Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-02T02:43:37.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag of a shear-thickening suspension on a rotating cylinder

Published online by Cambridge University Press:  04 September 2023

Francisco M. Rocha Open the ORCID record for Francisco M. Rocha [Opens in a new window] ,
Yoël Forterre Open the ORCID record for Yoël Forterre [Opens in a new window] ,
Bloen Metzger Open the ORCID record for Bloen Metzger [Opens in a new window]  and
Henri Lhuissier Open the ORCID record for Henri Lhuissier [Opens in a new window]
Francisco M. Rocha
Affiliation:
Aix Marseille University, CNRS, IUSTI, 13453 Marseille, France
Yoël Forterre
Affiliation:
Aix Marseille University, CNRS, IUSTI, 13453 Marseille, France
Bloen Metzger
Affiliation:
Aix Marseille University, CNRS, IUSTI, 13453 Marseille, France
Henri Lhuissier*
Affiliation:
Aix Marseille University, CNRS, IUSTI, 13453 Marseille, France
*
†Email address for correspondence: henri.lhuissier@univ-amu.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate experimentally the two-dimensional flow of a shear-thickening suspension around a rotating cylinder to which a constant torque is applied. While for low torques both the drag and the flow are steady and close to those for a Newtonian fluid, above the onset torque for discontinuous shear thickening the average velocity of the cylinder saturates and large periodic oscillations of the cylinder velocity are observed. The oscillations result from a hydrodynamic instability of the flow: slow-acceleration phases are followed by high-deceleration phases, triggered by the propagation of a thickening front, and so on. The slow-acceleration phases set the oscillation period, which is limited by the cylinder inertia and inversely proportional to the applied torque. Combined analyses of the cylinder motion and the flow reveal that the front typically nucleates when the shear rate at the cylinder surface reaches the discontinuous shear-thickening threshold. In addition, the characteristics (duration, stress) of the deceleration are set by the interplay between the thickening front propagation and the suspension and cylinder inertiae or the container size. Since for a slow acceleration the shear rate at the cylinder surface is essentially the cylinder angular velocity, this description of the unsteadiness elucidates the saturation of the average velocity. More generally, it illustrates how the hydrodynamics of a shear-thickening suspension with a strongly re-entrant rheology can lead to a marginally re-entrant, although steep, drag curve.

