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Observations of polymer conformation during flow through a fixed fibre bed

Published online by Cambridge University Press:  26 April 2006

Anthony R. Evans ,
Eric S. G. Shaqfeh  and
Paul L. Frattini
Anthony R. Evans
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Eric S. G. Shaqfeh
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Paul L. Frattini
Affiliation:
Eifle Inc., c/o 11465 Clayton Road, San Jose, CA 95127, USA
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Abstract

Linear birefringence measurements of dilute and semi-dilute polyisobutylene solutions following flow through a disordered fixed fibre bed of 2.47% solids volume fraction provide both transient and steady measurements of chain deformation. Our results indicate that the flexible polyisobutylene polymers undergo a large conformation change, stretching in the direction of the average flow. This occurs even though the average flow in the bed is a plug flow which would not cause any polymer stretch by itself. The polymer stretch or conformation change increases with the number of chain interactions with bed fibres and ultimately reaches a steady-state value that can be correlated with the pore-size Deborah number (i.e. a characteristic polymer relaxation time divided by a characteristic flow time in the bed pore). Large changes in the polymer conformation are noted for values of the Deborah number, De > 5. In addition, the time to steady state scales with the characteristic flow time within a pore over a large range of Deborah numbers. The pressure drop across the fibre bed was also measured simultaneously with the birefringence measurement and was found to be directly proportional to the birefringence throughout the range of De investigated. Thus, we show empirically, for the first time, that chain elongation, which produces normal stress anisotropy within the fluid, is directly responsible for the increased flow resistance. These findings are then analysed in the light of recent theories for the response of polymer molecules in fixed bed flow fields (Shaqfeh & Koch 1992). It is shown that our results are consistent with the interpretation that these flows are stochastic strong flows, which create an apparent ‘coil-stretch’ transition. After extending the theory of Shaqfeh & Koch to account for the specifics in the experiments, including the bed geometry and statistics as well as the polydispersity of the polymer solutions, it is shown that the theory can predict most of the experimental results both qualitatively and quantitatively.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 281 , 25 December 1994 , pp. 319 - 356
Copyright
© 1994 Cambridge University Press

