### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 309-325 |

Number of pages | 17 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 35 |

Issue number | 2-3 |

DOIs | |

State | Published - 1990 |

### Profile

### Keywords

- Boger fluids
- crossflow permeability
- extensional flow
- packing in cylinder arrays
- polymer degradation
- test fluid M1

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*Journal of Non-Newtonian Fluid Mechanics*,

*35*(2-3), 309-325. DOI: 10.1016/0377-0257(90)85056-5

**Crossflow of elastic liquids through arrays of cylinders.** / Chmielewski, C.; Petty, C. A.; Jayaraman, K.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol 35, no. 2-3, pp. 309-325. DOI: 10.1016/0377-0257(90)85056-5

}

TY - JOUR

T1 - Crossflow of elastic liquids through arrays of cylinders

AU - Chmielewski,C.

AU - Petty,C. A.

AU - Jayaraman,K.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

KW - Boger fluids

KW - crossflow permeability

KW - extensional flow

KW - packing in cylinder arrays

KW - polymer degradation

KW - test fluid M1

UR - http://www.scopus.com/inward/record.url?scp=0025456794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025456794&partnerID=8YFLogxK

U2 - 10.1016/0377-0257(90)85056-5

DO - 10.1016/0377-0257(90)85056-5

M3 - Article

VL - 35

SP - 309

EP - 325

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 2-3

ER -