Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-29T22:53:25.129Z Has data issue: false hasContentIssue false
  • English
  • Français

Emergence of a hexagonal pattern in shear-thickening suspensions under orbital oscillations

Published online by Cambridge University Press:  12 April 2024

Li-Xin Shi ,
Meng-Fei Hu  and
Song-Chuan Zhao Open the ORCID record for Song-Chuan Zhao [Opens in a new window]
Li-Xin Shi
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
Meng-Fei Hu
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
Song-Chuan Zhao*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
*
†Email address for correspondence: songchuan.zhao@outlook.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A dense particle suspension under shear may lose its uniform state to large local density and stress fluctuations, which challenge the mean-field description of the system. Here, we explore the novel dynamics of a non-Brownian suspension under orbital oscillations, where localized density waves along the flow direction appear beyond an excitation frequency threshold and self-organize into a hexagonal pattern across the system. The spontaneous occurrence of the inhomogeneity pattern arises from a coupling between particle advection and the shear-thickening nature of the suspension. Through linear stability analysis, we show that they overcome the stabilizing effects of particle pressure at sufficient particle volume fraction and oscillation frequency. In addition, the long-standing density waves degenerate into random fluctuations when replacing the free surface with rigid confinement. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions are crucial for developing local disturbance.

JFM classification

Complex Fluids: Suspensions Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 984 , 10 April 2024 , A69
Check for updates
Copyright
© The Author(s), 2024. 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

