The chain sucker: translocation dynamics of a polymer chain into a long narrow channel driven by longitudinal flow

Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a narrow channel of width $R$ embedded in two dimensions, driven by a force proportional to the number of monomers in the channel. Such a setup mimics typical experimental situations in nano/micro-fluidics. During the the translocation process if the monomers in the channel can sufficiently quickly assume steady state motion, we observe the scaling $\tau\sim N/F$ of the translocation time $\tau$ with the driving force $F$ per bead and the number $N$ of monomers per chain. With smaller channel width $R$, steady state motion cannot be achieved, effecting a non-universal dependence of $\tau$ on $N$ and $F$. From the simulations we also deduce the waiting time distributions under various conditions for the single segment passage through the channel entrance. For different chain lengths but the same driving force, the curves of the waiting time as a function of the translocation coordinate $s$ feature a maximum located at identical $s_{\mathrm{max}}$, while with increasing the driving force or the channel width the value of $s_{\mathrm{max}}$ decreases.

💡 Research Summary

In this work the authors investigate the translocation of a flexible polymer chain into a long, narrow two‑dimensional channel driven by a longitudinal flow. Unlike the conventional nanopore problem where the driving force acts only on the monomers inside a short pore, here the external force is assumed to act on every monomer that has already entered the channel. Consequently the total driving force grows linearly with the number of translocated monomers, s(t), i.e. F_ext = F · s(t) x̂, where F is the force per bead. This situation mimics recent micro‑/nanofluidic devices in which a high‑velocity flow inside a nano‑channel pulls the polymer into the channel, or an electric field that is confined to the channel length.

The polymer is modeled as a bead‑spring chain with Lennard‑Jones excluded‑volume interactions and finitely extensible nonlinear elastic (FENE) bonds. Langevin dynamics simulations are performed in two dimensions, with a friction coefficient ξ and a stochastic force satisfying the fluctuation‑dissipation theorem. The channel walls are represented by two parallel rows of fixed beads separated by a distance R; the channel length is taken much larger than the polymer’s radius of gyration. The translocation time τ is defined as the interval between the moment the first bead enters the channel and the moment the last bead has fully entered.

A scaling analysis based on the blob picture is developed. When the channel width R exceeds the monomer size σ, the confined polymer forms a series of blobs of size R. Each blob contains g ≈ (R/σ)^{1/ν_2D} monomers (ν_2D ≈ 0.75). The number of blobs is n_b = N/g ≈ N(σ/R)^{1/ν_2D}, leading to a longitudinal extension R_k ≈ n_b R ≈ N R^{−1/3}. For weak driving the translocation time follows τ_ss ≈ R_k/F ≈ N R^{−1/3}/F. Under strong driving the blobs are stretched and R_k scales linearly with N, giving the simple scaling τ ∝ N/F.

The authors also write down a force balance for the translocating segment: the frictional drag inside the channel, F_trans,f ≈ C R^{−1/3} ξ s(t) ds/dt (with C≈1.17 from simulations), the entropic resistance F_trans,e ≈ 2.12 k_BT/R, and the growing driving force s(t) F. When the entropic term is negligible (large F or long channels) the balance reduces to C R^{−1/3} ξ s ds/dt = s F, which integrates to τ ≈ ξ N/(F R^{1/3}). If the entropic term is retained, a more complex expression (Eq. 9 in the paper) results, predicting a crossover from τ ∝ N/F for long chains to a slower growth for short chains where the entropic barrier dominates.

Simulation results confirm these predictions. For channel widths R = 4.5σ and forces F = 0.1–0.5 ε/σ, the translocation probability increases almost linearly with F and is essentially independent of chain length. The translocation time τ scales linearly with N when the channel is wide enough for steady‑state motion to develop, i.e., τ ∝ N/F. When R is reduced, the steady‑state cannot be reached; τ then shows a non‑universal dependence on both N and F, reflecting the increased importance of entropic and frictional resistance.

The paper also examines the waiting‑time distribution w(s), the average time a given monomer spends at the channel entrance as a function of the translocation coordinate s. All chains of different length but the same driving force exhibit a maximum waiting time at the same s_max. Increasing either the driving force or the channel width shifts s_max toward smaller s, indicating that a larger fraction of monomers inside the channel accelerates the subsequent motion.

In summary, the study introduces a novel translocation scenario where the driving force grows with the number of monomers already inside the channel. By combining blob‑based scaling arguments with detailed Langevin dynamics simulations, the authors elucidate the conditions under which the simple τ ∝ N/F law holds and when deviations arise due to confinement and entropic effects. The waiting‑time analysis provides further insight into the microscopic dynamics of chain capture. These findings are directly relevant to the design of nanofluidic devices for polymer manipulation, DNA sequencing, and controlled drug delivery, where flow‑driven or field‑driven transport through long nano‑channels is a key operational principle.