| Abstract: |
| A simple kinetic model for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas are not treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined fro the equation of state for the van der Waals fluid, with the aide of the balance equation of momentum, (ii) a monotonically decreasing function in time is found from the H theorem and turns out to have a close relation to the Helmholtz free energy Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy in thermodynamics, and (iii) the Cahn-Hilliard type equation is obtained in the continuum limit of the proposed kinetic model. Numerical simulations based on the Cahn-Hilliard type equation are also performed. |
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