JFM classification

Complex Fluids: Suspensions Instability: Taylor-Couette flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A35
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdesselam, Y., Agassant, J.-F., Castellani, R., Valette, R., Demay, Y., Gourdin, D. & Peres, R. 2017 Rheology of plastisol formulations for coating applications. Polym. Engng Sci. 57, 982–988.CrossRefGoogle Scholar
Baumgarten, A. & Kamrin, K. 2019 A general constitutive model for dense, fine-particle suspensions validated in many geometries. Proc. Natl Acad. Sci. 116, 1908065116–9.CrossRefGoogle ScholarPubMed
Blanco, E., Hodgson, D., Hermes, M., Besseling, R., Hunter, G., Chaikin, P., Cates, M., Van Damme, I. & Poon, W. 2019 Conching chocolate is a prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content. Proc. Natl Acad. Sci. 116, 10303–10308.CrossRefGoogle ScholarPubMed
Boersma, W., Baets, P., Lavèn, J. & Stein, H. 1991 Time-dependent behavior and wall slip in concentrated shear thickening dispersions. J. Rheol. 35, 1093–1120.CrossRefGoogle Scholar
Chacko, R., Mari, R., Cates, M. & Fielding, S. 2018 Dynamic vorticity banding in discontinuously shear thickening suspensions. Phys. Rev. Lett. 121, 108003.CrossRefGoogle ScholarPubMed
Clavaud, C., Bérut, A., Metzger, B. & Forterre, Y. 2017 Revealing the frictional transition in shear-thickening suspensions. Proc. Natl Acad. Sci. 114, 5147–5152.CrossRefGoogle ScholarPubMed
Clavaud, C., Metzger, B. & Forterre, Y. 2020 The darcytron: a pressure-imposed device to probe the frictional transition in shear-thickening suspensions. J. Rheol. 64, 395–403.CrossRefGoogle Scholar
Comtet, J., Chatté, G., Niguès, A., Bocquet, L., Siria, A. & Colin, A. 2017 Pairwise frictional profile between particles determines discontinuous shear thickening transition in non-colloidal suspensions. Nat. Commun. 8, 15633.CrossRefGoogle ScholarPubMed
Darbois Texier, B., Lhuissier, H., Forterre, Y. & Metzger, B. 2020 Surface-wave instability without inertia in shear-thickening suspensions. Commun. Phys. 3, 232.CrossRefGoogle Scholar
Darbois Texier, B., Lhuissier, H., Metzger, B. & Forterre, Y. 2023 Shear-thickening suspensions down inclines: from Kapitza to Oobleck waves. J. Fluid Mech. 959, A27–30.CrossRefGoogle Scholar
Dong, J. & Trulsson, M. 2017 Analog of discontinuous shear thickening flows under confining pressure. Phys. Rev. Fluids 2, 081301.CrossRefGoogle Scholar
Fall, A., Bertrand, F., Ovarlez, G. & Bonn, D. 2012 Shear thickening of cornstarch suspensions. J. Rheol. 56, 575–591.CrossRefGoogle Scholar
Fall, A., Huang, N., Bertrand, F., Ovarlez, G. & Bonn, D. 2008 Shear thickening of cornstarch suspensions as a reentrant jamming transition. Phys. Rev. Lett. 100, 018301.CrossRefGoogle ScholarPubMed
Freundlich, H. & Röder, H.L. 1938 Dilatancy and its relation to thixotropy. Trans. Faraday Soc. 34, 308–316.CrossRefGoogle Scholar
Gauthier, A., Ovarlez, G. & Colin, A. 2023 Shear-thickening in presence of adhesive contact forces: the singularity of cornstarch. arXiv:2303.15915v1 [cond–mat.soft].CrossRefGoogle Scholar
Gauthier, A., Pruvost, M., Gamache, O. & Colin, A. 2021 A new pressure sensor array for normal stress measurement in complex fluids. J. Rheol. 65, 583–594.CrossRefGoogle Scholar
Guy, B.M., Hermes, M. & Poon, W.C.K. 2015 Towards a unified description of the rheology of hard-particle suspensions. Phys. Rev. Lett. 115, 088304.CrossRefGoogle ScholarPubMed
Han, E., Wyart, M., Peters, I. & Jaeger, H. 2018 Shear fronts in shear-thickening suspensions. Phys. Rev. Fluids 3, 073301.CrossRefGoogle Scholar
Hermes, M., Guy, B., Poon, W., Poy, G., Cates, M. & Wyart, M. 2016 Unsteady flow and particle migration in dense, non-Brownian suspensions. J. Rheol. 60, 905–916.CrossRefGoogle Scholar
von Kann, S., Snoeijer, J. & van der Meer, D. 2013 Velocity oscillations and stop-go cycles: the trajectory of an object settling in a cornstarch suspension. Phys. Rev. E 87, 042301–14.CrossRefGoogle Scholar
LaFarge 2013 Superplasticizers: the wonder of fluid concrete, 38. Available at: https://www.youtube.com/watch?v=CSZxjQwDKF0.Google Scholar
Larsen, R., Kim, J.-W., Zukoski, C. & Weitz, D. 2010 Elasticity of dilatant particle suspensions during flow. Phys. Rev. E 81, 011502–8.CrossRefGoogle ScholarPubMed
