A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system parameters, are established.
Alejandro Garcia and M. M. Mansour. "Hydrodynamic description of the adiabatic piston" Physical Review (2006): 016121-1-016121-13. doi:http://dx.doi.org/10.1103/PhysRevE.73.016121