Nanoparticle dispersion in porous media: Effects of array geometry and flow orientation

We investigate the effects of array geometry and flow orientation on transport of finite-sized particles in ordered arrays using Stokesian dynamics simulations. We find that quiescent diffusion is independent of array geometry over the range of volume fraction of the nanoposts examined. Longitudinal dispersion under flow depends on the direction of incident flow relative to the array lattice vectors. Taylor-Aris behavior is recovered for flow along the lattice directions, whereas a nonmonotonic dependence of the dispersion coefficient on the Péclet number is obtained for flow orientations slightly perturbed from certain lattice vectors, owing to a competition between directional locking and spatial velocity variations.

Figure 1

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

Figure 2

Streamlines for (a) lattice (${\theta }_l={45}^{\circ }$) and (b) nonlattice (${\theta }_{\mathrm{nl}}={20}^{\circ }$) flow orientations in square arrays with $\varphi =0.028$.

Figure 3

Normalized in-plane diffusion coefficients $D_{\mathrm{q}}/D_0$ as functions of nanopost volume fraction $\varphi$ in square (circles) and hexagonal (triangles) arrays. Estimated uncertainties are smaller than the symbol sizes.

Figure 4

Normalized average particle velocities $\langle V_{\mathrm{L}}\rangle /V_{\infty }$ as functions of flow orientation $\theta$ in (a), (c) square and (b), (d) hexagonal arrays with $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row). The lattice orientations ${\theta }_{\mathrm{l}}$ are indicated on the top $x$ axis in panels (a), (b).

Figure 5

Log-probability density distributions of particle positions ${log}_{10}P(x,y)$ for different flow orientations $\theta$ in square arrays at $V_{\infty }=1000$ for $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row). The intense blue color corresponds to the value ${log}_{10}P(x,y)<-3$.

Figure 6

Log-probability density distributions of particle positions ${log}_{10}P(x,y)$ for different flow orientations $\theta$ in hexagonal arrays at $V_{\infty }=1000$ for $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row). The intense blue color corresponds to the value ${log}_{10}P(x,y)<-3$.

Figure 7

Normalized longitudinal dispersion coefficients $D_{\mathrm{L}}/D_0$ as functions of flow orientation $\theta$ in (a), (c) square and (b), (d) hexagonal arrays with $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row). The lattice orientations ${\theta }_{\mathrm{l}}$ are indicated on the top $x$ axis in panels (a), (b).

Figure 8

Correlations between normalized longitudinal dispersion coefficient $D_{\mathrm{L}}/D_0$ and average normalized collision frequency $\langle C\rangle d_{\mathrm{p}}$ in (a), (c) square and (b), (d) hexagonal arrays with $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row). Open and closed symbols denote non-lattice ${\theta }_{\mathrm{nl}}$ and lattice ${\theta }_{\mathrm{l}}$ directions, respectively. The solid and dashed line arrows in (a) show the trend with increasing $V_{\infty }$ for lattice directions ${\theta }_{\mathrm{l}}$ and nonlattice directions ${\theta }_{\mathrm{nl}}$, respectively.

Figure 9

Normalized longitudinal dispersion coefficients $D_{\mathrm{L}}/D_0$ as functions of Péclet number $\mathrm{Pe}$ in square arrays with $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row) for (a), (c) ${\theta }_{\mathrm{l}}$ and (b), (d) ${\theta }_{\mathrm{nl}}$ flow orientations.

Figure 10

Normalized longitudinal dispersion coefficients $D_{\mathrm{L}}/D_0$ as functions of Péclet number $\mathrm{Pe}$ in hexagonal arrays with $\varphi =0.028$ (top row) and $\varphi =0.058$ (bottom row) for (a), (c) ${\theta }_{\mathrm{l}}$ and (b), (d) ${\theta }_{\mathrm{nl}}$ flow orientations.