Nanoparticle dispersion in porous media: Effects of attractive particle-media interactions

We investigate the effects of physicochemical attractions on the transport of finite-sized particles in three-dimensional ordered nanopost arrays using Stokesian dynamics simulations. We find that weak particle-nanopost attractions negligibly affect diffusion due to the dominance of Brownian fluctuations. Strong attractions, however, significantly hinder particle diffusion due to localization of particles around the nanoposts. Conversely, under flow, attractions significantly enhance longitudinal dispersion at low to moderate Péclet number (Pe). At high Pe, by contrast, advection becomes dominant and attractions weakly enhance dispersion. Moreover, attractions frustrate directional locking at moderate flow rates, and shift the onset of this behavior to higher Pe.

Figure 1

(a) Two-dimensional orthographic projection of a square nanopost array in the $x-y$ plane of the simulation cell. (b) Three-dimensional perspective view of a section of a square nanopost array. The spheres representing the nanoposts (gray, np) and the diffusing particle (orange, p) have the same diameter (i.e., $d_{\mathrm{np}}=d_{\mathrm{p}}$).

Figure 2

Yukawa potential with repulsive core $u\left(r_{ij}\right)$ [Eq. (1)] as a function of the surface-to-surface distance $r_{ij}$ for (a) different $u_0$ and fixed $\kappa =30$ and (b) different $\kappa$ and fixed $u_0=6$.

Figure 3

Normalized in-plane diffusion coefficients $D_{\mathrm{q}}/D_0$ as functions of (a) potential strength $u_0$ for $\kappa =30$ and (b) potential range ${\kappa }^{-1}$ for $u_0=3$ and 6. (c) Comparison of normalized three-dimensional diffusion coefficients $D_{\mathrm{q},3\mathrm{D}}/D_0$ as functions of nanopost volume fraction $\varphi$ with a hydrodynamic model for hindered diffusion [49]. Estimated uncertainties are smaller than the symbol sizes.

Figure 4

Normalized average particle velocities $\langle V_{\mathrm{L}}\rangle /V_{\infty }$ as functions of uniform suspension velocity $V_{\infty }$ at flow orientation $\theta ={45}^{\circ }$ for (a) different $u_0$ and fixed $\kappa =30$ and (b) different $\kappa$ and fixed $u_0=6$. Estimated uncertainties are smaller than the symbol sizes.

Figure 5

Trap time distribution $P\left(t_{\mathrm{R}}\right)$ for attractive potentials with different $u_0$ and fixed $\kappa =30$. Distributions are shown for a uniform suspension velocity $V_{\infty }$ of (a) 0, (b) 5, (c) 20, and (d) 80. The black dashed lines show fits to the function $P\left(t_{\mathrm{R}}\right)=c{exp}^{-t_{\mathrm{R}}/{\tau }_{\mathrm{R}}}$.

Figure 6

Characteristic trapping time ${\tau }_{\mathrm{R}}$ as a function of the magnitude of the potential strength $u_0$ for $\kappa =30$ at different $V_{\infty }$. The black dashed lines show fits to the function ${\tau }_{\mathrm{R}}=c_1{exp}^{-c_2{u}_0/k_{\mathrm{B}}T}$, where $c_1$ and $c_2$ are fitting constants.

Figure 7

Log-probability density distributions of particle positions ${log}_{10}P(x,y)$ for $u_0$ of (a), (d) 3, (b), (e) 5, and (c), (f) 7 at $V_{\infty }$ of (a)–(c) 80 and (d)–(f) 1000 for flow orientation $\theta ={45}^{\circ }$. The intense blue color corresponds to regions where ${log}_{10}P(x,y)<-3$.

Figure 8

Normalized longitudinal dispersion coefficients $D_{\mathrm{L}}/D_0$ as functions of Pe at flow orientation $\theta ={45}^{\circ }$ for (a) different $u_0$ and fixed $\kappa =30$ and (b) different $\kappa$ and fixed $u_0=6$. Estimated uncertainties are smaller than the symbol sizes.

Figure 9

Log-probability density distributions of particle positions ${log}_{10}P(x,y)$ for (a)–(c) $u_0=0$ and (d)–(f) $u_0=7$ at $V_{\infty }$ of (a), (b) 80, (c), (d) 320, and (e), (f) 1000 for flow orientation $\theta =1.{25}^{\circ }$. The intense blue color corresponds to regions where ${log}_{10}P(x,y)<-3$.

Figure 10

Normalized longitudinal dispersion coefficient $D_{\mathrm{L}}/D_0$ as a function of flow orientation $\theta$ in a square array with $\varphi =0.058$ for attractive potentials with $\kappa =30$ and (a) $u_0=0$ and (b) $u_0=6$.