Stability of the interface in two-layer couette flow of upper convected maxwell liquids

The linear stability of a two-layer Couette flow of upper convected Maxwell liquids is considered. The fluids have different densities, viscosities, and elasticities, with surface tension at the interface. At low speeds, the interfacial mode may become unstable, while other modes stay stable. The shortwave asymptotics of the interfacial mode is analyzed. It is found that an elasticity difference can stabilize or destabilize the flow even in the absence of a viscosity difference. As the viscosity difference increases, the range of elasticities for which there is shortwave stability widens. A linearly stable arrangement can be achieved by placing the less viscous fluid in a thin layer to stabilize longwaves and using elasticities to stabilize shortwaves. Such an arrangement can be stable even when the density stratification is adverse.