Role of Hydrodynamic Iteractions in the Migration of Polyelectrolytes

Experiments have shown that DNA molecules in capillary electrophoresis migrate across field lines if a pressure gradient is applied simultaneously [1]. We have proposed a mechanism for the migration involving a coupling between the electrically and hydrodynamically driven flows. The electric field causes a dipolar disturbance in the fluid flow around the polyelectrolyte, which couples with the asymmetric conformations resulting from the local shear rate to generate additional contributions to the center-of-mass velocity [2]. We have developed a kinetic theory based on this idea [3], where counterion screening in the polyelectrolyte is accounted for within a Debye-Hückel approximation [4]. The theory correctly predicts the migration towards the center of the channel when the flow and electric field act in the same direction, and the migration towards the walls when they act in opposite directions.

Brownian dynamics simulations, including the dipolar hydrodynamic interactions between charged beads, confirm the qualitative predictions of the kinetic theory model [5]. Moreover, the simulation results are in quantitative agreement with the experiment over a range of salt concentrations, electric fields and channel geometry. A sample of the results are shown below. The simulations have no adjustable parameters, making the agreement with experiment quite remarkable.

Comparison of DNA concentration profiles in a circular microchannel (radius R) from Brownian-dynamics (blue circles) and experiments [2] (red triangles). [2]. The figure on the left shows the case when the electric field and the pressure gradient are concurrent. while the figure on the right is for the counter-current case.

The work confirms the role of long-range hydrodynamic interactions in polyelectrolyte migration, first suggested in Ref. [2]. Currently we are imaging DNA during capillary electophoresis in the presence of an pressure gradient. One purpose is to check the theoretical prediction that the migration velocity is inversely proportional to ionic strength.


  1. J. Zheng and E. S. Yeung. Anal. Chem., 74:4536, 2002.
  2. O.B. Usta, J.E. Butler, and A.J.C. Ladd, Phys. Rev. Lett., 98:098301, 2007.
  3. J.E. Butler, O.B. Usta, R. Kekre, and A.J.C. Ladd, Phys. Fluids, 19:113101, 2007.
  4. D. Long and A. Ajdari, Eur. Phys. J. 4:29, 2001.
  5. R. Kekre, J.E. Butler, and A.J.C. Ladd, Phys. Rev. E 82:050803(R), 2010.


Mert Arca
Jason Butler

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