Colloidal Swarms Can Settle Faster than Isolated Particles: Enhanced Sedimentation near Phase Separation

By experimenting on model colloids where depletion forces can be carefully tuned and quantified, we show that attractive interactions consistently “promote” particle settling, so much that the sedimentation velocity of a moderately concentrated dispersion can even exceed its single-particle value. At larger particle volume fraction $\varphi$, however, hydrodynamic hindrance eventually takes over. Hence, $v(\varphi )$ actually displays a nonmonotonic trend that may threaten the stability of the settling front to thermal perturbations. Finally, by discussing a representative case, we show that these results are relevant to the investigation of protein association effects by ultracentrifugation.

Figure 1

Inset: Values of ${\tau }^{-1}$ as a function of the surfactant concentration $c$ obtained by virial coefficient matching as discussed in the text and in the Supplemental Material [18]. The square indicates the value ${\tau }_{\mathrm{PS}}^{-1}\simeq 10.5$ where phase separation is experimentally observed at $\varphi =0.04$, which is slightly higher than the critical value ${\tau }_c^{-1}\simeq 8.8$ (at ${\varphi }_c\simeq 0.26$) for AHS. Main figure: Settling velocity $v(\tau )$ for MFA suspensions at fixed particle volume fraction $\varphi =0.04$ and temperature $T=25°\mathrm{C}$, as a function of ${\tau }^{-1}$. The straight line is drawn from the measured value for hard spheres $v_{\mathrm{HS}}/v_s\simeq 0.77$, with the slope given by Eq. (3).

Figure 2

Inset: Full dependence of $\tau$ on $T$ obtained for $c=56\mathrm{g}/\mathrm{l}$ using the mapping strategy discussed in the text and detailed in the Supplemental Material [18]. Main figure: Normalized settling velocity as a function of the initial particle volume fraction $\varphi$ obtained for $\tau =0.21$ ($T=25°\mathrm{C}$, filled square) and $\tau =0.12$ ($T=30°\mathrm{C}$, filled circle) at fixed surfactant concentration $c=56\mathrm{g}/\mathrm{l}$. The corresponding open symbols are results from numerical simulations obtained by interpolating the set of results presented in Ref. [9]. Dotted lines show the low-$\varphi$ linear behavior predicted by Batchelor’s expression (1). The figure also compares the data obtained for MFA suspensions in the absence of added surfactant (filled triangle) with the SRD results for HS (open triangle), together with analytical (full line [21]) and numerical ($+$ [25]) results for $v_{\mathrm{HS}}(\varphi )$.

Figure 3

Comparison between the settling profiles obtained at $T=30°\mathrm{C}$ for MFA suspensions at $\varphi =0.04$ without added surfactant (top) and in the presence of a depletant concentration $c=56\mathrm{g}/\mathrm{l}$, corresponding to $\tau \simeq 0.12$ (bottom). In both panels, $\mathrm{\Delta }r$ is the displacement from the position of the top of the initially homogeneous suspension.