A conducting droplet is suspended in a conducting liquid of the same density. A constant horizontal potential difference is imposed far from the droplet. At equilibrium, surface tension balances the normal electrical stresses while recirculations are induced by tangential electrical stresses due to the variable charge distribution along the interface (Figure 209).
In the limit of Stokes flows, an analytical solution for the velocity field is available [41, 42]. Figure 210 gives a comparison of the numerical and theoretical results for the radial and azimuthal components of the velocity along a transect inclined at 45 degrees.
A more detailed discussion of this simulation is given in [26].
The total charge is conserved to within round-off errors.