Shear Induced Drainage in Foamy Yield-Stress Fluids

Shear induced drainage of a foamy yield-stress fluid is investigated using MRI techniques. Whereas the yield stress of the interstitial fluid stabilizes the system at rest, a fast drainage is observed when a horizontal shear is imposed. It is shown that the sheared interstitial material behaves as a viscous fluid in the direction of gravity, the effective viscosity of which is controlled by shear in transient foam films between bubbles. Results provided for several bubble sizes are not captured by the $R^2$ scaling classically observed for foams. Furthermore, foam films are found to be responsible for the unexpected arrest of drainage, thus trapping irreversibly a significant amount of interstitial liquid.

Figure 1

(a) Bubble volume fraction $\Phi$ vs height $z$ of a foamy yield-stress fluid with $275\mu \mathrm{m}$ radius bubbles, for a 12 h rest (*), and as function of shear duration at ${\dot{\gamma }}_{\mathrm{macro}}=18{\mathrm{s}}^{-1}$: (○) $t=0\mathrm{s}$, (▵) 135 s, (□) 245 s, (◇) 425 s, (×) 665 s, (●) 965 s, and (▴) 1265 s. (b) ${\Phi }_{\max }$ vs bubble radius. The solid line is the calculated gas volume fraction assuming that the liquid is contained in films of thickness $h_f=10\mu \mathrm{m}$ (see text). All materials where made with TTAB. Inset: Dimensionless velocity profiles $V(r)/V(r_i)$ as function of the position $r$ in the gap for a sample at ${\Phi }_0$ (●) and ${\Phi }_{\max }$ (×). The profiles were averaged over 4 cm at middle height of the sample; similar results were found in the upper and lower part of the cell.

Figure 2

Drainage front velocities vs macroscopic shear rate. (a) Influence of the bubbles radius: (■) $125\mu \mathrm{m}$, (●) $275\mu \mathrm{m}$, and (▲) $500\mu \mathrm{m}$. (b) Influence of the surface mobility for the $275\mu \mathrm{m}$ bubbles: (●) TTAB and (◆) $\mathrm{TTAB}+\mathrm{DOH}$.