# Bulk viscosity of CO$_2$ from Rayleigh-Brillouin lightscattering spectroscopy at 532 nm

## TL;DR

This study measures the bulk viscosity of CO₂ using Rayleigh-Brillouin light scattering at 532 nm across various pressures and temperatures, revealing it is primarily influenced by rotational relaxation modes rather than vibrational ones.

## Contribution

It provides the first detailed measurement of CO₂'s bulk viscosity via light scattering, comparing two models and showing minimal dependence on pressure and temperature.

## Key findings

- Bulk viscosity to shear viscosity ratio is approximately 0.41.
- Bulk viscosity is four orders of magnitude smaller than ultrasound-based estimates.
- Rotational modes dominate relaxation processes in light scattering of CO₂.

## Abstract

Rayleigh-Brillouin scattering spectra of CO$_2$ were measured at pressures ranging from 0.5 to 4~bar, and temperatures from 257 to 355~K using green laser light (wavelength 532~nm, scattering angle of 55.7$^\circ$). These spectra were compared to two lineshape models, which take the bulk viscosity as a parameter. One model applies to the kinetic regime, i.e. low pressures, while the second model uses the continuum, hydrodynamic approach and takes the rotational relaxation time as a parameter, which translates into the bulk viscosity. We do not find a significant dependence of the bulk viscosity with pressure or temperature. At pressures where both models apply we find a consistent value of the ratio of bulk viscosity over shear viscosity $\eta_b/\eta_s = 0.41 \pm 0.10$. This value is four orders of magnitude smaller than the common value that is based on the damping of ultrasound, and signifies that in light scattering only relaxation of rotational modes matters, while vibrational modes remain 'frozen'.