(414d) Kinetic Model for Polyelectrolyte Migration Induced By a Combination of Shear and Electric Fields

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 within the molecule lead to its migration towards the center of the channel. Experimental evidence indicates that there is an optimal strength of electric field that leads to the maximum concentration of polyelectrolytes in the channel center.

To explain this observation, we develop a kinetic model for polyelectrolyte migration. A polyelectrolyte molecule is modeled as a dumbbell and its motion is described by coupled Langevin equations for its center of mass and end-to-end vector. In addition to the usual Brownian force, the stochastic component of the Langevin equation for the center of mass contains a contribution of a fluctuating electrohydrodynamic force between the dumbbell beads. An analytical solution of the coupled Langevin equations elucidates the role of the Brownian force and the deterministic and stochastic components of the electrohydrodynamic force in determining the width of the polyelectrolyte distribution at the center of the channel. The obtained solution is in a qualitative agreement with experimental observations. In particular, it explains existence of an optimal electric field for focusing polyelectrolytes in the center of the channel.