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Roughness-dependent tribology effects on discontinuous shear thickening
Edited by Heinrich M. Jaeger, The University of Chicago, Chicago, IL, and accepted by Editorial Board Member Peter J. Rossky April 1, 2018 (received for review January 22, 2018)

Significance
Shear thickening is a ubiquitous rheological phenomenon whereby dense suspensions of particles in a fluid exhibit a viscosity increase at high shear, which can turn into a viscosity divergence [discontinuous shear thickening (DST)]. Although macroscopically well characterized, the microscopic origin of DST is still debated, especially in connection to particle surface properties, e.g., roughness and friction. We elucidate here the mechanisms underpinning DST by carrying out nanotribological measurements of the interparticle contacts of model rough colloids. We demonstrate that rough particles exhibit DST over a broader range of shear rates and for volume fractions much lower than for smooth colloids, due to interlocking of surface asperities, showing that taking an engineering-tribology approach is a powerful way to tune DST.
Abstract
Surface roughness affects many properties of colloids, from depletion and capillary interactions to their dispersibility and use as emulsion stabilizers. It also impacts particle–particle frictional contacts, which have recently emerged as being responsible for the discontinuous shear thickening (DST) of dense suspensions. Tribological properties of these contacts have been rarely experimentally accessed, especially for nonspherical particles. Here, we systematically tackle the effect of nanoscale surface roughness by producing a library of all-silica, raspberry-like colloids and linking their rheology to their tribology. Rougher surfaces lead to a significant anticipation of DST onset, in terms of both shear rate and solid loading. Strikingly, they also eliminate continuous thickening. DST is here due to the interlocking of asperities, which we have identified as “stick–slip” frictional contacts by measuring the sliding of the same particles via lateral force microscopy (LFM). Direct measurements of particle–particle friction therefore highlight the value of an engineering-tribology approach to tuning the thickening of suspensions.
Shear thickening (ST) is an intriguing rheological phenomenon, by which the viscosity η of a concentrated particulate suspension increases upon increasing shear rate
Although well characterized at the macroscale, the microscopic mechanisms governing the origins of ST are still not fully understood (5). Hydrodynamic interactions play an essential role in the viscosity increase in CST (6⇓⇓⇓–10), but alone they cannot predict the viscosity divergence in DST (11⇓–13). In contrast, dilatancy (N1 > 0) is a well-known feature of dense, frictional granular materials, reflecting the formation of anisotropic force-chain networks under shear (14⇓–16). This analogy has generated a growing consensus between theory (17), simulations (12, 18⇓⇓⇓–22), and experiments (1, 13, 23⇓⇓–26), which have connected DST to the formation of stress-bearing structures of particles making solid–solid frictional contacts when hydrodynamic lubrication films break at high shear.
Despite this significant body of work, often the friction coefficients used in numerical simulations do not reflect realistic values and only very few studies have actually attempted to measure the frictional properties of particles experimentally, either macroscopically (22) or microscopically (23, 26), and these have been limited to smooth spheres (27). Shear-thickening systems in applications, such as cementitious slurries or the paradigmatic case of cornstarch suspensions, often comprise irregularly shaped particles. The geometry of contact is an essential component to describe frictional interactions, but, to date, only few studies have investigated the effect of particle topography, i.e., surface roughness, on ST. In general, higher roughness was shown to lead to the reduction of the onset rate and stress for DST and a sign change in N1, from negative to positive, but no connection was made to the microscopic tribological properties of the particles (11, 13).
In this work, by experimentally studying the nanotribology of model silica colloids with tunable roughness, we demonstrate the existence of a direct link between particle topography, nanoscale friction, and macroscopic DST. Engineering of the surface design of the particles allows us to control both the critical rate and the critical solid loading for DST, driven by an interlocking mechanism that is qualitatively different from the case of smooth particles.
