How to deal with negative surface heat capacities
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Getreidemarkt 9/BA, 1060 Vienna, Austria
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Received: 31 July 2014
Revised: 16 February 2015
Published online: 8 April 2015
Negative surface heat capacities are observed for many liquids, at least in certain temperature regimes. Since thermodynamic stability of a system requires positive heat capacities, it is usually argued that the surface must not be considered as an autonomous system. This, however, is not possible when the energy balance of the surface plays the role of a boundary condition for the field equations, e.g. the heat diffusion equation. A heat pulse supplied to the surface of a liquid and the stretching of a liquid film provide two examples to demonstrate that negative surface heat capacities may lead to unbounded and unconfined growth of the temperature disturbances in the liquid. To deal with the instabilities associated with negative surface heat capacities it is proposed to introduce a surface layer of small, but finite, thickness that is defined solely in terms of macroscopic thermodynamic quantities. By considering the energy balance of the surface layer, which is an open system, it is shown that the isobaric heat capacity of the liquid contained in the surface layer is to be added to the (possibly negative) surface heat capacity to obtain a positive total heat capacity of the surface layer.
© EDP Sciences, Springer-Verlag, 2015