Experimental investigation of the solid-liquid separation in a stirred tank owing to viscoelasticity

In this study, we investigated the motion of solid particles dispersed in highly viscous complex fluids agitated in a stirred vessel. We used a refractive index matching method and a combination of planar laser-induced fluorescence (PLIF), particle image velocimetry (PIV), and particle-tracking velocimetry (PTV) techniques to measure the velocity fields of the solid and fluid phases simultaneously along with the spatiotemporal distribution of the solids in the tank. The experimental data show that in a Newtonian ambient fluid, particles disperse uniformly in the plane of measurement, while in a strongly shear-thinning viscoelastic ambient fluid they tend to accumulate in the core of the vortices formed in the flow domain. We found that the solids migrate to the core of the vortices also when the ambient fluid is a Boger fluid, i.e., viscoelastic but not shear thinning. The effect of the first normal stress difference, $N1$, on the vortex sizes and circulation intensities was also examined, with both properties decreasing for increasing $N1$. Finally, we observed that the clustering time of the solids in the vessel for viscoelasticity-induced migration was at least three orders of magnitude lower than that obtained from the literature for inertia-induced migration.

Figure 1

(a) Viscosity and (b) first normal stress difference, $N1$, as functions of the shear rate for mixtures GWZ-NN, GW-B1, and GW-B2.

Figure 2

(a) 3D visualizations of the dual blade impeller; (b) schematic of the tank geometry showing visualization areas for both PIV/PTV and solid mixing configurations; (c) experimental setup for the PIV.

Figure 3

Image analysis during pretreatment stages, for $\text{Re}=65$, GWZ-NN mixture and particle volumetric concentration of 1%, where (a) raw PIV image; (b) binarized image without the dye; (c) image with the detected solids; (d) image with only the PIV tracer particles.

Figure 4

Variation of the dimensionless mean fluid velocity magnitude, ${\left(\sqrt{u_r^2+u_z^2}\right)}^{*}$, as a function of the number of revolutions $N_s$ for the fluid mixture GWZ-N and $\text{Re}=65$.

Figure 5

(a) Phase-averaged fluid (left figure) and solid (right figure) velocity fields; (b) contour plots of the averaged solid volume fraction and dimensionless tangential component of the vorticity, ${\omega }_{\theta }$, of the upper part of the vessel for the fluid mixture GWZ-N at $\text{Re}=65$ and particle volumetric concentration of 1%.

Figure 6

Contour plot of the averaged solid volume fraction and dimensionless tangential component of the vorticity, ${\omega }_{\theta }$, and axial concentration profile, ${〈C〉}^{*}$, for fluid mixture GWZ-NN and particle volumetric concentrations of 1% and 2% at (a) $\text{Re}=65$ and (b) $\text{Re}=100$.

Figure 7

Variation of the Shannon entropy, $S$, with increasing $tN$ at $\text{Re}=65$ and particle volumetric concentration of 1% for (a) GWZ-N; (b) GWZ-NN. See the Supplementary Material [37].

Figure 8

Averaged solid volume fraction (left figure) and dimensionless vorticity contour plots along with the dimensionless phase-averaged velocity field (right figure) at $\text{Re}=45$ and particle volumetric concentration of 1% for fluid mixture: (a) GW ($\text{Wi}=0$) and (b) GW-B2 ($\text{Wi}=25$).

Figure 9

(a) Visualization of the area, $A_{\omega i}$, over which the circulation ${\mathrm{\Gamma }}^{*}$ has been estimated (GW mixture, $\text{Wi}=0$ and $\text{Re}=45$). Variation of the space-averaged dimensionless circulation intensity, ${\mathrm{\Gamma }}_{{\omega }_{\theta }=1}^{*}$, with increasing Re for (b) $A_{\omega 1}$, (c) $A_{\omega 2}$.

Figure 10

Horizontal plane measurements of the averaged solid volume fraction contour map (left half for each figure) and dimensionless velocity field (right half for each figure) at $\text{Re}=45, z/T=0.8$ and particle volumetric concentration of 1% for fluid mixtures: (a) GW ($\text{Wi}=0$) and (b) GW-B2 ($\text{Wi}=25$).

Figure 11

Comparison of the radial profiles of the phase-resolved: (a) radial ($u_r$), tangential ($u_{\theta }$), and axial ($u_z$) velocity profiles; (b) shear rates, $\dot{\gamma }{}_{\theta z}, \dot{\gamma }{}_{rz}$, and $\dot{\gamma }{}_{r\theta }$; obtained from vertical and horizontal plane measurements for the fluid mixture GW-B2 at $z/T=0.8$; (c) shear rate, $\dot{\gamma }{}_{r\theta }$, for the fluid mixtures GW ($\text{Wi}=0$) and GW-B2 ($\text{Wi}=25$) for $\text{Re}=45$ at $z/T=0.8$.

Figure 12

Schematic diagram of the vortex above the right top impeller and the dynamic of a single particle for (a) Newtonian and (b) purely viscoelastic ambient fluids.

Figure 13

Variation of the dimensionless solid clustering time, $t_{s}N$, with increasing Wi, solid volume fraction of 1%, and fluid mixtures GW-B1 and GW-B2.