The surface tension of non-critical interfaces near critical end points

We have calculated the surface tension σ of the non-critical interfaces which occur near the critical end point for liquid-liquid phase separation. Our calculations are based on a non-local, two-density, mean field approximation to the free energy functional. For both liquid-gas and solid-liquid non-critical interfaces we find that σ and its temperature derivative dσ/dT are continuous at the critical end point. If, however, our results are plotted on an unexpanded temperature scale dσ/dT sometimes appears discontinuous. Our analysis suggests that experiments aimed at testing the prediction that dσ/dT is continuous will have to be performed at temperatures closer to the critical end point than those performed hitherto.