Comparison of various crossover approaches for equations of state

As the thermodynamic behavior of fluids near the critical points is extremely different from the critical behavior implied by classical equations of state, many attempts have been made to develop a crossover theory to bridge the gap between non-classical critical behavior asymptotically close to the critical point and classical behavior further away from the critical point.

Fluids and fluid mixtures near the critical region belong to the universality class of Ising-like systems. I.e., the general theory of complete scaling for the critical phenomena concerns the asymptotic thermodynamic critical behavior.

It is possible to extend the theory to include a crossover from fluctuation-induced Ising-like critical behavior to classical mean-field critical behavior. For many applications one needs a global equation of state that not only incorporates the effects of critical fluctuations in the near-critical region, but also yields a representation of the thermodynamic properties of fluids over large ranges of temperatures and densities.

Therefore, we attempt to consider different approaches that have become available to deal with this problem. A general procedure for transforming any classical equation of state into a crossover equation of state was proposed by Kiselev in 1998.

This procedure is based on the renormalization group theory and is capable of accurately reproducing near critical fluid behavior as well as correctly going to the ideal gas limit. Besides of Kiselev’s procedure, White’s approach will be studied.

This approach is based on the work of Wilson to incorporate density fluctuations in the critical region using the phase space cell approximation and uses a recursive procedure to modify the free energy for non-uniform fluids, thereby accounting for the fluctuations in density.


Georgios Kontogeorgis
DTU Chemical Engineering
+45 45 25 28 59


Wei Yan
Associate Professor
DTU Chemistry
+45 45 25 23 79


Andre Pinto Coelho Muniz Vinhal
DTU Chemical Engineering