Thermocapillary instability in a viscoelastic liquid layer under an imposed oblique temperature gradient

Abstract

The linear stability analysis of a viscoelastic (Oldroyd-B) liquid layer subjected to an oblique temperature gradient (OTG) is investigated numerically. For the case of low liquid elasticity, the analysis shows a strong stabilizing effect of the horizontal component (HTG) of the OTG on the two elastic modes emerging due to the presence of the vertical component (VTG) of the OTG. However, if the liquid elasticity is sufficiently large, the HTG fails to stabilize the upstream elastic mode. The liquid elasticity stabilizes the Newtonian interaction mode arising out of the interaction between the HTG and the VTG. The thermocapillary flow introduced by the HTG leads to the development of a new elastic mode absent in the case of a Newtonian liquid layer. The present paper thus shows that the elasticity of the liquid plays a major role in the competition between various instability modes to determine the dominant mode of instability.