Shear Viscosity of SRD Kinetic Contribution

Linear response theory provides an alternative, and complementary, approach for evaluating the shear viscosity. This non-equilibrium approach is related to equilibrium calculations described in the previous section through the fluctuation-dissipation theorem. Both methods yield identical results. For the more complicated analysis of the hydrodynamic eqnations, the stress tensor, and the longitudinal transport coefficients such as the thermal conductivity, the reader is referred to [35]. 

Following Kikuchi et al. [26], we consider a two-dimensional liquid with an imposed shear 7= dux y)/dy. On average, the velocity profile is given by v = (iy,0). The dynamic shear viscosity q is the proportionality constant between the velocity gradient f and the frictional force acting on a plane perpendicular to y i.e.. 

The collision step redistributes momentum between particles and tends to reduce correlations. Making the assumption of molecular chaos, i.e., that the velocities of different particles are uncorrelated, and averaging over the two possible rotation directions, one finds 

Inserting this result into the definition of the viscosity, (42), yields the same expression for the kinetic viscosity in two-dimensions as obtained by the eqnilibrinm GK approach discussed in Sect. 4.1.1. 

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