We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.

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Electrohydrodynamic flow of a dielectric liquid around a wire electrode sandwiched between two parallel flat-plate electrodes is studied both numerically and experimentally. The Poisson-Nernst-Planck equations for the ion transport and the Navier-Stokes equations for the fluid flow are solved numerically by using a commercial code. Charge generation in a dielectric liquid (dodecane + 0.5% wt Span 80) due to Onsager effect is considered in the ion transport equations. Numerical results well predict the experimental ones both qualitatively and quantitatively. At high electric field the numerical approach slightly over-predicts the flow velocity measured from the experiment, but the level of discrepancy can be further lowered by using a truncated series for the Onsager function.

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