Diffuse interface simulations of phase separation of sheared binary mixtures using a finite volume solver

Multiphase flows are generally modeled assuming that the different phases are separated by an interface of zero thickness, hence all physical properties are allowed to change discontinuously across the interface. This may be an issue when the length-scales of the systems are comparable to the real interface thickness, as in presence of micro-devices or when treating droplet break up. Conversely, the “diffuse interface” model or “phase field theory” assumes that the interfaces are diffuse; hence the model is naturally able to adapt to a large variety of multiphase problems, also in presence of a change of flow morphology, as for instance: physical phenomena of binary mixtures (mixing, spinodal decomposition and nucleation of macroscopically quiescent regular mixtures); droplet dynamics (deformation, coalescence and break-up, moving contact angles) as well as structure development of polymer blends. So far the diffuse interface model has been developed using in-house spectral or finite element codes and simple geometries (boxes, channels…), and this has partly limited its applicability to cases of practical interest. The present work illustrates the implementation of the diffuse interface model in a finite volume solver able to deal with unstructured grids and thus more complex geometries, with the objective of enlarging the range of applicability of the model. The implementation is first validated using simple reference cases and then applied to model the phase separation of sheared binary mixtures.