We theoretically study the behavior of a liquid bridge formed between a pair of rigid and parallel plates. The plates are smooth, they may either be homogeneous or decorated by circular patches of more hydrophilic domains, and they are generally not identical. We calculate the mechanical equilibrium distance of the liquid bridge as a function of liquid volume, contact angle, and radius of the chemical domain. We show that a liquid bridge can be an equilibrium configuration as long as the sum of the contact angles at the two walls is larger than 180 degrees. When comparisons are possible, our results agree well with recent analytical and molecular dynamics simulation results. We also derive the effective spring constant of the liquid bridge as it is perturbed from its equilibrium distance. The spring constant diverges when the sum of the contact angles is 180 degrees and is finite otherwise. The value of the spring constant decreases with increasing contact angle and volume, and the rate at which it decreases depends strongly on the properties of the two plates.