Anderson, K., Sundaresan, S. & Jackson, R. 1995 Instabilities and the formation of bubbles in fluidized beds. J. Fluid Mech. 303, 327–366.CrossRefGoogle Scholar
Batchelor, G. 1988 A new theory of the instability of a uniform fluidized bed. J. Fluid Mech. 193, 75–110.CrossRefGoogle Scholar
Berthier, L., Biroli, G., Bouchaud, J.-P., Cipelletti, L. & van Saarloos, W. 2011 Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, vol. 150. Oxford University Press.CrossRefGoogle Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.CrossRefGoogle ScholarPubMed
Brown, E. & Jaeger, H. 2012 The role of dilation and confining stresses in shear thickening of dense suspensions. J. Rheol. 56 (4), 875–923.CrossRefGoogle Scholar
Brown, E. & Jaeger, H. 2014 Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Rep. Prog. Phys. 77 (4), 046602.CrossRefGoogle ScholarPubMed
Buscall, R., Goodwin, J., Ottewill, R. & Tadros, T. 1982 The settling of particles through Newtonian and non-Newtonian media. J. Colloid Interface Sci. 85 (1), 78–86.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
Cheng, X., McCoy, J., Israelachvili, J. & Cohen, I. 2011 Imaging the microscopic structure of shear thinning and thickening colloidal suspensions. Science 333 (6047), 1276–1279.CrossRefGoogle ScholarPubMed
Clavaud, C., Bérut, A., Metzger, B. & Forterre, Y. 2017 Revealing the frictional transition in shear-thickening suspensions. Proc. Natl Acad. Sci. USA 114 (20), 5147–5152.CrossRefGoogle ScholarPubMed
Darbois Texier, B., Lhuissier, H., Forterre, Y. & Metzger, B. 2020 Surface-wave instability without inertia in shear-thickening suspensions. Commun. Phys. 3 (1), 1–7.CrossRefGoogle Scholar
Duru, P. & Guazzelli, É. 2002 Experimental investigation on the secondary instability of liquid-fluidized beds and the formation of bubbles. J. Fluid Mech. 470, 359–382.CrossRefGoogle Scholar
Duru, P., Nicolas, M., Hinch, J. & Guazzelli, E. 2002 Constitutive laws in liquid-fluidized beds. J. Fluid Mech. 452, 371–404.CrossRefGoogle Scholar
Fall, A., Bertrand, F., Hautemayou, D., Mezière, C., Moucheront, P., Lemaître, A. & Ovarlez, G. 2015 Macroscopic discontinuous shear thickening versus local shear jamming in cornstarch. Phys. Rev. Lett. 114, 098301.CrossRefGoogle ScholarPubMed
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 (1), 018301.CrossRefGoogle ScholarPubMed
Fernandez, N., Mani, R., Rinaldi, D., Kadau, D., Mosquet, M., Lombois-Burger, H., Cayer-Barrioz, J., Herrmann, H., Spencer, N. & Isa, L. 2013 Microscopic mechanism for shear thickening of non-Brownian suspensions. Phys. Rev. Lett. 111 (10), 108301.CrossRefGoogle ScholarPubMed
Gallier, S., Lemaire, E., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles. J. Fluid Mech. 757, 514–549.CrossRefGoogle Scholar
Gauthier, A., Ovarlez, G. & Colin, A. 2023 Shear thickening in presence of adhesive contact forces: the singularity of cornstarch. J. Colloid Interface Sci. 650, 1105–1112.CrossRefGoogle ScholarPubMed
Gauthier, A., Pruvost, M., Gamache, O. & Colin, A. 2021 A new pressure sensor array for normal stress measurement in complex fluids. J. Rheol. 65 (4), 583–594.CrossRefGoogle Scholar
Glasser, B., Sundaresan, S. & Kevrekidis, I. 1998 From bubbles to clusters in fluidized beds. Phys. Rev. Lett. 81 (9), 1849–1852.CrossRefGoogle Scholar
Guazzelli, É. & Morris, J. 2011 A Physical Introduction to Suspension Dynamics, vol. 45. Cambridge University Press.CrossRefGoogle Scholar
Guazzelli, É. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.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 (5), 905–916.CrossRefGoogle Scholar
Hu, Y., Boltenhagen, P. & Pine, D. 1998 Shear thickening in low-concentration solutions of wormlike micelles. I. Direct visualization of transient behavior and phase transitions. J. Rheol. 42 (5), 1185–1208.CrossRefGoogle Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Johri, J. & Glasser, B. 2002 Connections between density waves in fluidized beds and compressible flows. AIChE J. 48 (8), 1645–1664.CrossRefGoogle Scholar
Kubelka, P. & Munk, F. 1931 An article on optics of paint layers. Z. Tech. Phys 12 (593-601), 259–274.Google Scholar
Larson, R. 1999 The Structure and Rheology of Complex Fluids, 1st edn. Oxford University Press.Google Scholar
Lootens, D., Van Damme, H. & Hébraud, P. 2003 Giant stress fluctuations at the jamming transition. Phys. Rev. Lett. 90 (17), 178301.CrossRefGoogle ScholarPubMed
Mari, R., Seto, R., Morris, J. & Denn, M. 2015 Nonmonotonic flow curves of shear thickening suspensions. Phys. Rev. E 91 (5), 052302.CrossRefGoogle ScholarPubMed
Morris, J. 2020 Shear thickening of concentrated suspensions: recent developments and relation to other phenomena. Annu. Rev. Fluid Mech. 52, 121–144.CrossRefGoogle Scholar
van der Naald, M., Singh, A., Eid, T., Tang, K., de Pablo, J. & Jaeger, H. 2024 Minimally rigid clusters in dense suspension flow. Nat. Phys. https://doi.org/10.1038/s41567-023-02354-3.CrossRefGoogle Scholar
Nabizadeh, M., Singh, A. & Jamali, S. 2022 Structure and dynamics of force clusters and networks in shear thickening suspensions. Phys. Rev. Lett. 129 (6), 068001.CrossRefGoogle ScholarPubMed
Olmsted, P. 2008 Perspectives on shear banding in complex fluids. Rheol. Acta 47 (3), 283–300.CrossRefGoogle Scholar
Ovarlez, G., Vu Nguyen Le, A., Smit, W., Fall, A., Mari, R., Chatté, G. & Colin, A. 2020 Density waves in shear-thickening suspensions. Sci. Adv. 6 (16), eaay5589.CrossRefGoogle ScholarPubMed
Oyarte Gálvez, L., de Beer, S., 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.CrossRefGoogle ScholarPubMed
Pan, Z., de Cagny, H., Weber, B. & Bonn, D. 2015 S-shaped flow curves of shear thickening suspensions: direct observation of frictional rheology. Phys. Rev. E 92 (3), 032202.CrossRefGoogle ScholarPubMed
Peters, I., Majumdar, S. & Jaeger, H. 2016 Direct observation of dynamic shear jamming in dense suspensions. Nature 532 (7598), 214–217.CrossRefGoogle ScholarPubMed
Rathee, V., Blair, D. & Urbach, J. 2017 Localized stress fluctuations drive shear thickening in dense suspensions. Proc. Natl Acad. Sci. USA 114 (33), 8740–8745.CrossRefGoogle ScholarPubMed
Rathee, V., Blair, D. & Urbach, J. 2020 Localized transient jamming in discontinuous shear thickening. J. Rheol. 64 (2), 299–308.CrossRefGoogle Scholar
Rathee, V., Blair, D.L. & Urbach, J. 2021 Dynamics and memory of boundary stresses in discontinuous shear thickening suspensions during oscillatory shear. Soft Matt. 17, 1337–1345.CrossRefGoogle ScholarPubMed
Reclari, M., Dreyer, M., Tissot, S., Obreschkow, D., Wurm, F. & Farhat, M. 2014 Surface wave dynamics in orbital shaken cylindrical containers. Phys. Fluids 26 (5), 052104.CrossRefGoogle Scholar
Richardson, J. 1954 Sedimentation and fluidisation: part I. Trans. Inst. Chem. Engrs 32, 35–53.Google Scholar
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
Seto, R., Mari, R., Morris, J. & Denn, M. 2013 Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111 (21), 218301.CrossRefGoogle ScholarPubMed
Singh, A., Mari, R., Denn, M. & Morris, J. 2018 A constitutive model for simple shear of dense frictional suspensions. J. Rheol. 62 (2), 457–468.CrossRefGoogle Scholar
Wagner, N. & Brady, J. 2009 Shear thickening in colloidal dispersions. Phys. Today 62 (10), 27–32.CrossRefGoogle Scholar
Wyart, M. & Cates, M. 2014 Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys. Rev. Lett. 112, 098302.CrossRefGoogle ScholarPubMed
Yih, C.-S. 1968 Instability of unsteady flows or configurations part 1. Instability of a horizontal liquid layer on an oscillating plane. J. Fluid Mech. 31 (4), 737–751.CrossRefGoogle Scholar
Zhao, S.-C., de Jong, R. & van der Meer, D. 2015 Raindrop impact on sand: a dynamic explanation of crater morphologies. Soft Matt. 11 (33), 6562–6568.CrossRefGoogle Scholar
Zhao, S.-C. & Pöschel, T. 2021 Spontaneous formation of density waves in granular matter under swirling excitation. Phys. Fluids 33 (8), 081701.CrossRefGoogle Scholar
Supplementary material: File

