Thermocapillary instability of core-annular flows

Abstract

Thermocapillary instability of a core-annular flow is asymptotically examined in the thin annulus limit. Two sets of scalings are established to study the interplays between base flows, interfacial tension, and thermocapillary effects. For each scaling case, an interfacial evolution equation is derived for describing the leading order stability of the system. Both linear and weakly nonlinear stabilities are examined. When the core fluid is warmer (cooler) than the wall, thermocapillarity linearly stabilizes (destabilizes) the system, and hence suppresses (promotes) the capillary instability. For a moderate thermocapillary force and a strong capillary force, the linear instability can be arrested within the weakly nonlinear regime. For a weak thermocapillary force and a moderately strong interfacial tension, the weakly nonlinear evolution is governed by a modified Kuramoto-Sivashinsky equation. The influence of thermocapillarity on the route to chaos is discussed.