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Onset of Convection in Two Liquid Layers with Phase Change



Geoffrey B. McFadden, Sam R. Coriell, Katharine F. Gurski, David Cotrell


We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects. We compare the familiar case of the stability of two immiscible fluids in a bilayer geometry with the less-studied case that the two fluids represent different phases of a single-component material, e.g., the water-steam system. The two cases differ in their interfacial boundary conditions: the condition that the interface is a material surface is replaced by the continuity of mass flux across the interface, together with an assumption of thermodynamic equilibrium that in the linearized equations represents the Claussius-Clapeyron relation relating the interfacial temperature and pressures. For the two-phase case, we find that the entropy difference between the phases plays a crucial role in determining the stability of the system. For small values of the entropy difference between the phases, the two-phase system can be linearly unstable to either heating from above or below. For larger values of the entropy difference the two-phase system is unstable only for heating from below, and the the Marangoni effect is masked by effects of the entropy difference.
Physics of Fluids


bilayer convection, linear stability, Marangoni effect, phase-change convection, Rayleigh-Benard convection


McFadden, G. , Coriell, S. , Gurski, K. and Cotrell, D. (2007), Onset of Convection in Two Liquid Layers with Phase Change, Physics of Fluids, [online], (Accessed May 28, 2024)


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Created December 31, 2006, Updated October 12, 2021