Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2016, Tutors: Jordi Ortín i Ramon PlanetWe have studied experimentally the morphology and dynamics of stable oil-air displacements in a gap-modulated Hele-Shaw cell, in the case where the modulation is persistent in the direction of front advancement. Local changes in capillary pressure result in non-local deformations of the two-phase fronts, which have been recorded with a high speed camera and digitized in space and time. The front morphologies observed experimentally in the steady state are in excellent agreement with the predictions of a linear theory, particularly for low intensities of the gap modulation and for both positive and negative modulations. We have also studied the spatio-temporal dynamics of deformation of a nearly initially at front towards the steady state. In the presence of a positive modulation of the gap thickness, the difference in height between the front tip at the central modulation of the cell and its lateral tails accelerates in time