Gravitational Stability of Suspensions of Attractive Colloidal Particles

Colloidal suspensions are susceptible to gravitationally induced phase separation. This can be mitigated by the formation of a particle network caused by depletion attraction. The effectiveness of this network in supporting the buoyant weight of the suspension can be characterized by its compressional modulus. We measure the compressional modulus for emulsion networks induced by depletion attraction and present a model that quantitatively predicts their gravitational stability. We also determine the relationship between the strength of the depletion attraction and the magnitude of the compressional modulus.

Figure 1

Time evolution of the heights of an emulsion gel with various initial height $H_0$ but the same composition, ${\varphi }_0=0.2$, $c_m=0.06\mathrm{g}/\mathrm{ml}$, $r=4.5\mathrm{nm}$, and $R=360\mathrm{nm}$. $H_0$ are 5, 9, 12, 26, 39 and 57 mm from bottom to top, respectively. Left inset: Picture of a sample. Right inset: Measured $H(t)$ compared with the values calculated with the nonlinear poroelastic model for the samples that do not exhibit a delayed collapse.

Figure 2

Gravitational stress as a function of ${\varphi }_{\infty }$ in the steady state at the top of emulsion gels with: $r=4.5\mathrm{nm}$ and $c_m=0.016\mathrm{g}/\mathrm{ml}$ (▪), $r=6\mathrm{nm}$ and $c_m=0.016\mathrm{g}/\mathrm{ml}$ (▾), $r=4.5\mathrm{nm}$ and $c_m=0.06\mathrm{g}/\mathrm{ml}$ (●), $r=6\mathrm{nm}$ and $c_m=0.06\mathrm{g}/\mathrm{ml}$ (▴). For all samples, $R=360\mathrm{nm}$. Lines are fits to Eq. (1) with $\alpha =1.8$, 1, 0.6, and 0.4 Pa for ▪, ▾, ●, and ▴, respectively. Inset: Log-log plot of gravitational stress normalized with $\alpha$ as a function of ${\varphi }_c-{\varphi }_{\infty }$, where ${\varphi }_c=0.64$.

Figure 3

Height profiles of ${\varphi }_{\infty }$ for emulsion with $R=360\mathrm{nm}$, $r=4.5\mathrm{nm}$, $c_m=0.16$, and $H_0=70\mathrm{mm}$ (▪), and $R=360\mathrm{nm}$, $r=6\mathrm{nm}$, $c_m=0.16$, and $H_0=57\mathrm{mm}$ (▾). The lines are fits to Eq. (4). Inset: Comparison between calculations and measurements of final volume fractions (filled symbols) at the top of emulsion gels and final heights (empty symbols). Symbols are the same as in Fig. 2. The dashed line corresponds to the exact match between calculation and measurement.

Figure 4

Scaling of the stiffness parameter, $\alpha$, predicted by Eq. (8). The samples with TO8 micelles (▿) have $R=360\mathrm{nm}$ and $r=4.5\mathrm{nm}$ with $c_m=0.06$, 0.13, and $0.16\mathrm{g}/\mathrm{ml}$ from a lower value to higher one. Those with A8 micelles (▵) have $R=360\mathrm{nm}$ and $r=6\mathrm{nm}$ with $c_m=0.06$ and $0.16\mathrm{g}/\mathrm{ml}$. The sample with small particles (□) has $R=170\mathrm{nm}$ and $r=4.5\mathrm{nm}$ with $c_m=0.16\mathrm{g}/\mathrm{ml}$. The final sample with PVP (○) has $R=360\mathrm{nm}$ and $r=25\mathrm{nm}$ with $c_m=0.016$, 0.03, 0.04, and $0.08\mathrm{g}/\mathrm{ml}$.