  Interfaces involving coexisting phases in condensed matter are essential in
various examples of soft matter phenomena such as wetting, nucleation,
morphology, phase separation kinetics, membranes, phase coexistence in
nanomaterials, etc. Most analytical theories available use concepts derived
from mean field theory which does not describe adequately these systems.
Satisfactory numerical simulations for interfaces at atomistic to mesoscopic
scales remains a challenge. In the present work, the interfacial tension
between mixtures of organic solvents and water is obtained from mesoscopic
computer simulations. The temperature dependence of the interfacial tension is
found to obey a scaling law with an average critical exponent mu = 1.23.
Additionally, we calculate the evolution of the correlation length, defined as
the thickness of the interface between the immiscible fluids, as a function of
temperature and find that it obeys also a scaling law with the average critical
exponent being nu = 0.67. Lastly, we show that the comparison of mu and nu for
these binary mixtures constitutes the first test of Widom hyperscaling relation
between these exponents in 3d, expressed as mu = nu (d - 1). Based on these
values and those for the 3d Ising model it is argued that both systems belong
to the same universality class, which opens up the way for the calculation of
new scaling exponents.
