It should also be noted that, unlike the thermodynamic
temperature, the granular temperature is not isotropic. This
should be obvious because the streaming mechanism of
temperature generation (Fig. 8b) only generates temperature
in the direction perpendicular to the velocity gradient. Fig. 11
shows the ratio of Tx and Ty the x- and y-direction temperatures,
from Campbell [36]. Note that at small ν, where the streaming
mode of temperature generation is largest, Tx/Ty is significantly
larger that unity reflecting the streaming generation of xdirection
temperature. But at large ν, where the collisional mode
dominates, Tx/Ty is near unity indicating the more isotropic
temperatures produced collisionally. Note also that the
coefficient of restitution ε has a strong effect, with the largest
anisotropies appearing at the smallest ε. The larger dissipation
at the smaller ε reduces the collisional generation of temperature
and thus enhances the relative importance of the streaming
mechanism, leading to larger temperature anisotropies. Note
that while higher order kinetic theories can produce normal
stress differences [46,47], they are strictly only valid in the limit
ν→0; furthermore, they predict that the differences are
functions only of the inelasticity and are independent of the
concentration.