Thermocapillary flow in double-layer fluid structures: An effective single-layer model

Thermocapillary flows are of considerable technological importance in materials processing applications such as crystal growth from the melt, particularly under microgravity conditions where the influence of buoyancy-driven convection is minimized. In this study, thermally driven convection within a differentially heated rectangular cavity containing two immiscible liquid layers is considered in the absence of gravity. The introduction of a more viscous encapsulant layer leads to a significant reduction in the intensity of the thermocapillary flow within the encapsulated layer. Interface deformations are small when the contact line of the interface is pinned on the solid boundaries. The higher viscosity of the encapsulant layer gives rise to a larger pressure gradient in that layer, thereby resulting in interface deformations that are qualitatively different from those observed at the free surface in the absence of the encapsulant layer. The flow pattern in the encapsulated layer and the resulting interface deformations are strongly dependent on both the thickness and the viscosity of the encapsulant layer. It is shown that the flow within the encapsulated layer may be closely approximated by simply considering the single-layer problem with a modified stress condition at the interface. The modified tangential stress balance for the effective single-layer model is derived based on asymptotic results for small-aspect-ratio double-layer systems and the insight gained from double-layer computations for finite-aspect-ratio systems. It is shown that the single-layer model accurately predicts the flow in the double-layer system even for large aspect-ratios.