  In this article we use analytical and numerical modeling to describe parallel
viscous two-phase flows in microchannels. The focus is on idealized
two-dimensional geometries, with a view to validating the various methodologies
for future work in three dimensions. In the first instance, we use analytical
Orr--Sommerfeld theory to describe the linear instability which governs the
formation of small-amplitude waves in such systems. We then compare the results
of this analysis with an in-house Computational Fluid Dynamics (CFD) solver
called TPLS. Excellent agreement between the theoretical analysis and TPLS is
obtained in the regime of small-amplitude waves. We continue the numerical
simulations beyond the point of validity of the Orr--Sommerfeld theory. In this
way, we illustrate the generation of nonlinear interfacial waves and reverse
entrainment of one fluid phase into the other. We justify our simulations
further by comparing the numerical results with corresponding results from a
commercial CFD code. This comparison is again extremely favourable -- this
rigorous validation paves the way for future work using TPLS or commercial
codes to perform extremely detailed three-dimensional simulations of flow in
microchannels.
