Evidence for Chaotic Behavior during the Yielding of a Soft Particle Glass

Materials comprised of deformable particles such as microgels and concentrated emulsions and foams display complex rheological behavior that includes a yielding transition from an elastic solid to viscous fluid. Most studies of this class of soft matter involve shear flows, and only a handful report both shear and normal stresses. We present measurements of the shear stress and two normal stress differences for a microgel subjected to constant shear rate flows. The shear stress evolves through the yield point in a manner indicative of simple yield stress fluid behavior. Prior to yielding, the normal stress differences are immeasurable; beyond the yield point, they evolve in a reproducibly chaotic manner.

Figure 1

Flow curve for 1% Carbopol microgel measured in cone-plate flow showing shear stress $\sigma$ ($\dot{\gamma }$ increasing $\otimes$, decreasing $○$) versus shear rate $\dot{\gamma }$. The solid curve is a fit of (2) with ${\tau }_y=112\mathrm{Pa}$, $K=123\mathrm{Pa}{\mathrm{s}}^m$, and $m=0.32$. The inset shows dynamic moduli $G^{\prime }(○)$ and $G^{\prime }(\square )$ versus frequency $\omega$.

Figure 2

Shear and normal stresses versus strain $\gamma ({\gamma }_R)$ for 1% Carbopol microgel for constant shear rate $\dot{\gamma }={\dot{\gamma }}_R=0.1{\mathrm{s}}^{-1}$. (a) $\sigma$ ($○$) and $N_1$ ($\square$) from cone-plate flow for 12 repeat experiments (different color symbols); (b) $2M/\pi R^3$ ($○$) and $2F/\pi R^2$ ($\square$) from parallel-plate flow for ten repeat experiments (different color symbols); (c) average $\sigma$ ($○$) and $N_1$ ($\square$) from (a) and computed $\sigma$ (red curve) and $N_1-N_2$ (blue curve) from averages of the data in (b). Symbols with error bars represent uncertainty of measured quantities in (a) and (b), and error bars in (c) represent standard deviations from repeat experiments or estimated errors in computed quantities.

Figure 3

Shear stress $\sigma$ ($○$) and $\sqrt{{\mathrm{II}}_{{\tau }^{\prime }}}$ (curves) versus strain $\gamma$ for shear rates $\dot{\gamma }[{\mathrm{s}}^{-1}]=0.01$ (black), 0.10 (blue), and 1.0 (red). The dashed line is linear elastic solid prediction (1) with $G=780$ Pa; the arrow indicates the yield stress ${\tau }_y=112$ Pa obtained from Fig. 1.

Figure 4

Steady state $\sigma$ ($○$), $N_1$ ($\square$), and $N_2$ ($⊠$) versus shear rate $\dot{\gamma }$ for 1% Carbopol microgel. Error bars on symbols represent standard deviation in measured and computed quantities.