The phase behaviour of a fluid confined between two plane-parallel solid su
bstrates is investigated within the framework of lattice-gas calculations w
here the mean-field intrinsic free energy is employed. By minimizing the gr
and potential numerically, phase diagrams are constructed. Substrates are c
omposed of alternating strips of weakly and strongly adsorbing material. Th
e lattice gas may consist of a high-density region stabilized by the strong
ly adsorbing portion of the substrate while a low-density region exists ove
r the weakly adsorbing ones (the 'bridge' phase). The 'bridge' phases coexi
st with either a liquidlike or a gaslike phase occupying the entire space b
etween the substrates. All three phases join at a triple point, and two cri
tical points exist at which the 'bridge' and gaslike phases or 'bridge' and
liquidlike phases become (separately) indistinguishable. By misaligning th
e substrates in the x-direction, the lattice gas can be exposed to a shear
strain which causes the width of the one-phase region for the 'bridge' phas
es to vary and the triple-point location to alter.