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Scaling the normal stresses in concentrated non-colloidal suspensions of spheres

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Abstract

We have collected six sets of results for the ratio of the second normal stress difference to the shear stress \((N_{2}/\tau )\) in non-colloidal suspensions of spheres in Newtonian matrices. They all show a near-cubic dependence on the volume fraction \(\varphi \) in the range \(0.1 < \varphi < 0.5\), in contrast to the square law predictions of Brady and Morris (J Fluid Mech 348:103–139, 1997) for dilute suspensions. We suggest that the difference can be resolved by using a dependence on the square of the effective volume fraction \(\varphi _{\textrm e}\), and good agreement is then found.

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Acknowledgement

We thank the Australian Research Council for support of this work via Grant DP10103414.

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Authors and Affiliations

  1. School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia

    Roger I. Tanner, Fuzhong Qi & Shaocong Dai

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  1. Roger I. Tanner
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  2. Fuzhong Qi
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  3. Shaocong Dai
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Correspondence to Roger I. Tanner.

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Tanner, R.I., Qi, F. & Dai, S. Scaling the normal stresses in concentrated non-colloidal suspensions of spheres. Rheol Acta 52, 291–295 (2013). https://doi.org/10.1007/s00397-013-0676-8

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  • DOI: https://doi.org/10.1007/s00397-013-0676-8

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