Flow of Some Carboxymethylcellulose Solutions Through Abrupt Axisymmetric Contractions. Experimental Study and Modelling of Shear Thinning and Elongational Effects

René Devienne 1 , Philippe Corvisier 1  and Abdel Lyazid 2
  • 1 LEMTA, , 54504, Vandoeuvre, France
  • 2 IMFS, , 67000, Strasbourg, France

Abstract

The focus of this paper will be on the modelling and simulation of contraction flow, with marked aspect ratio β = 6, 9, 12. Two fluid families are considered: a glycerol Newtonian solution and carboxy-methyl-cellulose (CMC) solutions which present particular rheological properties. Their shear thinning character are modelled by a Cross formula over a large scale of shear rates. The elongational properties are taken via a simplified Ericksen model into account. Experimental velocity profiles are determined using the Laser Doppler Anemometry (L.D.A) technique. They are found to be in good agreement with numerical velocity profiles obtained using a finite volume method with extra source terms traducing the particular rheological behaviour proposed here. The simulations allow to determine the different values of an elongational parameter μ3. Then, some numerical results concerning the total energy losses are presented using the usual concept of the equivalent length.

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  • [1] Xue SC, Phan-Thien N, Tanner RI: Three dimensional numerical simulation of viscoelastic flows trough planar contractions, J. Non-Newtonian Fluid Mech. 74 (1998) 195-245.

  • [2] Cable PJ, Boger DV: A comprehensive experimental investigation of tubular entry flow of viscoelastic fluids, AIChE J. 24 (1978) 869-879.

  • [3] Kim ME, Brown RA, Armstrong RC: The role of inertia and shear-thinning in flow of an inelastic liquid through an axisymmetric sudden contraction, J. Non-Newtonian Fluid Mech. 13 (1983) 341-363.

  • [4] Nigen S, Walters K: Viscoelastic contraction flows: comparison of axisymmetric and planar configurations, J. Non-Newtonian Fluid Mech. 102 (2002) 343-359.

  • [5] Aboudacar M, Matallah H, Tamaddon-Jahromi HR, Webster MF: Numerical prediction of extensional flows in contraction geometries: hybrid finite volume/element method, J. Non-Newtonian Fluid Mech. 104 (2002) 125-164.

  • [6] Maders H, Vergnes B, Demay Y and Agassant JF: Steady flow of a White-Metzner fluid in a 2-D abrupt contraction: computation and experiments, J. Non-Newtonian Fluid Mech. 45 (1992) 63-80.

  • [7] Halmos AL, Boger DV: The behavior of a power-Law fluid flowing trough a sudden expansion, AIChE J. 21 (1975) 550-554.

  • [8] Binding DM: An approximate analysis for contraction and converging flows, J. Non-Newtonian Fluid Mech. 27 (1988) 173-189.

  • [9] Maia JM and Binding D: Influence of the elongational properties on the contraction flow of a polyisobutylene in a mixed solvent, Rheol. Acta 38 (1999) 160-171.

  • [10] Piau JM, El Kissi N and Tremblay B: Low Reynolds number flow vizualisation of linear and branched silicones upstream of orifice dies? J. Non-Newtonian Fluid Mech. 30 (1998) 197-232.

  • [11] Cartlos U and Piau JM: Creeping flow regimes of low concentration polymer solutions in thick solvents trough an orifice die. J. Non-Newtonian Fluid Mech. 45 (1992) 231-285.

  • [12] Rothstein J and McKinley G: Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisym-metric contraction/expansion, J. Non-Newtonian Fluid Mech. 86 (1999) 61-88.

  • [13] Rothstein P and McKinley G: The axisymmetric contraction expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop, J. Non-Newtonian Fluid Mech. 98 (2001) 33-66.

  • [14] Durst F, Melling A, Whitelaw JH: Principles and practice of laser Doppler anemometry, Academic Press, London (1976).

  • [15] Durrani TS, Greated CA, Laser systems in flow measurement, Plenum Press, New York (1977).

  • [16] Kulicke WM, Kull AH, Kull W, Thielking H: Char-acterisation of aqueous carboxymethylcellulose solutions in terms of their molecular structure and its influence on rheological behaviour, Polymer 37 (1995) 2723-2731.

  • [17] Ericksen JL: Transversaly isotropic fluids, Kolloid Z. 173 (1960) 117-122.

  • [18] Lipscomb GG: Analysis of suspension rheology in complex flows, Ph.D. Thesis, University of California, Berkeley (1986).

  • [19] Advani SG and Tucker CL: The use of tensors to describe and predict fibre orientation in short fibre composite, J. Rheol. 31 (1987) 751-762.

  • [20] Papanastasiou TC and Alexandrou AN: Isothermal Extrusion of non-dilute fiber suspensions, J. Non-Newtonian Fluid Mech. 25 (1987) 313-245.

  • [21] Kröger M. and Sellers H.S : Viscosity coefficients for anisotropic nematic fluids based on structural theories of suspensions, J. Chem. Phys. 103 (1995) 807-817.

  • [22] Manéa G, Ecoulements de fluides non-newtoniens dans une contraction axisymétrique : influence des zones de recirculation sur l’établissement du régime hydrodynamique dans le capillaire, Thèse de doctorat, Université Louis Pasteur, Strasbourg (1998).

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