Velocity Fluctuations in Sedimenting Brownian Particles

We report a gradual transition of dynamics in sedimenting suspensions of charge stabilized Brownian particles prior to the onset of the macroscopic sedimentation front. Using multispeckle ultrasmall-angle x-ray photon correlation spectroscopy (USA-XPCS), we show that well-defined advective motions dominate the colloid dynamics during the early stages of sedimentation. With elapsing time, these advective currents decay and diffusive motions become the dominating contribution in the dynamics. Probing the temporal development of these fluctuations at smaller Peclet numbers ($<1$) provides a new perspective for the mechanism determining the transient nature of velocity fluctuations in sedimentation and demonstrates new experimental capabilities enabled by multispeckle USA-XPCS.

Figure 1

Intensity autocorrelation functions measured in vertical (first row) and horizontal (second row) directions at different times after the sample was homogenized (2–52 min). The different colors correspond to $q$ values of $q(\times {10}^{-3}{\mathrm{nm}}^{-1})=4.7(\text{dark}\text{blue})6.3(\text{light}\text{blue})7.7(\text{cyan})9.3(\text{green})10.7(\text{yellow})12.3(\text{orange})$. In the third row, measurements in horizontal (blue) and vertical (red) directions are shown together for $q=6.3\times {10}^{-3}{\mathrm{nm}}^{-1}$.

Figure 2

Comparison between the proposed model for velocity fluctuations and the measured XPCS $g_2(\overrightarrow{q},t)$. Experimental data are shown for $q=6.3\times {10}^{-3}{\mathrm{nm}}^{-1}$, measured within the first hour after sample homogenization. Corresponding plots for other $q$ values can be found in the Supplemental Material [26]. Plots of expressions (2) and (6) are displayed in (a) and (c), respectively. Measurements in the vertical direction, and the ratio of vertical and horizontal signals, corresponding to ${|g_{1,v}(q_{\parallel },t)|}^2$, are shown in (b) and (d), respectively. The fits were calculated by refining the model at all $q$ values simultaneously.

Figure 3

(a) Time dependence of velocity fluctuations, $v_{\mathrm{fluc}}$, $\alpha$, and volume percent, $\varphi$ for height, $z=30\mathrm{mm}$. (b) Velocity fluctuations as a function of height and time. (c) $\alpha$ as a function of height and time. (d) Corresponding photographs of the solution taken at initial stage, 1 hour and 24 hours after onset of sedimentation. (e) Macroscopic stratification for different times after the onset of the sedimentation. Concentration profiles measured at 15 and 45 min superimpose.

Figure 4

(a) Time dependence of the velocity fluctuations for different particle concentrations, the container diameter (0.9 mm) and the height ($z=23\mathrm{mm}$) are fixed. (b) Normalized velocity fluctuations for volume fractions between 0.005 and 0.15 and container dimensions between 0.2 and 2 mm. The corresponding unnormalized data are shown in (a) and Supplemental Material [26] [Figs. 5(a) and 5(b)].