Rheological State Diagrams for Rough Colloids in Shear Flow

To assess the role of particle roughness in the rheological phenomena of concentrated colloidal suspensions, we develop model colloids with varying surface roughness length scales up to 10% of the particle radius. Increasing surface roughness shifts the onset of both shear thickening and dilatancy towards lower volume fractions and critical stresses. Experimental data are supported by computer simulations of spherical colloids with adjustable friction coefficients, demonstrating that a reduction in the onset stress of thickening and a sign change in the first normal stresses occur when friction competes with lubrication. In the quasi-Newtonian flow regime, roughness increases the effective packing fraction of colloids. As the shear stress increases and suspensions of rough colloids approach jamming, the first normal stresses switch signs and the critical force required to generate contacts is drastically reduced. This is likely a signature of the lubrication films giving way to roughness-induced tangential interactions that bring about load-bearing contacts in the compression axis of flow.

Figure 1

Effect of particle roughness on suspension rheology. (a) Atomic force microscopy images of (left to right): smooth, SL, MR, and VR colloids. Scale $\text{bars}=1\mu \mathrm{m}$. (b), (c) Flow curves of suspensions consisting of smooth, SL, MR, and VR colloids (top to bottom). Colors represent volume fractions ($\varphi =0.30$, red; $\varphi =0.35$, orange; $\varphi =0.40$, green; $\varphi =0.45$, blue; $\varphi =0.48$, pink; $\varphi =0.50$, purple; $\varphi =0.535$, brown; $\varphi =0.55$, gray). Solid lines are power law fits to the data. The data for VR colloids at $\varphi =0.45$ represent a limited stress range; a dashed line is extrapolated for visibility. Gray regions in (b) indicate instrument sensitivity limits on the left and inertial/fracture effects on the right, and gray regions in (c) centered about $N_1=0\mathrm{Pa}$ indicate instrument limits. Error bars, where available, represent standard deviations from three independent upward stress sweeps.

Figure 2

Simulations and experiments of frictionless (smooth) and frictional (rough) particles. (a) Normalized steady state viscosity and (b) $N_1$ values of colloidal suspensions. Both plots are generated for $\varphi =0.535$ (except for VR colloids plotted at $\varphi =0.50$). Data from experiments are plotted as open circles for four types of roughness (smooth, red; SL, orange; MR, green; VR, blue) and data from DPD simulations are plotted as solid lines for DPD particles with varying friction coefficients ($\mu =0$, red; $\mu =0.1$, orange; $\mu =0.3$, green; $\mu =1$, blue). (Inset in a) The critical onset stress as a function of roughness in experiments and as a function of $\mu$ in DPD simulations. Error bars represent standard deviations from three independent measurements.

Figure 3

Suspension properties as a function of roughness. (a) The relative quasi-Newtonian viscosity plotted against $\varphi$ for smooth (red open circles), SL (orange open triangles), MR (blue open squares), and VR colloids (purple open diamonds). Solid lines are fits with the Eilers model. Gray solid symbols are literature data for sterically stabilized PMMA [21, 42, 43] and silica colloids [26]. (b) Maximum packing fraction plotted against rms roughness (open purple squares). Gray solid symbols are data of smooth colloids in literature [21, 26, 42, 43]. Dashed lines guide the eye. (c) Shear thickening power for different $\varphi$. (d) Onset force $F^{*}$ to push particles into contact. Dashed line indicates constant $F^{*}$ for smooth colloids. In (c) and (d) the symbols follow the same legend as in (a). Solid symbols indicate flow curves for dilatant samples. Error bars represent standard deviation from three independent measurements where available.

Figure 4

Rheological state diagrams for rough colloids in sheared suspensions. (a)–(d) Transitions from quasi-Newtonian behavior to shear thickening and dilatancy are shown as a function of roughness. Gray crosses represent quasi-Newtonian flows ($\beta <0.10$), green open circles represent weak thickening ($0.10\le \beta \le 0.70$), blue open circles represent strong thickening ($0.70\le \beta \le 1.0$), and red solid circles are dilatant flows ($N_1>0$).