No abstract

The stability of a two-layer return thermocapillary flow in the presence of an inclined temperature gradient is investigated. Both a linear stability analysis and nonlinear simulations have been performed for an air–water system. It is found that a rather weak deviation of the mean temperature gradient from the vertical direction suppresses Pearson's instability mechanism and leads to the appearance of oblique hydrothermal waves. In a certain region of parameters, transverse convective rolls drifting with the mean flow appear.

Recently, it was found that the anomalous thermocapillary effect (the interfacial tension increases with temperature) is typical for various liquid-liquid systems. We consider the combined action of buoyancy and thermocapillary instability mechanisms in systems with an anomalous thermocapillary effect on the interface. The problem is solved in both linear and nonlinear formulations. A special type of oscillatory instability has been found and investigated.

At temperatures somewhat above room level, the interfacial tension between a 10 cS silicone oil and ethylene glycol increases with temperature, whereas it typically decreases for other systems of immiscible viscous fluids. The convective flows produced by the combined action of this so-called anomalous thermocapillary effect and buoyancy in this particular liquid-liquid system are studied by direct three-dimensional nonlinear simulation. The liquids are situated between rigid horizontal plates that are kept at different temperatures. A pseudospectral code is used to solve the evolution equations with periodic boundary conditions in the horizontal directions. Depending on the Grashof and Marangoni numbers G and M , the motionless state can either have a stationary or oscillatory instability. The corresponding finite amplitude solutions show a variety of regular structures ͑stationary rolls, stationary hexagons, pulsating hexagons, alternating rolls͒ as well as spatio-temporal chaos. The properties of the alternating rolls are investigated in some detail. Irregular patterns arising from the transition between hexagons and alternating rolls are briefly discussed.