We fabricate our model rough colloids by electrostatic adsorption of silica nanoparticles (“berries”) onto larger silica colloids (“cores”). We then grow a controlled smoothing layer via a sol-gel route, creating all-silica raspberry-like particles, as shown in Fig. 1A (28). Surface roughness can be tuned by independently choosing the size of the berries (12–39 nm) as well as by adjusting the thickness of the smoothing layer (10–15 nm) (Fig. 1 B–G). Surface roughness is then characterized by atomic force microscopy (AFM), and we extract a dimensionless roughness parameter
Fabrication and characterization of smooth (SM) and rough (RB) particles. (A) Schematics of the fabrication of raspberry-like silica particles. (B–G) SEM images of (B) SM, (C) RB_0.25, (D) RB_0.31, (E) RB_0.36, (F) RB_0.45, and (G) RB_0.53. (Scale bars, 500 nm.) The numbers represent the value of
We first quantify the role of surface roughness on the maximum packing fraction
Results of compressive- and shear-rheology experiments. (A) Schematics of the centrifugation experiments. H is the height of the sediment and L is the length of the capillary. (B) Images of particle suspensions (SM) after centrifugation. The initial volume fraction
In fact, smooth colloids (SM, Fig. 2D) start to display CST for
To account for these rheological observations, we turn to studying microscopic particle-to-particle contacts. These measurements are carried out by means of lateral force microscopy (LFM), where smooth and rough colloids are attached onto tipless cantilevers (Fig. S3) and scanned over planar substrates of varying roughness (roughness gradients), as shown in Fig. 3 A and B (see SI Materials and Methods for further details). The substrates are produced by a process analogous to the synthesis of the rough colloids, to provide representative, realistic countersurfaces (SI Materials and Methods and Fig. S2). The LFM results from sliding an RB_0.53 probe over a roughness gradient with 22-nm-high asperities are shown in Fig. 3C. (See Figs. S4–S7 for the friction results of all other particles.) Starting from the smooth end of the sample (Fig. 3C, rightmost curve, magenta), we observe a very narrow friction loop, i.e., a small difference in the lateral force signals between trace and retrace of the same scan on the substrate, indicative of a low friction coefficient. As soon as the area density of asperities increases, distinctive spikes arise in the friction-loop scans (Fig. 3C, cyan curve). These are typical of stick–slip frictional behavior. During scanning, when the probe meets an asperity, the lateral force increases steeply as the probe becomes locally stuck and then rapidly slides as the asperity is overcome. The frequency of the stick–slip events increases with increasing roughness (Fig. 3C, from right to left), which corresponds to higher dissipation during scanning and hence to an increase in the friction coefficient μ (Fig. 3D). We remark here that we measure “effective” friction coefficients, which already take into account the geometry of the contact, with interlocking asperities. The Amontons-type relation,
Friction measurements on model rough substrates. (A) Schematics of a smooth probe on a rough sample and SEM image of a smooth colloidal probe. (Scale bar, 500 nm.) (B) Schematics of a rough probe on a rough sample and SEM image of an RB_0.53 colloidal probe. (Scale bar, 500 nm.) (C, Top) RB_0.53 probe scanning at different locations on a 22-nm rough gradient substrate. (C, Bottom) Friction loops at 60 nN applied load for various
Interestingly, smooth and rough probes sliding on surfaces with increasing
The unique dependence of both μ and
Finally, this correlation allows us to engineer the macroscopic rheological response, i.e., the
Engineering the rheological response using a tribological approach. (A)
In conclusion, our results clearly confirm that there exists a strong link between the tribology of interparticle contacts and the rheology of DST suspensions. The frictional properties greatly depend on the contact geometry, and surface roughness has emerged as an essential design parameter for the thickening response. We have, for instance, shown that one can increase the solid loading and delay undesired shear thickening by introducing a small amount of particles displaying lower friction into the system, which could be of interest for slurry processing, for example. Conversely, increasing surface roughness enables a great reduction of the volume fraction, while retaining very strong thickening but having lower viscosities in the unthickened region of the flow curve, which could be of interest in fluid materials for vibration or impact absorption. As the importance of tribology in thickening fluids is increasingly becoming more widely accepted, we expect many exciting opportunities for nanoscale surface design.
Acknowledgments
We thank Jan Vermant for fruitful discussions. We thank Svetoslav Anachkov for providing the Mathematica code, Thomas Schweizer for assistance with shear-rheology measurements, Rebecca Huber for assistance with gradient-sample preparation, Christopher McLaren for help with high-speed video recording, and Andre Studart for SEM access. C.-P.H., M.Z., and L.I. acknowledge financial support from the Swiss National Science Foundation Grants PP00P2_144646/1 and PP00P2_172913/1 and the ETH Zurich Research Grant ETH-49-16-1.
Footnotes
- ↵1To whom correspondence should be addressed. Email: lucio.isa{at}mat.ethz.ch.
Author contributions: N.D.S. and L.I. designed research; C.-P.H., S.N.R., M.Z., and L.I. performed research; C.-P.H., S.N.R., M.Z., N.D.S., and L.I. analyzed data; and C.-P.H., S.N.R., M.Z., N.D.S., and L.I. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. H.M.J. is a guest editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1801066115/-/DCSupplemental.
- Copyright © 2018 the Author(s). Published by PNAS.
This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
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