Renormalization group theory for fluids including critical region. II. Binary mixtures

Can the Speed of Sound Be Used for Detecting Critical States of Fluid Mixtures?

The phenomenology of sound speeds in fluid mixtures is examined near and across critical lines. Using literature data for binary and ternary mixtures, it is shown that the ultrasound speed along an isotherm-isopleth passes through a minimum value in the form of an angular (or V-shaped) point at critical states. The relation between critical and pseudo-critical coordinates is discussed. For nonazeotropic fixed-composition fluid mixtures, pseudo-critical temperatures and pressures are found to be lower than the corresponding critical temperatures and pressures. The analysis shows that unstable pseudo-critical states cannot be detected using acoustic methods. The thermodynamic link between sound speeds and isochoric heat capacities is formulated and discussed in terms of p-Vm-T derivatives capable of being calculated using cubic equations of state. Based on the Griffiths-Wheeler theory of critical phenomena, a new specific link between critical sound speeds and critical isochoric heat capacities is deduced in terms of the rate of change of critical pressures and critical temperatures along the p-T projection of the critical locus of binary fluid mixtures. It is shown that the latter link can be used to obtain estimates of critical isochoric heat capacities from the experimental determination of critical speeds of sound. The applicability domain of the new link does not include binary systems at compositions along the critical line for which the rate of change in pressure with temperature changes sign. The new equation is combined with thermodynamic data to provide approximate numerical estimates for the speed of sound in two mixtures of carbon dioxide and ethane at different temperatures along their critical isochores. A clear decrease in the sound speed is found at critical points. A similar behavior is suggested by available critical heat capacity data for several binary fluid mixtures. Using an acoustic technique, the critical temperature and pressure were determined for three different mixtures of methane and propane, and compared with literature data obtained using conventional methods. It is concluded that acoustic-based techniques are reliable to determine, for the most part, critical surfaces of fluid mixtures. The remaining few cases where the present analysis cannot be applied could be tested by the thermodynamic calculation of critical sound speeds using crossover equations of state in conjunction with experimentally determined critical isochoric heat capacities.