Shi et al. supplementary movie 1

Experimental video illustrates the movement of density waves (Φ=0.42, h = 5 mm, f = 7.67 Hz). The grayscale indicates the local density of particles; the darker, the higher the density. See Appendix A for technical details.
Download Shi et al. supplementary movie 1(File)
File 404 KB
Supplementary material: File

Shi et al. supplementary movie 2

the growth and disappearance of uneven density. Experimental conditions are Φ = 0.405, h = 6.6 mm, f = 3.67 Hz. The suspension was first subjected to the swirling excitation with a co-moving top plate at the same f (not included in the video). Note that under the comoving confinement, the flow field of the uniform state of a suspension thickness h is equivalent to that of a thickness h/2 with the free surface overlayed with its mirror image with respect to the surface. The onset frequency ωc increases with h. The experimental parameters here are selected as such that ω = 2πf is larger than ωc(h/2) (with the confinement) but is smaller than ωc(h) (without the confinement).
Download Shi et al. supplementary movie 2(File)
File 1.8 MB
Supplementary material: File

Shi et al. supplementary movie 3

suspension of silica beads under swirling excitation. The two experiments depicted in the video differ only in the density of the electrolyte. In the absence of electrolyte (using deionized solution), persistent density waves are observed occupying the center of the system. Conversely, when electrolyte (0.1 mol/L NaCl) is added, the density gradient induced by the motion of the side walls becomes dominant. The manuscript focuses on the state of density waves.
Download Shi et al. supplementary movie 3(File)
File 1.2 MB