This work deals with the modelling of dendritic solidification in binary mixtures. Large scale phenomena are represented by volume averaging of the local conservation equations. This method allows to rigorously derive the partial differential equations of averaged fields and the closure problems asociated to the deviations. Such problems can be resolved numerically on periodic celles, representative of dentritic structures, in order to give a precise evaluation of macroscopic transfer coefficients (Drag coefficients, exchange coefficients, diffusion-dispersion tensors ...). The method had already been applied for a model of columnar dentritic mushy zone and it is extended to the case of equiaxed dendritic solidification, where solid grains can move. The two-phase flow is modelled with an Eulerian-Eulerian approach and the novelty is to account for the dispersion of solid velocity through the kinetic agitation of the particles. A coupling of the two models is proposed thanks to an original adaptation of the columnar model, allowing for undercooling calculation: a solid-liquid interfacial area density is introduced and calculated. At last, direct numerical simulations of crystal growth are proposed with a diffuse interface method for a representation of local phenomena.