(155a) Electrohydrodynamic Dispersion of Polyelectrolytes

Electric fields are commonly utilized to manipulate macromolecular transport within microfluidic devices for analysis and processing. In particular, simultaneous application of axial electric and flow fields within a microfluidic channel containing polyelectrolyte molecules, such as DNA, can drive transverse migration of polyelectrolytes [1]. This transverse motion has been used to trap and concentrate polyelectrolytes within microfluidic devices and has even been used to separate long and flexible polyelectrolytes from other molecules [2].

The transverse migration is caused by electrohydrodynamic interactions between different portions of the polymer molecule, i.e. interactions due to disturbances in the fluid flow caused by motion of charged particles (polymer backbone and counterions), which in turn are induced by an external electric field. In addition to the net transverse migration, the electrohydrodynamic interactions lead to dispersion of the molecular concentration. As a polyelectrolyte molecule undergoes thermal fluctuations, each of its configurations corresponds to a different instantaneous electrohydrodynamic velocity and these velocity fluctuations contribute to effective polymer diffusivity. For electric fields of magnitude commonly used in microfluidic devices, the magnitude of this dispersion-induced diffusivity is comparable with or exceeds diffusivity due to the regular Brownian forces. Recently we showed [3,4] that the electrohydrodynamic dispersion explains an apparent paradox observed in the experiments [1], namely a non-monotonic dependence of the polyelectrolyte concentration in the channel center on the magnitude of the electric field.

In this talk, we present a model for the electrohydrodynamic dispersion. This model is developed by a combination of a numerical solution and a theoretical analysis of the Langevin and Fokker-Planck equations for dynamics of the polymer backbone. Effect of these dynamics on the polymer transport properties are explored and the fluctuation modes responsible for dominant contribution to the dispersion are identified. This analysis allows us to develop a mean-field model for the polyelectrolyte transport, namely an effective convective-diffusion equation for the center of mass of the polymer, with the internal degrees of freedom of the polymer modeled by effective diffusion and convection terms. Predictions of this model are in quantitative agreement with Brownian dynamics simulations and in qualitative agreement with experiments.

[1] M. Arca, J. E. Butler and A. J. C. Ladd, Soft Matter, 11, 4375–4382 (2015).

[2] B. E. Valley, A. D. Crowell, J. E. Butler, and A. J. C. Ladd, Analyst 145, 5532–5538 (2020).

[3] D. Kopelevich, S. He, R. Montes, and J. E. Butler, J. Fluid Mech., 915, A59 (2021).

[4] D. Kopelevich and J. E. Butler, Phys. Rev. Fluids 6, 094203 (2021).