We study the translocation of polymers along channels with oscillating varying cross section and under the action of a constant external force. We use the Fick-Jacobs approximation and an effective potential to reduce the translocation of polymers through a three-dimensional channel to that of an effective point-like particle potential [1].

We study numerically the dynamics for Gaussian polymers when symmetric and asymmetric channels are time modulated.  As in previous works for the case of colloidal particles [2,3], we analyze the effect that the interplay between the characteristics time scales associated to diffusion, frequency and external force has on the flow induced by the oscillations.

We also study analytically a simplified model for the case of colloids in an oscillating symmetrical channel in order to achieve a deeper understanding of the interplay between time scales and their role on the flow. Within the Fick-Jacobs approximation and doing a Fourier representation of the effective force we obtain an expression for the velocity. The theoretical predictions are in good agreement with the numerical simulations and adequately explain the flow dependence on the time scales.

Comparison between analytical results for the case of colloids and numerical results for polymers explains how parameters related to the geometry of the channel and the structure of the polymers affect the flow behavior. Moreover, analytical results indicate that for small forces the time modulation and not asymmetry, is the key element behind the velocity behavior obtained numerically.

[1] Bianco V. and Malgaretti, P., J. Chem. Phys. 145, 114904 (2016).

[2] Carusela M.F, Rubi M.J. , J. Chem. Phys. 146, 184901 (2017)