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References

Bird, R. B., Curtiss, C. F., Armstrong, R. C. & Hassager, O. 1978 Dynamics of Polymeric Liquids: Volume 2. Kinetic Theory. John Wiley and Sons.
Brandrup, J. & Immergut, E. H. 1989 Polymer Handbook. Wiley Interscience.
Cathey, C. A. & Fuller, G. G. 1990 The optical and mechanical response of flexible polymer solutions to extensional flow. J. Non-Newtonian Fluid Mech. 34, 63.Google Scholar
Chilcott, M. D. & Rallison, J. M. 1988 Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29, 381.Google Scholar
Chirinos, M. L., Crain, P., Lodge, A. S., Schrag, J. L. & Yaritz, J. 1990 Measurements of N1–-N2 and η in steady shear flow and η′, η″, and birefringence in small-strain oscillatory shear for the polyisobutylene solution M1. J. Non-Newtonian Fluid Mech. 35, 105.Google Scholar
Chmielewski, C., Petty, C. A. & Jayaraman, K. 1990 Crossflow of elastic liquids through arrays of cylinders. J. Non-Newtonian Fluid Mech. 35, 309.Google Scholar
Coleman, B. D., Dill, E. H. & Toupin, R. A. 1970 A phenomenological theory of streaming birefringence. Arch. Rat. Mech. Anal. 39, 358.Google Scholar
Deiber, J. A. & Schowalter, W. R. 1979 Flow through tubes with sinusoidal axial variations in diameter. AIChE J. 25, 638.Google Scholar
Doi, M. & Edwards, S. F. 1986 The Theory of Polymer Dynamics. Oxford Science Publications.
Dupuis, D., Layec, Y. & Wolff, C. 1986 Rheo-Optical Properties of Polymer Solutions. In Optical Properties of Polymers (ed. G. H. Meeten). Elsevier.
Durst, F., Haas, R. & Kaczmar, B. U. 1981 Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions. J. Appl. Polymer Sci. 26, 3125.Google Scholar
Flory, P. J. 1953 Principles of Polymer Chemistry. Cornell University Press.
Frattini, P. L. & Fuller, G. G. 1984 A note on phase-modulated flow birefringence. A promising rheo-optical method. J. Rheol. 28, 61.Google Scholar
Frattini, P. L., Shaqfeh, E. S. G., Levy, J. L. & Koch, D. L. 1991 Observations of axisymmetric tracer particle orientation during flow through a dilute fixed bed of fibers. Phys. Fluids A 3, 2516.Google Scholar
Fuller, G. G. 1990 Optical rheometry. Ann. Rev. Fluid Mech. 22, 387.Google Scholar
Fuller, G. G. & Leal, L. G. 1980 Flow birefringence of dilute polymer solutions in two-dimensional flows. Rheol. Acta 19, 580.Google Scholar
Galante, S. R. 1991 An investigation of planar entry flow using a high resolution flow birefringence method. PhD thesis, Carnegie Mellon University.
Galante, S. R. & Frattini, P. L. 1993 Spatially resolved birefringence studies of planar entry flow. J. Non-Newtonian Fluid Mech. 47, 289.Google Scholar
Geffroy, E. & Leal, L. G. 1990 Flow birefringence studies in transient flows of a two-roll mill for the test-fluid Ml. J. Non-Newtonian Fluid Mech. 35, 361.Google Scholar
Gennes, P. G. de 1979 Scaling Concepts in Polymer Physics. Cornell University Press.
Harlen, O. G., Hinch, E. J. & Rallison, J. M. 1992 Birefringent pipes: The steady flow of a dilute polymer solution near a stagnation point. J. Non-Newtonian Fluid Mech. 44, 229.Google Scholar
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech. 83, 695.Google Scholar
Jackson, G. W. & James, D. F. 1986 The permeability of fibrous porous media. Can. J. Chem. Engng 64, 364.Google Scholar
James, D. F. & McLaren, D. R. 1975 The laminar flow of dilute polymer solutions through porous media. J. Fluid Mech. 70, 733.Google Scholar
Janeschitz-Kreigl, H. 1983 Polymer Melt Rheology and Flow Birefringence. Springer.
Kishbaugh, A. J. & McHugh, A. J. 1993 A rheo-optical study of shear-thickening and structure formation in polymer solutions. Rheo. Acta. 32, 9.Google Scholar
Kuhn, W. & Grun, F. 1942 Relationships between elastic constants and stretching double refraction of highly elastic substances. Kolloid Z. 101, 248.Google Scholar
Larson, R. G. 1988 Constitutive Equations for Polymer Melts and Solutions. Butterworths.
Larson, R. G., Khan, S. A. & Raju, V. R. 1988 Relaxation of stress and birefringence in polymers of high molecular weight. J. Rheol. 32, 145.Google Scholar
Marshall, R. J. & Metzner, A. B. 1967 Flow of viscoelastic fluids through porous media. Ind. Eng. Chem. Fundam. 6, 393.Google Scholar
McHugh, A. J., Mackay, M. E. & Khomami, B. 1988 Measurement of birefringence by the method of isoclines. J. Rheol. 31, 619.Google Scholar
McKinley, G. H., Armstrong, R. C. & Brown, R. A. 1993 The wake instability in viscoelastic flow past confined circular cylinders. Phil. Trans. R. Soc. Lond. A 344, 1.Google Scholar
Menasveta, M. J. & Hoagland, D. A. 1991 Light scattering from dilute poly(styrene) solutions in uniaxial elongational flow. Macromolecules 24, 3427.Google Scholar
Muller, A. J., Odell, J. A. & Tatham, J. P. 1990 Stagnation-point extensional flow behavior of M1. J. Non-Newtonian Fluid Mech. 35, 231.Google Scholar
Ng, R. C.-Y. & Leal, L. G. 1993 Concentration effects on birefringence and flow modification of semidilute polymer solutions in extensional flows. J. Rheol. 37, 443.Google Scholar
Nguyen, D. A. & Sridhar, T. 1990 Preparation and some properties of M1 and its constituents. J. Non-Newtonian Fluid Mech. 35, 93.Google Scholar
Olbricht, W. L., Rallison, J. M. & Leal, L. G. 1982 Strong flow criteria based on microstructure deformation. J. Non-Newtonian Fluid Mech. 10, 291.Google Scholar
Pearson, D. S., Kiss, A. D., Fetters, L. J. & Doi, M. 1989 Flow-induced birefringence of concentrated poly-isoprene solutions. J. Rheol. 33, 517.Google Scholar
Peterlin, A. 1961 Streaming birefringence of soft linear macromolecules with finite chain length. Polymer 2, 257.Google Scholar
Peterlin, A. 1976 Optical effects in flow. Ann. Rev. Fluid Mech. 8, 35.Google Scholar
Phillippoff, W. 1964 Streaming birefringence of polymer solutions. J. Polymer Sci. 5, 1.Google Scholar
Pilitsis, S. & Beris, A. N. 1989 Calculations of steady-state viscoelastic flow in an undulating tube. J. Non-Newtonian Fluid Mech. 31, 231.Google Scholar
Quinzani, G. H., McKinley, G. H., Brown, R. A. & Armstrong, R. C. 1990 Modeling the rheology of polyisobutylene solutions. J. Rheol. 34, 705.Google Scholar
Shaqfeh, E. S. G. & Koch, D. L. 1990 Orientational dispersion of fibers in extensional flows. Phys. Fluids A 2, 1077.Google Scholar
Shaqfeh, E. S. G. & Koch, D. L. 1992 Polymer stretch in dilute fixed beds of fibres or spheres. J. Fluid Mech. 244, 17.Google Scholar
Skartsis, L., Khomami, B. & Karoos, J. L. 1992 Polymeric flow through fibrous media. J. Rheol. 36, 589.Google Scholar
Sridhar, T. 1990 An overview of the project M1. J. Non-Newtonian Fluid Mech. 35, 85.Google Scholar
Tanner, R. I. 1985 Engineering Rheology. Oxford Science Publications.
Townsend, P. 1980 A numerical simulation of Newtonian and viscoelastic flow past stationary and rotating cylinders. J. Non-Newtonian Fluid Mech. 6, 219.Google Scholar
Wales, J. L. S. 1976 The Application of Flow Birefringence to Rheological Studies of Polymer Melts. Delft University Press.
Zick, A. A. & Homsy, G. M. 1984 Numerical simulation of the flow of an Oldroyd fluid through a periodically constricted tube. Proc. IX Intl Cong. on Rheology, p. 663.