A hydrodynamic model is established to study the interactions of a dust particle with a radio-frequency (rf) sheath, taking into account the influence of the spatial inhomogeneity of the ~rf! sheath, as well as the influence of the ion-neutral collisions. Numerical results are obtained for the charge on the dust particle and for the spatial distribution of the induced potential around this particle, based on a self-consistent modeling of the sheath parameters such as the sheath electric field, the ion velocity, and the ion and electron densities. The induced potential exhibits the familiar oscillatory structure of a wake potential, which is, however, strongly damped due to the collisional effects. The spatial inhomogeneity of the rf sheath gives rise to a further damping of the induced potential, as well as to a reduction of the oscillations at large distances from the dust particle.