The role of friction in non-colloidal suspensions is examined with a model which splits the viscosity into a frictionless component (τ*) plus a frictional component which depends on the ratio of the particle pressure (P) to the shear stress (τ). The model needs the input by computation of τ* and P and a suitable choice of particle friction coefficient (μ). It can be extended to elongational flows and cases where sphere roughness is important; volume fractions up to 0.5 are considered. It is shown that friction acts in a feedback or “bootstrap” manner to increase the suspension viscosity. The analysis is also useful for deducing the friction coefficient in suspensions from experimental data. It was applied to several sets of experimental data and reasonable correlations of the viscosities were demonstrated. An example of the correlation for spheres in a silicone oil is shown for volume fractions 0.1–0.5.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bertevas E, Fan XJ, Tanner RI (2010) Simulation of the rheological properties of suspensions of oblate spheroidal particles in a Newtonian fluid. Rheol Acta 49:53–73
Bowden FP, Tabor D (1956) Friction and lubrication. Methuen, London
Boyer F, Guazzelli É, Pouliquen O (2011) Unifying suspension and granular rheology. Phys. Rev. Letters 107:art 188301
Chatté G, Comtet J, Nigues A, Bocquet L, Siria A, Ducouret G, Lequeux F, Lenoir N, Ovarlez G, Colin A (2018) Shear-thinning in non-Brownian suspensions. Soft Matter 14:879–893
Cheal O, Ness C (2018) Rheology of dense granular suspensions under extensional flow. J Rheol 62:501–512
Dai SC, Tanner RI (2017) Elongational flows of some non-colloidal suspensions. Rheol Acta 56:63–71
Dai SC, Bertevas E, Qi F, Tanner RI (2013) Viscometric functions for non-colloidal sphere suspensions with Newtonian matrices. J Rheol 57:493–510
Dai SC, Qi F, Tanner RI (2014) Viscometric functions of concentrated non-colloidal suspensions of spheres in a viscoelastic matrix. J Rheol 58:183–198
Gallier S, Lemaire E, Peters F, Lobry L (2014) Rheology of sheared suspensions of rough frictional particles. J Fluid Mech 757:514–549
Guy BM, Hermes M, Poon WCK (2015) Towards a unified description of the rheology of hard-particle suspensions. Phys. Rev. Lett 115:art 088304
Huang N, Ovarlez G, Bertrand F, Rodts S, Coussot P, Bonn D (2005) Flow of wet granular materials. Phys Rev Lett 94:028301
Keentok M, Xue SC (1999) Edge fracture in cone-plate and parallel plate flows. Rheol Acta 38:321–348
Kroupa M, Soos M, Kosek J (2017) Slip on a particle surface as the possible origin of shear thinning in non-Brownian suspensions. Phys Chem Chem Phys 19:5979–5984
Mahmud A, Dai SC, Tanner RI (2018) A quest for a model of non-colloidal suspensions with Newtonian matrices. Rheol Acta 57:29–41
Mari R, Seto R, Morris JF, Denn MM (2014) Shear thickening, frictional and frictionless rheologies in non-Brownian suspensions. J Rheol 58:1693–1724
Moon JY, Dai SC, Chang L, Lee JS, Tanner RI (2015) The effect of sphere roughness on the rheology of concentrated suspensions. J Non- Newt Fluid Mech 223:233–239
Moore DF (1975) Principles and applications of tribology. Pergamon Press, Oxford
Ovarlez G, Mahaut F, Deboeuf S, Lenoir N, Hormozi S, Chateau X (2015) Flows of suspensions of particles in yield stress fluids. J Rheol 59:1449–1486
Qi F, Tanner RI (2011) Relative viscosity of bimodal suspensions. Korea-Australia Rheology J 23:105–111
Seto R, Giusteri GG, Martinello A (2017) Microstructure and thickening of dense suspensions under extensional and shear flows. J Fluid Mech Rapids 825:art. R3
Sierou A, Brady JF (2002) Rheology and microstructure in concentrated noncolloidal suspensions. J Rheol 46:1031–1056
Tanner RI, Dai SC (2016a) Rheology of non-colloidal suspensions with corn syrup matrices. Rheol Acta 55:739–747
Tanner RI, Dai SC (2016b) Particle roughness and rheology in noncolloidal suspensions. J Rheol 60:809–818
Thomas DG (1965) Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J Colloid Sci 20:267–277
Vázquez-Quesada A, Mahmud A, Dai SC, Ellero M, Tanner RI (2017) Investigating the causes of shear-thinning in non-colloidal suspensions. J. Non- Newt. Fluid Mech. 248:1–7
Zarraga IE, Hill DA, Leighton DT (2000) The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J Rheol 44:185–220
Zarraga IE, Hill DA, Leighton DT (2001) Normal stress and free surface deformation in concentrated suspensions of noncolloidal spheres in a viscoelastic fluid. J Rheol 45:1065–1084
We thank the University of Sydney for providing scholarship support for Arif Mahmud. JiYoung Moon acknowledges that his research was supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A03003276). C.N. acknowledges financial support from the Maudslay-Butler Research Fellowship at Pembroke College, Cambridge.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Tanner, R.I., Ness, C., Mahmud, A. et al. A bootstrap mechanism for non-colloidal suspension viscosity. Rheol Acta 57, 635–643 (2018). https://doi.org/10.1007/s00397-018-1103-y
- Shear viscosity
- Elongational flow