Using a two-dimensional collisional fluid model, the dynamics of the collisional sheath is investigated when a zero-rise-time negative voltage pulse is applied to a planar target with a rectangular trench immersed in the plasma. In this investigation, the temporal evolution of the sheath edge, ion velocity, density distribution, incidence angle and ion flux along the trench surfaces (sidewall and bottom) are studied numerically for different degrees of ion collisionality during the time. The results obtained show that ion-neutral collisions affect the spatial distribution of the ion flux, ion velocity and, hence, ion impact energy on the surfaces of the trench differently (e.g., they cause the profiles of ion flux and ion velocity along the sidewall and bottom of the trench to be nonmonotonic and monotonic, respectively). Moreover, ion-neutral collisions cause the magnitude of the ion impact energy and the ion flux along the bottom and sidewall of the trench to decrease. Furthermore, ion-neutral collisions weaken the dependence of the ion velocity along the trench surfaces on time. In addition, it is shown that ion-neutral collisions maintain the deviation of the sheath edge from the straight line for long time and decrease the incidence angle of the ions on the trench surfaces. Moreover, we show that the incidence angle of the ions decreases in the presence of collisions and, regardless of neutral gas pressure, this angle is more oblique near the corners of the trench. Additionally, it is shown that the ion density increases near the convex corner of the trench in both collisional and collisionless sheaths. Also, it is found that the sheath expansion near the convex corner is slower than that in the concave corner.