We study the scaling properties of heterogeneities in
nematic (liquid crystal) polymers that are generated by pressure-driven,
capillary Poiseuille flow. These studies complement our earlier
drag-driven structure simulations and analyses. We use the mesoscopic
Doi-Marrucci-Greco model, which incorporates excluded-volume
interactions of the rod-like particle ensemble, distortional elasticity
of the dispersion, and hydrodynamic feedback through orientation
dependent viscoelastic stresses. The geometry likewise introduces
anchoring conditions on the nano-rods which touch the solid boundaries.
We first derive flow-orientation steady-state structures for three
different anchoring conditions, by asymptotic analysis in the limit of
weak pressure gradient. These closed-form expressions yield scaling
laws, which predict how lengthscales of distortions in the flow and
orientational distributions vary with strength of the excluded volume
potential, molecule geometry, and distortional elasticity constants.
Next, the asymptotic structures are verified by direct numerical
simulations, which provide a high level benchmark on the numerical code
and algorithm. Finally, we calculate the effective (thermal or
electrical) conductivity tensor of the composite films, and determine
scaling behavior of the effective property enhancements generated by
capillary Poiseuille flow.