In this paper we present a numerical study of the dynamics of partially ionized coronal rain blobs. We use a two-fluid model to perform a high-resolution 2D simulation that takes into account the collisional interaction between the charged and neutral particles contained in the plasma. We follow the evolution of a cold plasma condensation as it falls through an isothermal vertically stratified atmosphere that represents the much hotter and lighter solar corona. We study the consequences of the different degrees of collisional coupling that are present in the system. On the one hand, we find that at the dense core of the blob there is a very strong coupling and the charged and neutral components of the plasma behave as a single fluid, with negligible drift velocities (of a few cm s-1). On the other hand, at the edges of the blob the coupling is much weaker and larger drift velocities (of the order of 1 km s-1) appear. In addition, frictional heating causes large increases of temperature at the transition layers between the blob and the corona. For the first time we show that such large drift velocities and temperature enhancements can develop as a consequence of ion-neutral decoupling associated to coronal rain dynamics. This can lead to enhanced emission coming from the plasma at the coronal rain-corona boundary, which possesses transition region temperature.