Self-Limited Accumulation of Colloids in Porous Media

We present local direct imaging of the progressive adsorption of colloidal particles inside a 3D model porous medium. By varying the interparticle electrostatic interactions, we observe a large range of particle deposition regimes, from a single layer of particles at the surface of the medium to multiple layers and eventually clogging of the system. We derive the complete deposition dynamics and show that colloid accumulation is a self-limited mechanism towards a deposited fraction associated with a balance between the particle interactions and the imposed flow rate. These trends are explained and predicted using a simple probability model considering the particle adsorption energy and the variation of the drag energy with evolving porosity. This constitutes a direct validation of speculated particle transport mechanisms, and a further understanding of accumulation mechanisms.

Figure 1

Confocal microscopy images of particles (red) deposited in the pore space between glass beads (black) in a $150\times 150\mu {\mathrm{m}}^2$ window at the entrance of the porous media [see Fig. 2], with the suspension flowing upwards. 4 conditions of ionic strength are presented at 4 times.

Figure 2

Local transport and adsorption mechanisms. All scale bars are $10\mu \mathrm{m}$. (a) Time projection of confocal imaging, with the suspension flowing upwards. $I={10}^{-6}\mathrm{M}$. Steady particles appear as white dots, while moving particles are represented by their trajectories. Selected trajectories: particle 1 along wall, 2 close to wall, 3 far from wall. (b) Schematic velocity profile in a pore of initial and current radii ${\mathit{r}}_0$ and $\mathit{r}$. Dashed area shows positions favorable to adsorption: $[{\mathit{r}}_{\mathit{c}}:\mathit{r}-{\mathit{r}}_{\mathit{p}}]$. (c) Schematics of the three scales used in Figs. 1, 2 and 3. (d) Selected area under steady state for different flow rates $[Q_0;8Q_0;16Q_0]$, at $I={10}^{-1}\mathrm{M}$. (e) Cluster formed on a surface at $I={10}^{-1}\mathrm{M}$ (top), detaching and moving to a more stable position (bottom). Dashed lines highlight bead surfaces.

Figure 3

(a) Overall deposition $F$ over time rescaled by surface saturation $S_0$, at the entrance of the porous media for increasing ionic strengths (bottom to top). Plain lines correspond to data. Values above the horizontal line are not quantitative due to resolution limitations (see Ref. [29]). Dashed lines show the fitted model: $s(t)$ for $I={10}^{-6}\mathrm{M}$, with $k=5.0\times {10}^{-4}{\mathrm{s}}^{-1}$; $s(t)+\beta b(t)$ for larger values of $I$, with $\tau =3.0\times {10}^4\mathrm{s}$. (b) Calculated and measured values for the initial bulk deposition probability $p_0$ (dotted line, squares) and the bulk deposition at saturation $b_{\mathrm{sat}}$ (dashed line, diamonds), as a function of the ionic strength. The vertical line shows the limit of application of the model (i.e., suspension instability).