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Migration of a sphere suspended in viscoelastic liquids in Couette flow: experiments and simulations

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Abstract

The intrinsically coupled effects of the curvature of the flow-field and of the viscoelastic nature of suspending medium on the cross-stream lateral migration of a single non-Brownian sphere in wide-gap Couette flow are studied. Quantitative videomicroscopy experiments using a counterrotating device are compared to the results of 3D finite element simulations. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features, including a reference Newtonian fluid, a single relaxation time wormlike micellar surfactant solution, a broad spectrum shear-thinning elastic polymer solution and a constant viscosity, highly elastic Boger fluid. As expected for conditions corresponding to Stokes flow, migration is absent in the Newtonian fluid. In the wormlike micellar solution and the shear-thinning polymer solution, spheres are observed to migrate in the direction of decreasing shear rate gradient, i.e. the outer cylinder, except when the sphere is initially released close to the inner cylinder, in which case the migration is towards it. The migration is enhanced by faster relative angular velocities of the cylinders. Shear-thinning reduces the migration velocity, showing an opposite behavior as compared to previous results in planar shear flow. In the Boger fluid, within experimental error no migration could be observed, likely due to the large solvent contribution to the overall viscosity. For small Deborah numbers the migration results are well described by an heuristic argument based on a local stress balance.

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Notes

  1. This procedure is used for the shear-thinning fluids. For the BF the power-law exponent is set to \(n_{\text{PL}}=1\) (no shear-thinning).

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Acknowledgements

FS acknowledges a graduate fellowship of the Fund for Scientific Research-Flanders (FWO-Vlaanderen). GDA and JV acknowledge the research council of K.U. Leuven for a postdoctoral fellowship.

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Authors and Affiliations

  1. Department of Chemical Engineering, K.U. Leuven, W. de Croylaan 46, 3001, Leuven, Belgium

    G. D’Avino & J. Vermant

  2. Center for Advanced Biomaterials for Health Care @CRIB, Istituto Italiano di Tecnologia, P.le Tecchio 80, 80125, Naples, Italy

    G. D’Avino

  3. Foundation for Research and Technology Hellas (FORTH), Institute of Electronic Structure and Laser, Heraklion, 71110, Crete, Greece

    F. Snijkers & R. Pasquino

  4. Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600, MB, Eindhoven, The Netherlands

    M. A. Hulsen

  5. Istituto di Ricerche sulla Combustione, IRC-CNR, P.le Tecchio 80, 80125, Naples, Italy

    F. Greco

  6. Department of Chemical Engineering, University of Naples Federico II, P.le Tecchio 80, 80125, Naples, Italy

    P. L. Maffettone

  7. Interdisciplinary Research Center in Biomaterials (CRIB), University of Naples Federico II, P.le Tecchio 80, 80125, Naples, Italy

    P. L. Maffettone

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  1. G. D’Avino
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  2. F. Snijkers
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  4. M. A. Hulsen
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  5. F. Greco
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  6. P. L. Maffettone
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  7. J. Vermant
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Correspondence to G. D’Avino.

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D’Avino, G., Snijkers, F., Pasquino, R. et al. Migration of a sphere suspended in viscoelastic liquids in Couette flow: experiments and simulations. Rheol Acta 51, 215–234 (2012). https://doi.org/10.1007/s00397-011-0592-8

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  • DOI: https://doi.org/10.1007/s00397-011-0592-8

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