  In this Letter, three physical predictions on the phase separation of binary
systems are derived based on a dynamic transition theory developed recently by
the authors. First, the order of phase transitions is precisely determined by
the sign of a parameter Kd (or a nondimensional parameter K) such that if Kd>0,
the transition is first-order with latent heat and if Kd <0, the transition is
second-order. Second, a theoretical transition diagram is derived, leading in
particular to a prediction that there is only second-order transition for molar
fraction near 1/2. This is different from the prediction made by the classical
transition diagram. Third, a critical length scale is derived such that no
phase separation occurs at any temperature if the length of the container is
smaller than the critical length scale.
