  We consider a nematic liquid crystal, in coexistence with its isotropic
phase, in contact with a substrate patterned with rectangular grooves. In such
a system, the nematic phase may fill the grooves without the occurrence of
complete wetting. There may exist multiple (meta)stable filled states, each
characterised by the type of distortion (bend or splay) in each corner of the
groove and by the shape of the nematic-isotropic interface, and additionally
the plateaux that separate the grooves may be either dry or wet with a thin
layer of nematic. Using numerical simulations, we analyse the dynamical
response of the system to an externally- applied electric field, with the aim
of identifying switching transitions between these filled states. We find that
order-electric coupling between the fluid and the field provides a means of
switching between states where the plateaux between grooves are dry and states
where they are wet by a nematic layer, without affecting the configuration of
the nematic within the groove. We find that flexoelectric coupling may change
the nematic texture in the groove, provided that the flexoelectric coupling
differentiates between the types of distortion at the corners of the substrate.
We identify intermediate stages of the transitions, and the role played by the
motion of the nematic-isotropic interface. We determine quantitatively the
field magnitudes and orientations required to effect each type of transition.
