on the other hand there is a drag-reducing mechanism of the
hydrophobic surface interacting with the bubbly liquid. The balance between
these two effects determines whether there is overall drag reduction or drag
enhancement. For further increased bubble concentration $\alpha = {6}\,\%$ we
find a saturation of the drag reduction effect. Our study gives guidelines for
industrial applications of bubbly drag reduction in hydrophobic wall-bounded
turbulent flows.
