In the classical hydrodynamic stability theory (see, e.g., [26, 27]), the base flow is obtained as a simple one-dimensional steady solution of the equations of motion (e.g., a plane Poiseuille flow is obtained as a steady one-dimensional solution of the Navier-Stokes equations).

Stuart, "A non-linear instability theory for a wave system in plane Poiseuille flow," Journal of Fluid Mechanics, vol.

[4] were the first to observe the Segre-Silberberg effect for the motion of a single circular particle in

plane Poiseuille flow by using the finite-element method.

Aziz, "Second law analysis for a variable viscosity

plane Poiseuille flow with asymmetric convective cooling," Computers & Mathematics with Applications, vol.

Subsequently, we performed direct numerical simulations of viscosity-stratified two-layer plane Poiseuille flow employing a front-tracking/finite difference method (Cao et al., 2004).

Yih (1967) used a long-wave perturbation analysis to show that two-layer, viscosity-stratified plane Poiseuille flow and plane Couette flow can be unstable for arbitrarily small Reynolds numbers.

The time-dependent, incompressible, one-dimensional

plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall.

Su and Khomami (12), using a modified Oldroyd-B fluid model and a pseudospectral formulation, investigated the effect of shear thinning viscosity and elasticity on the interfacial stability of superposed

plane Poiseuille flow of viscoelastic fluids.

Lee and White (12) studied the interfacial deformation of superposed plane poiseuille flow of polystyrene (PS) and high-density polyethylene (HDPE) and showed the existence of interfacial instabilities.

In an earlier study, we have experimentally determined the stability of superposed plane poiseuille flow of the PP/HDPE system at 204 [degrees] C (14).

[2] CHENG K.C., WU R.S., (1976), Axial heat conduction effects on thermal instability of horizontal

plane Poiseuille flows heated from below, J.

KANDA, Difference in critical Reynolds number between Hagen-Poiseuille and

plane Poiseuille flows, Proc.