Transport coefficients of bulk viscous pressure in the 14-moment approximation

We compute the transport coefficients that appear in the fluid-dynamical equations for the bulk viscous pressure and shear-stress tensor using the 14-moment approximation in the limit of small, but finite, masses. In this limit, we are able to express all these coefficients in terms of known thermodynamic quantities, such as the thermodynamic pressure, energy density, and the velocity of sound. We explicitly demonstrate that the ratio of bulk viscosity to bulk relaxation time behaves very differently, as a function of temperature, than the ratio of shear viscosity to shear relaxation time. We further explicitly compute, for the first time, the transport coefficients that couple the bulk viscous pressure to the shear-stress tensor and vice versa. The coefficient that couples bulk viscous pressure to shear-stress tensor is found to be orders of magnitude larger than the bulk viscosity itself, suggesting that bulk viscous pressure production owes more to this coupling than to the expansion rate of the system.

Figure 1

In this figure we compare the approximate expressions (circles) of the transport coefficients obtained in the main text with their exact values (solid red lines), as a function of $\text{mass}/T$. The left panel contains the transport coefficients appearing in the equations of motion for the bulk viscous pressure while the right panel contains the transport coefficients contained in the equations of motion for the shear-stress tensor.