  Non equilibrium coarse grained, dissipative particle dynamics simulations of
complex fluids, made up of polymer brushes tethered to planar surfaces immersed
in a solvent yield non monotonic behavior of the friction coefficient as a
function of the polymer grating density on the substrates, \Gamma, while the
viscosity shows a monotonically increasing dependence on \Gamma. This effect is
shown to be independent of the degree of polymerization, N, and the size of the
system. It arises from the composition and the structure of the first particle
layer adjacent to each surface that results from the confinement of the fluid.
Whenever such layers are made up of as close a proportion of polymer beads to
solvent particles as there are in the fluid, the friction coefficient shows a
minimum, while for disparate proportions the friction coefficient grows. At the
mushroom to brush transition (MBT) the viscosity scales with an exponent that
depends on the characteristic exponent of the MBT (6/5) and the solvent quality
exponent (\nu = 0.5, for theta solvent), but it is independent of the
polymerization degree (N). On the other hand, the friction coefficient at the
MBT scales as {\mu}~N^(6/5), while the grafting density at the MBT scales as
{\Gamma}~ N^(-6/5) when friction is minimal, in agreement with previous scaling
theories. We argue these aspects are the result of cooperative phenomena that
have important implications for the understanding of biological brushes and the
design of microfluidics devices, among other applications of current academic
and industrial interest.
