Shear flow of non-Brownian rod-sphere mixtures near jamming

We use the discrete element method, taking particle contact and hydrodynamic lubrication into account, to unveil the shear rheology of suspensions of frictionless non-Brownian rods in the dense packing fraction regime. We find that, analogously to the random close packing volume fraction, the shear-driven jamming point of this system varies in a nonmonotonic fashion as a function of the rod aspect ratio. The latter strongly influences how the addition of rodlike particles affects the rheological response of a suspension of frictionless non-Brownian spheres to an external shear flow. At fixed values of the total (rods plus spheres) packing fraction, the viscosity of the suspension is reduced by the addition of “short”($\le 2$) rods but is instead increased by the addition of “long”($\ge 2$) rods. A mechanistic interpretation is provided in terms of packing and excluded-volume arguments.

Figure 1

Randomly packed rod-sphere mixture. The spheres have diameter $D,$ while the rods (spherocylinders formed by glued spheres) have aspect ratio $L/D=4.$ Packing fraction is $\varphi =0.6.$

Figure 2

(a) Dimensionless viscosity $\eta /{\eta }_{\text{f}}$ of a suspension of pure (no spheres in the mixture) spherocylinders, fixed aspect ratio $L/D=4$ and packing fraction $\varphi =0.412$ as a function of the shear strain $\dot{\gamma }t$ for several values of the shear rate $\dot{\gamma }$. (b) After a start up regime in which the viscosity increases with strain, a plateau is reached. At this plateau, orientational order (negligible for short ARs) has been developed as proved by a plot of the nematic scalar order parameter $S$ as a function of $\dot{\gamma }t$, (c). The shear rate is measured in simulation units.

Figure 3

Shear viscosity $\eta /{\eta }_f$ of a rod-sphere mixture as a function of the total (rods plus spheres) particle concentration $\varphi$ for several values of the rod aspect ratio $L/D$ at fixed concentration of spheres x=0 (a), and for several values of $x$ at fixed $L/D=0.5$ (red points) and $L/D=4$ (blue points) (b). All data can be fitted to the KD relation [Eq. (1)]. The ${\varphi }_{\text{J}}$ and $\beta$ coefficients of the curves in (a) are plotted in (c) and (d), respectively. The ${\varphi }_{\text{J}}$ and $\beta$ coefficients of the curves in (b), i.e., at fixed $L/D=0.5$ (red) and $L/D=4$ (blue), are plotted in (e) and (f), respectively.

Figure 4

Mean contact numbers ($z$) in a rod-sphere mixture at the shear-driven jamming point ${\varphi }_{\text{J}},$ versus the concentration $x$ of spheres in the mixture. The number of rods in contact with each rod is $z_{\text{RR}},$ the number of rods in contact with each sphere is $z_{\text{RS}},$ the number of spheres in contact with each rod is $z_{\text{SR}}$, and the number of spheres in contact with each sphere is $z_{\text{SS}}.$ Left: the rods have aspect ratio $L/D=4$. Right: the rods have aspect ratio $L/D=0.36.$