Dynamics of Concentrated Hard-Sphere Colloids Near a Wall

We investigate the Brownian motion of hard-sphere colloids near a solid wall by Evanescent Wave Dynamic Light Scattering (EWDLS). We carried out measurements for various volume fractions of sterically stabilized poly(methyl methacrylate) (PMMA) particles over a range of scattering wave vectors, $\mathbf{q}$. While in the dilute regime, the near wall short-time diffusion is significantly slowed down due to particle-wall hydrodynamic interactions (HI); as volume fraction increases, the wall effect is progressively diminished at all $\mathbf{q}$’s. We present a new analysis for the EWDLS short-time self- and collective diffusivities applicable to all volume fractions and a simple model for the self-diffusion describing the interplay between particle-wall and particle-particle HI. Moreover, a weaker decay of the near-wall self-diffusion coefficient with volume fraction is predicted by Stokesian dynamics simulations.

Figure 1

$f(\mathbf{q},t;\kappa )$ from DLS (3D) and EWDLS (quazi-2D) at $qR=4.58$ (and $2/\kappa =4.37R$ in the latter case) for a dilute ($\varphi =0.0018$) and a concentrated suspension ($\varphi =0.25$). The insets portray the initial decay of these functions.

Figure 2

Normalized $q$-dependent diffusivity as a function of $qR$ in 3D and quazi-2D for several ${\phi }^{\prime }$s. The arrow denotes the $qR$ where $q_{\parallel }\sim q_{\perp }$ (${\theta }_s\sim 90°$) and the lines denote the theoretical predictions of Beenaker and Mazur [24] for diffusion in 3D.

Figure 3

The $\varphi$-dependence of the short-time collective, $D_C$, and self, $D_S$, diffusivity, in 3D and near the wall normalized by the Stokes-Einstein-Sutherland diffusivity $D_0$. The errors in $D_C$ result from the extrapolation to $q=0$. The last two points (squares) were measured with $R=154\mathrm{nm}$ ($\varphi =0.4$) and 114 nm ($\varphi =0.42$) particles. The solid lines correspond to Batchelor’s dilute predictions for the collective and self-diffusion [23] while the dashed line is the Stokesian dynamics prediction for self-diffusion [19].

Figure 4

(a) The ratio of 3D to the near-wall self-diffusivity as a function of volume fraction. The last two points were measured with $R=154\mathrm{nm}$ and $R=118\mathrm{nm}$ particles. The line corresponds to the simple model prediction [Eq. (3)]. (b) Dilute limit quazi-2D short-time self-diffusion and order $\varphi$ coefficient from Stokesian dynamics simulations. The stars represent experimental data, and the arrow corresponds to Batchelor’s order $\varphi$ prediction [23] in 3D (i.e., 1.83).