Steady two-layer flow in narrow channels of variable width

Abstract

The shape of the interface and pressure buildup for two-layered steady creeping flow inside a narrow channel of variable topography are examined in this study. The flow is assumed to be induced by the translation of the lower flat plate, similarly to lubrication flow. The interplay between channel topography and viscosity ratio, R_{micro}, is emphasized, in the absence of interfacial tension and gravity. For contracting channel and in the low R_{micro} range, the pressure increases everywhere in the channel monotonically with R_{micro}, reaching a maximum, and decreases as R_{micro} is increased further. In contrast, the interface level increases monotonically with R_{micro}. Channel modulation causes considerable pressure buildup. However, unlike the interface, which exhibits modulation, the pressure distribution along the channel remains qualitatively unaffected.