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Simple shear flow of a suspension of fibres in a dilute polymer solution at high Deborah number

Published online by Cambridge University Press:  26 April 2006

O. G. Harlen  and
Donald L. Koch
O. G. Harlen
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

The behaviour of fibre suspensions in dilute polymer solutions at high Deborah numbers is analysed. In particular, we calculate the change to the extension of the polymers and the orientation of the fibres caused by hydrodynamic interactions between the polymers and the fibres. At a sufficiently high Deborah number the combined effect of the fibre velocity disturbances and the mean shear flow produce a dramatic increase in the extension of the polymers, similar to the coil-stretch transition observed in extensional flow.

The non-Newtonian stresses caused by the polymers produce a perturbation to the angular velocity of the fibres, giving rise to a net drift across Jeffery orbits towards the vorticity axis. Unlike the second-order-fluid analysis of Leal (1975), this effect does not depend on the second-normal-stress difference.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 187 - 207
Copyright
© 1993 Cambridge University Press

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References

Anczurowski, E. & Mason, S. G. 1967 Kinetics of flowing dispersions III. Equilibrium orientations of rods and discs. J. Colloid Interface Sci. 23, 533.Google Scholar
Bartram, E., Goldsmith, H. L. & Mason, S. G. 1975 Particle motions in non-Newtonian media III. Further observations in elasticoviscous fluids. Rheol. Acta 14, 776.Google Scholar
Batchelor, G. K. 1970 Slender body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419.Google Scholar
Boger, D. V. 1977 A highly-elastic constant-viscosity fluid. J. Non-Newtonian Fluid Mech. 3, 87.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 fibres. Phys. Fluids A 3, 2516.Google Scholar
Ganani, E. & Powell, R. L. 1985 Suspensions of rodlike particles: literature review and data correlations. J. Composite Mater. 19, 195.Google Scholar
Gauthier, F., Goldsmith, H. L. & Mason, S. G. 1971 The kinetics of flowing dispersions V. Orientation distributions of cylinders in Newtonian and non-Newtonian systems. Kolloid-Z. Z. Polymere 248, 1000.Google Scholar
Iso, Y., Koch, D. L. & Cohen, C. 1993 Orientation of fibers in non-Newtonian fluids subject to simple shear. (in preparation).
James, D. F. & McClaren, D. R. 1975 The laminar flow of dilute polymer solutions through a porous media. J. Fluid Mech. 70, 733.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161.Google Scholar
Johnson, S. J., Salem, A. J. & Fuller, G. G. 1990 Dynamics of colloidal particles in sheared non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 34, 89.Google Scholar
Kitano, T., Funabashi, M., Klason, C. & Kubat, J. 1988 Shear flow properties of carbon fibre-filled polyethylene melts. Intl Polym. Proc.III 2 61.Google Scholar
Koch, D. L. & Shaqfeh, E. S. G. 1990 The average rotation rate of a fiber in the linear flow of a semidilute suspension. Phys. Fluids A 2, 2093.Google Scholar
Kuhn, W. & Kuhn, H. 1945 Bedeutung beschränkt freir drehbarkeit für die Viskosität und Strömungsdoppelbrechung von Fadenmolekellosungen. I. Helv. Chim. Acta 28, 1533.Google Scholar
Leal, L. G. 1975 The slow motion of slender rod-like particles in a second order fluid. J. Fluid Mech. 69, 305.Google Scholar
Magda, J. J., Lou, J., Baek, S.-G. & DeVries, K. L. 1991 Second normal stress difference of a Boger fluid. Polymer 32, 2000.Google Scholar
Peterlin, A. 1966 Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J. Polym. Sci. 4, 287.Google Scholar
Rallison, J. M. & Hinch, E. J. 1988 Do we understand the physics in the constitutive equation? J. Non-Newtonian Fluid Mech. 29, 37.Google Scholar
Shaqfeh, E. S. G. & Fredrickson, G. H. 1990 The hydrodynamic stress in a suspension of rods. Phys. Fluids A 2, 7.Google Scholar
Shaqfeh, E. S. G. & Koch, D. L. 1988a The effect of hydrodynamic interactions on the orientation of axisymmetric particles flowing through a fixed bed of spheres or fibers. Phys. Fluids 31, 728.Google Scholar
Shaqfeh, E. S. G. & Koch, D. L. 1988b The combined effects of hydrodynamic interactions and Brownian motion on the orientation of particles flowing through fixed beds. Phys. Fluids 31, 2769.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
Stover, C. A. & Cohen, C. 1990 The motion of rod-like particles in the pressure driven flow between two flat plates. Rheol. Acta 29, 203.Google Scholar
Stover, C. A., Koch, D. L. & Cohen, C. 1992 Observations of fibre orientation in simple shear flows of semi-dilute suspensions. J. Fluid Mech. 238, 277.Google Scholar
Warner, H. R. 1972 Kinetic theory and rheology of finitely extensible dumbbells. Ind. Engng Chem. Fundam. 20, 227.Google Scholar