Rheological Signature of Frictional Interactions in Shear Thickening Suspensions

Abstract

Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fraction elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find N1 < 0, consistent with hydrodynamic models, however at higher volume fractions and shear stresses these models break down and we instead observe dilation (N1 > 0), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity, instead this change in the sign of N1 occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model which combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fraction and shear stress. [3] suggesting that contact friction plays a dominant role in colloidal shear thickening, however this assertion is controversial because of contrary evidence. While friction-based models and simulations capture the viscosity increase observed in experiments, other experimental signatures, particularly the stress anisotropy, are at odds with expectations for frictional interactions [4].Shear thickening, where a suspension's viscosity η = σ/γ increases with increasing shear stress σ (or shear rateγ), is important in a wide array of industrial processes and applications, either something to be avoided or a desired, engineered property [5][6][7]. Shear thickening is observed in both granular suspensions, where the particle diameter d is generally d 10 µm, and colloidal suspensions, where d 10 µm. In granular suspensions, the evidence that friction drives shear thickening is well established [8][9][10][11][12][13][14][15][16] but in colloidal suspensions shear thickening is instead commonly attributed to diverging hydrodynamic lubrication forces, which lock particles together in correlated 'hydroclusters' [17][18][19][20][21].A key difference between friction and lubrication forces lies in the stress anisotropy generated by these two types of interactions. This difference is captured by the first normal stress difference N 1 ≡ σ xx − σ zz , where σ ij is the stress tensor for a shear flow in the x direction with a gradient along z. Simulations based on hydrodynamic interactions show that shear-induced distortions of the suspension microstructure and short ranged lubrication forces drive N 1 < 0 [7,18,19,22]. Including repulsive interactions or elastic particle deformations to these hydrodynamic models does not change the sign of N 1 [23][24][25], and N 1 is predicte...

Negative pressure in shear thickening band of a dilatant fluid

“…Detailed description of the model is given in Sec.IIIA. The normal stress difference N 1 shown in Fig.2(b) are negative for small shear rate, but upon DST they jump to large positive values in agreement with previous results [25]. Figure 3 shows the typical time developments of the off-center force f rod on the center rod and the normal pressure p n at the outer cylinder during the shear thickening oscillation.…”

Revealing the frictional transition in shear-thickening suspensions

“…4B, Bottom). These measurements corroborate previous rheological characterizations using Brownian silica microspheres (17,40,41) and confirm the link between the existence of a repulsive force, friction, and shear-thickening rheology.…”

“…As expected in such a framework, only the contact contribution to the viscosity increases with increasing shear rate, confirming the key role of contacts in shear-thickening suspensions. Another study reported that in shear-thickening suspensions, the first normal stress difference changes sign at the transition (17). This behavior was interpreted as indicating the formation of frictional contacts between particles, although this point is still a matter of debate (10,18).…”

Effect of confinement in wall-bounded non-colloidal suspensions

“…Other simulations by Mari et al (2014) show that prior to shear thickening, the average value of N 1 is nearly zero but is dominated by large fluctuations. In contrast, experiments report either negative N 1 (Zarraga et al 2000;Singh & Nott 2003;Dai et al 2013), or almost zero (Couturier et al 2011), or positive N 1 (Dbouk et al 2013;Royer et al 2016;Lootens et al 2005), or, at last, either positive or negative values depending on the size and polydispersity of particles (Gamonpilas et al 2016). Interestingly, recent simulations by Yeo & Maxey (2010b) in wall-bounded suspensions have shown that |N 1 | was smaller than in unbounded suspensions.…”