The dynamical behavior of the surface tension of two initially immisci
ble phases on raising the temperature to a value greater than or equal
to the critical temperature is studied using analytic techniques, mea
n field dynamical equations, Monte Carlo simulations, and molecular dy
namics simulations. Distinct behavior is predicted in situations with
a conserved order parameter and when no conservation law is operative.
A novel scaling form is obtained for a system evolving to equilibrium
at its critical temperature.