A review on the porous medium approaches to model the flow of interdendritic liquid during the solidification of alloys in casting processes: theory and experiments

The porous medium approach is one of the most popular methods to model the flow of liquid alloys through the solid interdendritic channels in the mushy zone, which is crucial to predict casting defects. In particular, characterizing the permeability of the mushy zone is of vital importance to reliably predict shrinkage porosity and blowholes. Nevertheless, this is not as simple task as permeability continuously evolves through the different stages of the solidification process. For these reasons, a great effort has been made in the past to obtain relationships relating the microstructural parameters to the permeability of the mushy zone. Also, some researchers have taken advantage of the advances in pore network modeling to predict permeability, obtaining promising results. Although a number of numerical experiments have been performed, their reliability has traditionally been hampered by the technical difficulties in reproducing real process conditions. The recent development of imaging techniques with improved spatial and temporal resolution, such as synchrotron 4D (3D + time) X-ray microtomography, has marked a turning point in the experimental validation of the models and is an efficient means to explore the solidification mechanisms. This context of prolific theoretical modeling and major technical achievements provides an excellent opportunity for the materials processing research community to apply the recent progress in fluid flow modeling through complex porous media to the field of casting processes. The aim of this article is to review the state of the art in modeling and experimental evaluation of the permeability of semi-solid zone of casting alloys during solidification so as to smooth the way to future studies. The main stumbling blocks in the field are also presented.