Computations of the flow of non-Newtonian fluids in the presence of a reentrant
comer have a long history of convergence problems, which are believed to
originate from a nonsquare-integrable stress singularity. Local flow analyses
near such a comer have been inconclusive, due to the nonlinearity and the model
dependence of the governing equations. We have used molecular dynamics
simulations to compute the flow of both a Newtonian liquid and a model polymer
melt through a channel with a reentrant comer, providing an unbiased and
convergent calculation. The fluids interact via Lennard-Jones potentials, and
for the polymer case we employ FENE chains of length up to 30. For the Newtonian
fluid, the shear stress near the comer is found to agree with the Stokes flow
prediction of Moffatt. In the non-Newtonian case, the shear stress has a
stronger apparent divergence, increasing with velocity but not with chain
length, which appears to saturate at an integrable value of approximately 0.8.
The molecular origin of the stress enhancement is the additional elongation and
rotation of the molecules near the reentrant comer.
J. Koplik, Banavar, J.R., Reentrant Corner Flows of Newtonian and Non-Newtonian Fluids, J. Rheol., The Society of Rheology, Inc., Vol. 41(3), pp. 787-805, May/June 1997.