  We derive a minimal continuum model to investigate the hydrodynamic mechanism
behind the fingering instability recently discovered in a suspension of
microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model,
consisting of two continuous lines of rotlets, exhibits a linear instability
driven only by hydrodynamics interactions, and reproduces the lengthscale
selection observed in large scale particle simulations and in experiments. By
adjusting only one parameter, the distance between the two lines, our
dispersion relation exhibits quantitative agreement with the simulations and
qualitative agreement with experimental measurements. Our linear stability
analysis indicate that this instability is caused by the combination of the
advective and transverse flows generated by the microrollers near a no-slip
surface. Our simple model offers an interesting formalism to characterize other
hydrodynamic instabilities that have not been yet well understood, such as size
scale selection in suspensions of particles sedimenting adjacent to a wall, or
the recently observed formations of traveling phonons in systems of confined
driven particles.
