  We report on direct numerical simulations of the effect of electrostatic
charges on particle-laden duct flows. The corresponding electrostatic forces
are known to affect particle dynamics at small scales and the associated
turbophoretic drift. Our simulations, however, predicted that electrostatic
forces also dominate the vortical motion of the particles, induced by the
secondary flows of Prandtl's second kind of the carrier fluid. Herein we
treated flows at two frictional Reynolds numbers ($Re_\mathrm{\tau}=$ 300
and~600), two particle-to-gas density ratios ($\rho_\mathrm{p}/\rho=$ 1000 and
7500), and three Coulombic-to-gravitational force ratios
($F_\mathrm{el}/F_\mathrm{g}=$ 0, 0.004, and 0.026). In flows with a high
density ratio at $Re_\mathrm{\tau}=$ 600 and $F_\mathrm{el}/F_\mathrm{g}=$
0.004, the particles tend to accumulate at the walls. On the other hand, at a
lower density ratio, respectively a higher $F_\mathrm{el}/F_\mathrm{g}$ of
0.026, the charged particles still follow the secondary flow structures that
are developed in the duct. However, even in this case, the electrostatic forces
counteract the particles' inward flux from the wall and, as a result, their
vortical motion in these secondary structures is significantly attenuated. This
change in the flow pattern results in an increase of the particle number
density at the bisectors of the walls by a factor of five compared to the
corresponding flow with uncharged particles. Finally, at $Re_\mathrm{\tau}=$
300, $\rho_\mathrm{p}/\rho=$ 1000, and $F_\mathrm{el}/F_\mathrm{g}=$ 0.026 the
electrostatic forces dominate over the aerodynamic forces and gravity and,
consequently the particles no longer follow the streamlines of the carrier gas.
