Longitudinal viscosity of 2D Yukawa liquids

The longitudinal viscosity ${\eta }_l$ is obtained for a two-dimensional (2D) liquid using a Green-Kubo method with a molecular dynamics simulation. The interparticle potential used has the Debye-H"{u}ckel or Yukawa form, which models a 2D dusty plasma. The longitudinal ${\eta }_l$ and shear ${\eta }_s$ viscosities are found to have values that match very closely, with only negligible differences for the entire range of temperatures that is considered. The bulk viscosity ${\eta }_b$ is determined to be either negligibly small or not a meaningful transport coefficient, for a 2D Yukawa liquid.