Does the electric Lehmann effect exist in cholesteric liquid crystals?

Experiments have shown that cholesteric droplets or cholesteric fingers may be put into motion by the action of an electric field. The former rotate whereas the latter drift perpendicularly to their axes. In all cases, the texture moves without visible material transport. The electric Lehmann effect was initially used to interpret these observations but, recently, alternative explanations were found, based on electrohydrodynamics. Another experiment in this area was that of Padmini and Madhusudana (Liq. Cryst. 14, 497 (1993)). Performed in 1993 with a compensated cholesteric liquid crystal under fixed planar boundary conditions, it was also explained in terms of electric Lehmann effect. We conducted the same experiment and extended it to a pi -twisted planar geometry. Although our experimental results agree with those of Padmini and Madhusudana, we demonstrate that they are incompatible with an electric Lehmann effect. By contrast, an explanation based on flexoelectricity allows us to interpret the whole data set obtained in both geometries. The consequence is that there is at the moment no clear experimental evidence of the electric Lehmann effect.