Microscopic expressions for the surface and line tension

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Abstract
The authors consider the change in grand potential of a fluid under a deformation of its containing vessel. Thermodynamically, the change is expressed in terms of the pressure, the surface tension and the line tension of the fluid. As the change can also be expressed in the fluid's microscopic properties, one obtains microscopic expressions for thermodynamic quantities. They consider two types of such expressions, the first one relating the pressure, surface and line tension to the density at the hard walls of the vessel, the second one relating them to the pressure tensor. Moreover, they can generalize these two types of expressions to a single expression which contains them both. Besides the distinction between surface and line tension, they consider two models of the wall: a 'hard wall' and a 'structured, soft wall'. It is shown that the expressions for the surface and the line tension are similar for all types of walls.

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