Emergent slow dynamics of collapsed polymers flowing through porous media

Using hydrodynamic simulations, we study the single polymers flowing through model porous media (close-packed colloidal crystal). In good solvent or high flow rates, the polymer transport is similar to gel electrophoresis, with size-dependent sieving for $L_c/L\lesssim 1$ and size-independent biased reptation for $L_c/L\gtrsim 1$ ($L_c$ is the polymer contour length and $L$ is the diameter of colloids forming the porous media). Importantly, in bad solvent and low flow rates, the polymers show an extra window of size-dependent velocity for $1\lesssim L_c/L\lesssim 2$, where the polymer transport is controlled by a globule-stretch transition at pore throats, and the transport velocity is much slower than reptation.

Figure 1

Time sequences of the displacements of polymer center of mass along the flow direction $\mathrm{\Delta }R\left(t\right)/L$ with different polymer lengths $L_c/L$ in (a) good ($\varepsilon =0.41$) or (b) bad solvents ($\varepsilon =2.08$) for flow rate $Pe=15$. Inset: representative simulation snapshot for a polymer flowing through model porous media (face-centered-cubic colloidal crystal).

Figure 2

(a) Ratios of polymer center of mass velocity and pore fluid velocity $V/V_p$, and (b) polymer radius of gyration $\langle R_g\rangle /L$ as a function of polymer lengths $L_c/L$ at different flow rates and solvent properties. Note the error bars represent the standard deviations between block averages by separating the total simulation sequences into three or four segments (cf. Fig. 1).

Figure 3

Representative time sequences of the polymer displacement $\mathrm{\Delta }R\left(t\right)/L$ and radius of gyration $R_g\left(t\right)/L$ for a long polymer $\left(L_c/L=3.33\right)$ passes through pore throats and representative simulation snapshots for the $\varepsilon =2.08$, $Pe=15$ case. In the snapshots, the porous media are drawn with transparent spheres, and the collapsed polymer is drawn with red beads.

Figure 4

Representative time sequences of the polymer displacement $\mathrm{\Delta }R\left(t\right)/L$ and radius of gyration $R_g\left(t\right)/L$ for a long polymer $\left(L_c/L=3.33\right)$ passes through pore throats and representative simulation snapshots for the $\varepsilon =0.41$, $Pe=15$ case. In the snapshots, the porous media are drawn with transparent spheres, and the noncollapsed polymer is drawn with yellow beads.