Bridge phases associated with a phase transition between two liquid phases occur when a two-component liquid mixture is confined between chemically patterned walls. In the bulk the liquid mixture with components A, B undergoes phase separation into an A-rich phase and a B-rich phase. The walls bear stripes attractive to A. In the bridge phase A-rich and B-rich regions alternate. Grand canonical Monte Carlo studies are performed with the alignment between stripes on opposite walls varied. Misalignment of the stripes places the nanoscopic liquid bridges under shear strain. The bridges exert a Hookean restoring force on the walls for small displacements from equilibrium. As the strain increases there are deviations from Hooke's law. Eventually there is an abrupt yielding of the bridges. Molecular dynamics simulations show the bridges form or disintegrate on time scales which are fast compared to wall motion and transport of molecules into or from the confined space. Some interesting possible applications of the phenomena are discussed. (C) 2004 American Institute of Physics.