  We study the stability of two-fluid flow through a plane channel at Reynolds
numbers of a hundred to a thousand in the linear and nonlinear regimes. The two
fluids have the same density but different viscosities. The fluids, when
miscible, are separated from each other by a mixed layer of small but finite
thickness, across which viscosity changes from that of one fluid to that of the
other. When immiscible, the interface is sharp. Our study spans a range of
Schmidt numbers, viscosity ratios and location and thickness of the mixed
layer. A region of instability distinct from that of the Tollmien-Schlichting
mode is obtained at moderate Reynolds numbers. We show that the overlap of the
layer of viscosity-stratification with the critical layer of the dominant
disturbance provides a mechanism for this instability. At very low values of
diffusivity, the miscible flow behaves exactly like the immiscible in terms of
stability characteristics. High levels of miscibility make the flow more
stable. At intermediate levels of diffusivity however, in both linear and
non-linear regimes, miscible flow can be more unstable than the corresponding
immiscible flow without surface tension.
