Orientation of spheroidal colloids near a charged surface

We look at an uncharged spheroidal colloid in a water near a charged flat surface.
We solve
the nonlinear Poisson-Boltzmann equation outside of the colloid
for various tilt angles θ with respect to the surface.
The colloid's size is assumed to be comparable to the Debye's length and hence field
gradients are essential.
The Maxwell stress tensor, including a contribution from the ideal gas of ions, can be
integrated along the colloid's surface to give the total force and torque on the colloid.
The calculation is for a static colloid but if it were to move translation and
rotations would be coupled via the tilt angle. From the torque we calculate the effective
angular potential u(θ). The colloid tends to align in
the direction perpendicular to the surface (parallel to the field, θ=0) if it is far enough from it.
Surprisingly, we find that at short separations or large voltages the colloid will align
parallel to the surface (θ=90 degs). Interestingly, colloid orientation parallel to the
surface is promoted at a finite value of the eccentricity.
Lastly, and this needs to be yet verified, the nonuniform forces on the
surface of the colloid seem to amount to a net translational force along the surface although
the system is invariant in this direction.