Abstract
In this chapter, we study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relationship between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a pre-factor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of a phenomenological model originally developed to describe steady-state shear-thickening. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from start-up response to steady-state behavior. The theoretical framework we obtain points out a linkage between transient and steady-state properties of shear-thickening materials.
This chapter is based on [98].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Since in our 1D system, γ always changes monotonically, we only consider the absolute value of \(\dot {\gamma }\) and γ. In this thesis, the signs on \(\dot {\gamma }\) and γ are ignored.
- 2.
This is a simplification, as the viscosity should not only depend on the fraction of frictional contacts, but also on the anisotropy of the contact network characterized by γ. Our results support that this dependence is not essential to describe fronts.
- 3.
To describe propagating fronts in two or three dimensions, one may further assume that ϕ is constant in space since particle migration is slow, and the material is incompressible.
References
D.J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 2005)
E. Brown, H.M. Jaeger, Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Rep. Prog. Phys. 77(4), 046602 (2014)
E. Brown, H.M. Jaeger, The role of dilation and confining stresses in shear thickening of dense suspensions. J. Rheol. 56(4), 875 (2012)
I.R. Peters, S. Majumdar, H.M. Jaeger, Direct observation of dynamic shear jamming in dense suspensions. Nature 532(7598), 214–217 (2016)
F. Boyer, E. Guazzelli, O. Pouliquen, Unifying suspension and granular rheology. Phys. Rev. Lett. 107(18), 188301 (2011)
C. Ness, J. Sun, Shear thickening regimes of dense non-Brownian suspensions. Soft Matter 12(3), 914–924 (2016)
M. Wyart, M.E. Cates, Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys. Rev. Lett. 112(9), 098302 (2014)
B.M. Guy, M. Hermes, W.C. Poon, Towards a unified description of the rheology of hard-particle suspensions. Phys. Rev. Lett. 115(8), 088304 (2015)
B. Liu, M. Shelley, J. Zhang, Focused force transmission through an aqueous suspension of granules. Phys. Rev. Lett. 105(18), 188301 (2010)
S.R. Waitukaitis, H.M. Jaeger, Impact-activated solidification of dense suspensions via dynamic jamming fronts. Nature 487(7406), 205–209 (2012)
M. Roche, E. Myftiu, M.C. Johnston, P. Kim, H.A. Stone, Dynamic fracture of nonglassy suspensions. Phys. Rev. Lett. 110(14), 148304 (2013)
M.I. Smith, R. Besseling, M.E. Cates, V. Bertola, Dilatancy in the flow and fracture of stretched colloidal suspensions. Nat. Commun. 1, 114 (2010)
I.R. Peters, H.M. Jaeger, Quasi-2d dynamic jamming in cornstarch suspensions: visualization and force measurements. Soft Matter 10(34), 6564–6570 (2014)
E. Han, I.R. Peters, H.M. Jaeger, High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming. Nat. Commun. 7, 12243 (2016)
E. Han, M. Wyart, I.R. Peters, H.M. Jaeger, Shear fronts in shear-thickening suspensions. Phys. Rev. Fluids 3(7), 073301 (2018)
S. Majumdar, I.R. Peters, E. Han, H.M. Jaeger, Dynamic shear jamming under extension in dense granular suspensions. Phys. Rev. E 95, 012603 (2017)
L.R. Gomez, A.M. Turner, M. van Hecke, V. Vitelli, Shocks near jamming. Phys. Rev. Lett. 108(5), 058001 (2012)
L.R. Gomez, A.M. Turner, V. Vitelli, Uniform shock waves in disordered granular matter. Phys. Rev. E 86(4), 041302 (2012)
S. Ulrich, N. Upadhyaya, B. van Opheusden, V. Vitelli, Shear shocks in fragile networks. Proc. Natl. Acad. Sci. 110(52), 20929–20934 (2013)
S.R. Waitukaitis, L.K. Roth, V. Vitelli, H.M. Jaeger, Dynamic jamming fronts. Europhys. Lett. 102(4), 44001 (2013)
I. Buttinoni, J. Cha, W.H. Lin, S. Job, C. Daraio, L. Isa, Direct observation of impact propagation and absorption in dense colloidal monolayers. Proc. Natl. Acad. Sci. 114(46), 12150–12155 (2017)
M.E. Cates, M. Wyart, Granulation and bistability in non-Brownian suspensions. Rheol. Acta 53(10-11), 755–764 (2014)
M. Hermes, B.M. Guy, W.C.K. Poon, G. Poy, M.E. Cates, M. Wyart, Unsteady flow and particle migration in dense, non-Brownian suspensions. J. Rheol. 60(5), 905–916 (2016)
M. Pailha, M. Nicolas, O. Pouliquen, Initiation of underwater granular avalanches: influence of the initial volume fraction. Phys. Fluids 20(11), 111701 (2008)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Han, E. (2020). Modeling Shear Fronts in One Dimension. In: Transient Dynamics of Concentrated Particulate Suspensions Under Shear. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-38348-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-38348-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38347-3
Online ISBN: 978-3-030-38348-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)