CROSS-FLOW OF ELASTIC LIQUIDS THROUGH ARRAYS OF CYLINDERS

The flow of a dilute solution of polyisobutylene in polybutene transverse to unidirectional arrays of cylinders has been investigated at Reynolds numbers less than 0.1. Two different arrays were used-a triangular pitch array and a rectangular pitch array. Both arrays have a porosity of 0.704, the same bed length and comprise identical cylinders. Steady state permeation experiments were run over a range of superficial velocities in both arrays, to study the onset of departure from Darcy's law. The rheology of the fluid was evaluated in shear before and after each set of runs. While departures from Darcy's law occurred in both arrays at similar values of Deborah number, mechanical degradation of the polymer solution was much more severe with the triangular pitch array than with the rectangular pitch array. Specifically, after several runs through the triangular array the relaxation time was halved while the change in viscosity was relatively minor; this reveals loss of the high molecular weight tail in the original polymer. This degradation was irrecoverable; no recovery was noted after two weeks. Measurements of molecular weight distribution on the same samples in Odell's laboratory confirm that the highest molecular weight components are degraded. Finite element simulations of Stokes flow were carried out for the two different geometries to determine extensional strain rates along the flow direction in several regions. This was followed by calculations of polymer chain deformation in these regions, with the nonlinear elastic dumbbell model. These calculations reveal that the maximum stretch rate in the triangular pitch array occurs along the streamline joining the stagnation points on adjacent cylinders; this leads to nearly complete extension of the polymer chain at a nominal Deborah number of 1 in the triangular array. However, in the rectangular pitch array, the maximum stretch rate occurs along streamlines considerably removed from the stagnation points, and the polymer chains are not extended along those streamlines up to a Deborah number of 1. © 1990.