Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions

Abstract

There was an error in data reduction, resulting in incorrect values for the normal stress differences N 1 and N 2 shown in Figs. 7-10, and the corrected figures are shown here. In particular, the algebraic sign of N 1 is changed, as are the relative magnitudes of N 1 and N 2 . The negative values of N 1 for these non-shear-thickening suspensions are larger in magnitude than those reported by other workers, but both N 1 and N 2 are in general agreement with the accelerated Stokesian Dynamics calculations of Sierou and Brady [1].FIG. 7. Normal stress differences N 1 and N 2 of monodisperse suspensions at volume fractions of 0.4 and 0.5 for both 10 and 52.6 µm particles as functions of (a) shear rate and (b) shear stress (Insets are the same data on a semilog scale). SYNOPSISWe have measured the viscometric functions of mono-and bimodal non-colloidal suspensions of PMMA spheres in a density-matched aqueous Newtonian suspending fluid using parallelplate and cone-and-plate rheometry for particle volume fractions in the range 0.20 to 0.50.Cone-and-plate normal stress measurements employed the method of Marsh and Pearson, in which there is a finite gap between the cone tip and the plate. The monodisperse suspensionsshowed an unexpected particle size dependence of the viscometric functions, with the viscosity increasing with decreasing particle size. Normal stresses were very small in magnitude and difficult to measure at volume fractions below 0.30. At higher concentrations, N 2 was negative and much larger in magnitude than N 1 , for which the algebraic sign was positive over most of the shear rate range for the monodisperse suspensions but indeterminate and possibly negative for the bimodal suspensions. The normal stresses were insensitive to bidispersity when plotted as functions of the shear stress at each volume fraction.

Effect of confinement in wall-bounded non-colloidal suspensions

“…The question of which stress is measured in experiments seems still open and should deserve attention in future works. As a final remark, it is interesting to note that results by Gamonpilas et al (2016) show a difference in the sign of N 1 depending whether the suspension is monodisperse (positive N 1 ) or bidisperse (negative N 1 ). Monodispersity is well known to promote ordering -as seen in present simulations -which is consistent with our conclusion that N 1 is positive because of wall-induced layering.…”

“…An important result is that this ratio is negative for dense suspensions, meaning that the overall suspension N 1 becomes positive due to confinement. It is therefore possible that the combined action of walls and friction is liable to explain some experimental results showing almost zero or positive values of N 1 (Couturier et al 2011;Dbouk et al 2013;Gamonpilas et al 2016). This point will be reconsidered hereinafter.…”

“…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.…”

“…Figure 20 compiles experimental results on normal stress differences (normalized by shear stress τ = η r ηγ) compared to our frictional (µ d =0.5) simulations in a bounded (κ=20) and unbounded suspension. The experiments are taken from six sources from the literature (Zarraga et al 2000;Singh & Nott 2000;Dbouk et al 2013;Dai et al 2013;Couturier et al 2011;Gamonpilas et al 2016) using different techniques. These seem to be the major experiments measuring simultaneously N 1 and N 2 (other experiments are available but for N 2 only, e.g.…”

Rheology of dense suspensions of non colloidal particles

“…Some experiments using more conventional rheometry find that N 1 is quite small and negative [10][11][12][13], while others report positive values [14]. Some recent studies point to the effect of polydispersity [15] and of confinement [16] which may explain these discrepancies.…”