The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics
(NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring’s
model (EM) for shear thinning are derived. It is argued that an “incremental viscosity,”
η
i
, or IV which
is the derivative of the steady state stress with respect to the shear rate is a better measure of the physical
state of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shear
stress divided by the strain rate). The stress relaxation function,
C
i
(
t
), associated with
η
i
is consistent
with Boltzmann’s superposition principle and is computed by NEMD and the EM. The IV of the Eyring
model is shown to be a special case of the Carreau formula for shear thinning. An analytic solution
for the transient time correlation function for the EM is derived. An extension of the EM to allow for
significant local shear stress fluctuations on a molecular level, represented by a gaussian distribution,
is shown to have the same analytic form as the original EM but with the EM stress replaced by its time
and spatial average. Even at high shear rates and on small scales, the probability distribution function
is almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formula
approximately satisfies the Fluctuation Theorem, which may in part explain its success in representing
the shear thinning curves of a wide range of different types of chemical systems.