Transient shear banding in time-dependent fluids

We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered.

Figure 1

Steady state flow curve, showing Newtonian response, with $A_s=0.665$, $B_s=1.000$. (Inset) The transient behavior of the viscosity for ${\varphi }_0=0.6799$, and $k=1.5$.

Figure 2

Schematic phase diagram of the instability/stability regimes as a function of $k$ and ${\varphi }_0$. In regions (a) and (c) spatially homogeneous relaxation is observed, whereas region (b) exhibits transient shear banding.

Figure 3

Volume fraction (a), shear rate (b), and velocity (c) profiles during the startup flow for $A_s=0.665$, $B_s=1.000$, $k=1.5$, $\langle \dot{\gamma }\rangle =1.0$ s${}^{-1}$ and $\varphi (r,t=0)=0.6799$.

Figure 4

Fluidization times as a function of $\langle \dot{\gamma }\rangle$, for different values of $k$.

Figure 5

Normalized shear rate evolution close to the inner and outer cylinder (a), and the normalized evolution of the shear band edge position in the gap (b).