  We investigate the stability of the pressure-driven, low-Reynolds flow of
Brownian suspensions with spherical particles in microchannels. We find two
general families of stable/unstable modes: (i) degenerate modes with symmetric
and anti-symmetric patterns; (ii) single modes that are either symmetric or
anti-symmetric. The concentration profiles of degenerate modes have strong
peaks near the channel walls, while single modes diminish there. Once excited,
both families would be detectable through high-speed imaging. We find that
unstable modes occur in concentrated suspensions whose velocity profiles are
sufficiently flattened near the channel centreline. The patterns of growing
unstable modes suggest that they are triggered due to Brownian migration of
particles between the central bulk that moves with an almost constant velocity,
and highly-sheared low-velocity region near the wall. Modes are amplified
because shear-induced diffusion cannot efficiently disperse particles from the
cavities of the perturbed velocity field.
