The kinetics of liquid-gas phase transitions
of a Van der Waals
substance with fluctuations taken
into account
A.N. Malakhov, N.V. Agudov
State University of N. Novgorod,
Nizhny Novgorod, Russia
Although 120 years have passed since Van der Waals proposed his well-known equation of state of matter, the steam of investigations devoted to this equation has far from dried up. This is attributable to the fact that the physical model of the state of matter, proposed by Van der Waals (VdW), despite its simplicity, reflects the basic properties of the liquid and gaseous phase of actual substances correctly and uniquely and it is a basic model for understanding phase transition phenomena, metastable states, and the critical point. The weak aspects of the VdW equation are also well known: the presence of an unstable not physically realizable branch and the absence of the horizontal portion of the isotherm of the two phase state of a substance that is observed in experiments. One can also include among these deficiencies that the experimentally observable instability of metastable states does not follow from the VdW equation.
By using the thermodinamic potential, which describes the
nonequilibrium state, for VdW substance with fluctuation taken
into account the isothermal curve of phase equilibrium is now
obtained that contains only stable points on the pressure versus
volume plane for liquid 
gas transitions, its
interrelationship with the horizontal line obtained from the
equilibrium condition of the individual phases is investigated,
and the conditions for which long-lived metastable states appear
are discussed phenomenologically (See also A.N.Malakhov,
N.V.Agudov, CHAOS, 4, (1994) 665).
Thus, the VdW equation which gives unstable points on the isotherm and is artificially corrected (to agree with experimental data) by introducing a horizontal stright line in accordance with Maxwell's rule, in reality (i.e., when the always existing fluctuations are taken into account) does not lead to unstable points in the two phase region and reflects the experimentally observed isotherms completely satisfactorily. The metastable states of the VdW substance (which are stable according to VdW equation) are shown to have the finite lifetimes, which depend on the intensity of the external fluctuations and the number of the particles in the system.