Reverting to the
notation we introduce an appropriate perturbative term in the Hamiltonian:
is the hydrodynamic velocity field, and
For reasons of his own, W. Hoover dubbed the construct
Written in dummy index notation we have (omitting the particle index )
and the resulting equations of motion are
To avoid gradual heating of the sample, a Gaussian (or other) thermostat
may be added.
For the simple homogeneous shear with
as the only non-vanishing element of
above equations read
Shearing boundary conditions as introduced by Lees and Edwards
may be applied. But now the flow is driven by the additional terms
in the equations of motion.
Again, the stress tensor element is evaluated, and from
its average the viscosity is determined as
The method may used with an oscillatory applied shear,
yielding the frequency-dependent viscosity. Also, a volume dilation may
be applied to determine the bulk visosity.
F. J. Vesely / University of Vienna