  We study the temporal linear instability of channel flow subject to a
tensorial slip boundary condition that models the slip effect induced by
microgroove-type super-hydrophobic surfaces. The microgrooves are not
necessarily aligned with the driving pressure gradient. Pralits et al. Phys.
Rev. Fluids 2, 013901 (2017) investigated the same problem and reported that a
proper tilt angle of the microgrooves about the driving pressure gradient can
reduce the critical Reynolds number and that the flow with a single
superhydrophobic wall is much more unstable/less stable than that with two
superhydrophobic walls. In contrast, we show that the lowest critical Reynolds
number is always realized with two superhydrophobic walls, and we obtain
critical Reynolds numbers significantly lower than the reported. Besides, we
show that the critical Reynolds number can be further reduced by increasing the
anisotropy in the slip length. As the tilt angle changes, there appears to be a
strong correlation between the strength of the instability and the magnitude of
the cross-flow component of the base flow incurred by the tilt angle. In case
the tilt angles of the microgrooves differ on the two walls, the critical
Reynolds number increases as the difference in the tilt angles increases, i.e.
two superhydrophobic walls with parallel microgrooves give the lowest critical
Reynolds number. The results are informative for designing the microgroove-type
wall texture to introduce instability at low Reynolds number channel flow,
which may be of interest for enhancing mixing or heat transfer in small flow
systems where turbulence cannot be triggered.
