  We present an approach to studying directed polymers in interaction with a
defect line and subject to a force, which pulls them away from the line. We
consider in particular the case of inhomogeneous interactions. We first give a
formula relating the free energy of these models to the free energy of the
corresponding ones in which the force is switched off. We then show how to
detect the presence of a re-entrant transition without fully solving the model.
We discuss some models in detail and show that inhomogeneous interaction, e.g.
disordered interactions, may induce the re-entrance phenomenon.
