In this work, we propose a model for describing the dynamics in polymer-solvent blends. We focus on situations where at least one of the species corresponds to molecular weight below the entanglement threshold. Our model incorporates the strong heterogeneous nature of dynamics close to Tg on a scale of dynamical heterogeneities of size ξ of order 3-5 nm. We assume that spatial distributions of relaxation times are the consequence of concentration fluctuations. We have proposed a Gibbs free energy model (which is an extension of the Flory-Huggins model) for compressible blends, which allows for calculating the driving forces. The spatial dynamics follows then from an Onsager like description. The evolution of concen-trations is calculated by Langevin equations on the scale of dynamical heterogeneities. This model takes also into account a ”facilitation mechanism” which describes the relaxation of slow dynamic heterogeneities when surrounded by faster subunits as due to free volume diffusion or diffusion of different components. Finally, this model is solved on a 2D lattice. 

We consider the situation where the system is far below the pure polymer glass transition temperature and is put in contact with a solvent reservoir. In addition, the activity of the solvent reservoir is varied in order to describe either films drying or swelling. Our model allows for explaining case-II diffusion -i.e. solvent propagation at constant velocity with a well defined front- in the context of the plactification of a glassy polymer by penetrating solvent during swelling. The mechanism is the following : the solvent penetrates first through fast path within the glassy matrix, and then melts the polymer under the os-motic pressure it exerts. Our model allows for calculating the time it takes for the polymer matrix to yield and melt under the applied osmotic stress, as a function of the solvent chemical potential and the age of the polymer matrix. Regarding the process of film drying, we show that films up to 1 micrometer thick can be completely dried. This is a consequence : 1- of the presence of the fast path through which the solvent evaporates 2- the separation of time scales between solvent evapo-ration (fast path) and the subsequent film contraction (controlled by the α-relaxation process). When drying a thicker film, we show that a glassy crust may appear on the free surface, as shown experimentally.