Role of Hydrodynamic Interactions in the Migration of Polyelectrolytes

Figure 1: How an electric field can induce a cross-stream migration.

Experiments [1,2] have shown that DNA molecules in capillary electrophoresis migrate across field lines if a pressure gradient is applied simultaneously [1]. Figure 1 illustrates how an electric field (green arrows) causes a dipolar disturbance in the fluid flow around the polyelectrolyte (cyan arrows), which couples with the asymmetric conformations resulting from the local shear rate (blue arrows) to generate additional contributions to the center-of-mass velocity (black circles). When the flow and electric field act in the same direction [1] the migration is towards the centerline, while when they act in opposite directions [2] the polyelectrolyte migrates towards the walls. Although the polyelectrolyte is represented here as two blobs (a dumbbell model), calculations based on a Gaussian coil lead to similar conclusions [3].

Figure 2: How cross-stream migration can lead to DNA trapping.

Migration towards the walls can be used to create a novel mechanism to trap DNA molecules within a small volume, as illustrated schematically in Figure 2. Uniformly distributed DNA (chains of red blobs) is convected into a microfluidic channel by the parabolic flow field (blue arrow). The resulting shear rate in the channel stretches and rotates the molecules relative to the flow and field lines. The electric field then causes a cross stream migration towards the walls by the mechanism suggested by Figure 1. The molecules stretch further as they approach the wall (because of the higher shear rate) and slow down because of the reduced flow velocity in the vicinity of the wall. Close to the wall the flow velocity vanishes and DNA is convected back to the inlet by the (generally smaller) electrophoretic velocity (green arrows). This mechanism provides opportunities to both concentrate and separate DNA molecules. Further information can be found here and in Ref. [2].


  1. M. Arca, J. E. Butler, and A. J. C. Ladd. Soft Matter, 11:4375-4382, 2015.
  2. M. Arca, A. J. C. Ladd, and J. E. Butler. Soft Matter, 12:6975-6984, 2016.
  3. A. J. C. Ladd. Mol. Phys., In Press, 2018.


Jason Butler

Chemical Engineering Home Page | University of Florida Home Page
Last updated August 2018