Implicit Method for Simulating Electrohydrodynamics of Polyelectrolytes

We introduce a novel method to couple Lennard-Jones beads to a lattice-Boltzmann fluid by adding a term which represents the slip within the Debye layer with respect to the surrounding fluid. The method produces realistic electrophoretic dynamics of charged free chains, as well as the correct stall force in the limit of a thin Debye layer. Our simulations also demonstrate how a net-neutral polyampholyte can have a nonzero net force due to hydrodynamic interactions. This method represents an efficient way to simulate a wide variety of complex problems in electrohydrodynamics.

Figure 1

The diffusion coefficient of polymers of various lengths $N$ for several values of ${\mu }_{0}E$. The dotted lines are slopes of $-0.588$ (the prediction for Zimm dynamics) and $-1$ (the prediction for Rouse dynamics). The inset shows the velocity renormalized by ${\mu }_{0}E$.

Figure 2

The velocity of an overall neutral linear polymer renormalized by ${\mu }_{0}E$ as a function of the charge distribution. The polymers are formed by taking the same ring copolymer and cutting it at different points along the positive block as depicted schematically. The dashed line represents the predictions of Long et al. [15] with a scaling factor.

Figure 3

Force needed to hold polymers of different lengths $N$ stationary in a random walk or rod configuration for various values of the coupling constant ${\mu }_{0}E$. Curves for $F\propto N^{0.5}$ and $F\propto N$ are shown as dashed lines, along with a solid line of the form $N/[\ln (2N/b)-0.5]$ for the rod data.

Figure 4

The force perpendicular to the electric field on a cross of zero net charge as a function of the applied field ${\mu }_{0}E$ showing $F_{\perp }\propto ({\mu }_{0}E{)}^3$. The inset shows a schematic of the bead configuration along with the curved fluid flow lines which cause a force perpendicular to the electric field.