 Solution

Positive dielectrophoresis acts up the gradient of the squared RMS field, towards stronger-field regions; negative dielectrophoresis acts down that gradient, towards weaker-field regions. The sign is the sign of $\Re \tilde{K}(\omega )$.

The force is not generally tangent to an electric field line. Field lines show the direction of the field itself, whereas $\nabla |{\mathbf{E}}_{\mathrm{RMS}}{|}^2$ describes how its strength changes in space. A spatially uniform field gives zero dipole-order dielectrophoretic force even when it is large. Reversing the field each half-cycle does not reverse this time-averaged force, because the relevant intensity-like quantity is quadratic.