  We consider a nematic liquid crystal confined by two parallel flat substrates
whose anchoring conditions vary periodically in one lateral direction. Within
the Gaussian approximation, we study the effective forces between the patterned
substrates induced by the thermal fluctuations of the nematic director. The
shear force oscillates as function of the lateral shift between the patterns on
the lower and the upper substrates. We compare the strength of this
fluctuation-induced lateral force with the lateral van der Waals force arising
from chemically structured adsorbed monolayers. The fluctuation-induced force
in normal direction is either repulsive or attractive, depending on the model
parameters.