Lin, N., Guy, B., Hermes, M., Ness, C., Sun, J., Poon, W. & Cohen, I. 2015 Hydrodynamic and contact contributions to continuous shear thickening in colloidal suspensions. Phys. Rev. Lett. 115, 228304.CrossRefGoogle ScholarPubMed
Lootens, D., Van Damme, H. & Hébraud, P. 2003 Giant stress fluctuations at the jamming transition. Phys. Rev. Lett. 90, 178301.CrossRefGoogle ScholarPubMed
Mari, R., Seto, R., Morris, J. & Denn, M. 2014 Shear thickening, frictionless and frictional rheologies in non-brownian suspensions. J. Rheol. 58, 1693–1724.CrossRefGoogle Scholar
Nagahiro, S.-I., Nakanishi, H. & Mitarai, N. 2013 Experimental observation of shear thickening oscillation. Europhys. Lett. 104, 28002.CrossRefGoogle Scholar
Nakanishi, H. & Mitarai, N. 2011 Shear thickening oscillation in a dilatant fluid. J. Phys. Soc. Japan 80, 033801–4.CrossRefGoogle Scholar
Nakanishi, H., Nagahiro, S. & Mitarai, N. 2012 Fluid dynamics of dilatant fluids. Phys. Rev. E 85, 011401–11.CrossRefGoogle ScholarPubMed
Ovarlez, G., Le, A., Smit, W., Fall, A., Mari, R., Chatté, G. & Colin, A. 2020 Density waves in shear-thickening suspensions. Sci. Adv. 6, eaay5589.CrossRefGoogle ScholarPubMed
Oyarte Galvez, L., van der Meer, D. & Pons, A. 2017 Dramatic effect of fluid chemistry on cornstarch suspensions: linking particle interactions to macroscopic rheology. Phys. Rev. E 95, 030602–6.CrossRefGoogle ScholarPubMed
Peters, I. & Jaeger, H.M. 2014 Quasi-2D dynamic jamming in cornstarch suspensions: visualization and force measurements. Soft Matt. 10, 6564–6570.CrossRefGoogle ScholarPubMed
Peters, I., Majumdar, S. & Jaeger, H. 2016 Direct observation of dynamic shear jamming in dense suspensions. Nature 532, 214–217.CrossRefGoogle ScholarPubMed
Rathee, V., Blair, D. & Urbach, J. 2017 Localized stress fluctuations drive shear thickening in dense suspensions. Proc. Natl Acad. Sci. 114, 8740–8745.CrossRefGoogle ScholarPubMed
Rathee, V., Miller, J., Blair, D. & Urbach, J. 2022 Structure of propagating high-stress fronts in a shear-thickening suspension. Proc. Natl Acad. Sci. 119, e2203795119.CrossRefGoogle Scholar
Richards, J., Royer, J., Liebchen, B., Guy, B. & Poon, W. 2019 Competing timescales lead to oscillations in shear-thickening suspensions. Phys. Rev. Lett. 123, 038004.CrossRefGoogle ScholarPubMed
Saint-Michel, B., Gibaud, T. & Manneville, S. 2018 Uncovering instabilities in the spatiotemporal dynamics of a shear-thickening cornstarch suspension. Phys. Rev. X 8, 031006.Google Scholar
Sedes, O., Singh, A. & Morris, J. 2020 Fluctuations at the onset of discontinuous shear thickening in a suspension. J. Rheol. 64, 309–319.CrossRefGoogle Scholar
Seto, R., Mari, R., Morris, J. & Denn, M. 2013 Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111, 218301.CrossRefGoogle ScholarPubMed
Singh, A., Mari, R., Denn, M.M. & Morris, J.F. 2018 A constitutive model for simple shear of dense frictional suspensions. J. Rheol. 62, 457–468.CrossRefGoogle Scholar
Waitukaitis, S. & Jaeger, H. 2012 Impact-activated solidification of dense suspensions via dynamic jamming fronts. Nature 487, 205–209.CrossRefGoogle ScholarPubMed
Waitukaitis, S., Roth, L., Vitelli, V. & Jaeger, H. 2013 Dynamic jamming fronts. Europhys. Lett. 102, 44001.CrossRefGoogle Scholar
Wyart, M. & Cates, M. 2014 Discontinuous shear thickening without inertia in dense non-brownian suspensions. Phys. Rev. Lett. 112, 098302.CrossRefGoogle ScholarPubMed

Rocha et al. Supplementary Movie 1

Real-time movie showing the typical behaviour observed in the high-torque unsteady regime, for a layer of cornstarch suspension subjected to a constant torque ( $\phi = 0.44$, $h = 8$\,mm, $\Gamma = 3.5\Gamma_c$) .

Download Rocha et al. Supplementary Movie 1(Video)
Video 45.2 MB

Rocha et al. Supplementary Movie 2

Movie of the thickening-front propagation observed during the cylinder deceleration phase ( $\phi = 0.44$, $h = 35 mm$, $\Gamma = 3.5 \Gamma_c$, same as Fig. 6). The movie starts at the onset of cylinder deceleration ($t = 0$) and finishes at the release time ($t = 124$ ms), when the cylinder starts re-accelerating. Arrows indicate the suspension velocity. Colour encodes the relative norm of the velocity $\sqrt{u_\theta^2 + u_r^2}/R\Omega_c$.

Download Rocha et al. Supplementary Movie 2(Video)
Video 7.8 MB