(425h) Importance of Electrohydrodynamic Dispersion in Migration of Polyelectrolytes

Polyelectrolyte molecules such as DNA can be concentrated in the center of a microfluidic channel by a combination of a pressure-driven flow and a parallel electric field. Local shear of the flow stretches and reorients a polyelectrolyte molecule so that electrohydrodynamic interactions (EHI) within the molecule lead to its migration towards the center of the channel. The EHI-induced migration velocity is proportional to the magnitude of the electric field, which suggests that increasing strength of the electric field should increase concentration of polyelectrolytes in the center of the channel. However, experiments show that this trend holds only for sufficiently weak electric fields and the opposite trend is observed when the electric field strength exceeds a threshold value.

In this talk, we demonstrate that this apparent paradox is explained by EHI-induced dispersion of polyelectrolytes. As a polyelectrolyte molecule undergoes thermal fluctuations, each of its configurations corresponds to a different instantaneous EHI-induced velocity. Average of these instantaneous velocities corresponds to the drift velocity driving the polymer towards the center of the channel, while the velocity fluctuations contribute to the effective polymer diffusivity. This EHI-induced dispersion increases with the strength of the electric field, leading to an increasing diffusive flux away from the channel center.

To analyze this competition between the EHI-induced drift towards the channel center and the EHI-induced dispersion away from the center, we develop a kinetic model for the polymer transport. This model is based on the dumbbell model for polyelectrolytes. Performing an adiabatic elimination of the internal degree of freedom of the dumbbell, we obtain an effective convection-diffusion equation for its center of mass. Predictions of this equation are in excellent agreement with Brownian Dynamics simulations and in a qualitative agreement with the experiment. The developed model confirms that the experimentally observed dependence of the polymer concentration in the channel center on the electric field is caused by the competition between the EHI-induced migration and dispersion.