Correspondence between the pressure expression and van der Waals theory for a curved surface

We investigate the apparent contradiction between the pressure expressions, or “mechanical expressions,” and the van der Waals squared-gradient expressions for the curvature coefficients k/R0, k, and math. We show that, in the context of the mean-field theory discussed, both types of expression are indeed equivalent, with the differences only being caused by the thermodynamic conditions used to vary the curvature.