High-frequency propagating density fluctuations in deeply supercooled water: evidence of a single viscous relaxation

We performed a Brillouin scattering experiment on deeply supercooled water and compared the results with similar literature data obtained both at the same and at higher values of the exchanged wave vector. The whole set of available experimental data can be well reproduced with the use of the generalized hydrodynamic model where all the involved thermodynamic parameters are fixed to their literature values. On the contrary, the model based on the memory function approach generates the wrong estimates for measurables when the same values of the thermodynamic parameters are used. This result confirms our recent criticisms against the utilization of models originating from linear response theory [Phys. Rev. E 84, 051202 (2011)]. The inconsistency between models explains apparent discrepancies between the different conclusions on water acoustic behavior which may be found in the literature. We demonstrate that the observed behavior can be explained by assuming only a single relaxation process that is typical of any viscoelastic system. With all thermodynamics quantities fixed, the hydrodynamic description needs only two parameters to model the experimental data, namely, the relaxation time and the high-frequency limit of the sound velocity. The whole body of the experimental data can be well reproduced when the relaxation time behaves in an Arrhenian manner and the difference between the relaxed and not relaxed sound velocities is a constant. The high-frequency sound velocity is never higher than 2200 m/s. We conclude that, at least from experiments performed within the hydrodynamic regime, there is no indication for a fast sound close to the hypersonic velocity observed in ice.