Kinetic theory of a confined polymer driven by an external force and pressure-driven flow

Abstract

Kinetic theory is used to investigate the mechanisms causing cross-stream migration of confined polymers and polyelectrolytes under the influence of external forces and flow fields. Numerical simulations and experiments have demonstrated that confined polymers migrate towards the center of the channel in response to both external forces and uniaxial flows. Yet, migration towards the walls has been observed with combinations of external force and flow. In this paper, the kinetic theory for an elastic dumbbell developed by Ma and Graham [Phys. Fluids 17, 083103 (2005)] has been extended to account for the effects of an external force. Further modifications account for counterion screening within a Debye-Hückel approximation. This enables qualitative comparison with experimental results [Zheng and Yeung, Anal. Chem. 75, 3675 (2003)] on DNA migration under combined electric and pressure-driven flow fields. The comparison supports the contention [Long, Phys. Rev. Lett. 76, 3858 (1996)] that the hydrodynamic interactions in polyelectrolytes decay algebraically, as 1/r3, rather than exponentially. The theory qualitatively reproduces results of both simulations and experiments for the migration of neutral polymers and polyelectrolytes. Concentration profiles similar to those found in numerical simulations are observed, but the Peclet numbers differ by factors of 2-3. © 2007 American Institute of Physics.