Modeling of release and absorption of gas in liquid–gas flows within a consistent thermodynamic framework

This work presents a consistent thermodynamic model to describe the gas release and gas absorption phenomena in homogeneous liquid–gas flows undergoing isothermal transformations. The liquid–gas mixture is regarded as a pseudo-fluid whose constitutive behavior is obtained from two thermodynamic potentials: the Helmholtz free energy and a pseudo-potential of dissipation. Thanks to the inclusion of the concentration of dissolved gas in the liquid in the list of state variables, along with the gas volume fraction and the mass densities of the liquid and gas constituents, a suitable and simple expression for the rate of mass transfer of gas is derived. Besides of unconditionally satisfying the Second Law of the Thermodynamics, the proposed expression is capable to properly describe experimental data available in the literature with great accuracy for a relatively wide range of saturation pressures. Numerical simulations carried out for an water–air mixture, subjected to a single expansion and cyclic expansion–contraction loadings, illustrate the influence of the gas release on the mechanical response of the fluid, which exhibits dispersion and attenuation and also hysteresis.