Morphological assessment with the maximum entropy production rate (MEPR) postulate

•Review of the three main theories for describing solidification bifurcation regimes and shapes.•The linear stability theory suggests that the diffusion coefficient in the liquid scales linearly with the solidus temperature and not exponentially with temperature.•Diffusion coefficient comparisons for predictions made by linear stability theory to direct measurements indicate significant deviation from each other at the same temperature.•Discussions on maximum entropy production rate postulate for the prediction of solidification microstructures.

The three established techniques that are currently employed for the prediction of solidification bifurcations and the shape of cast microstructures are reviewed. The main limitations of these established techniques are discussed with examples. A more recent model called the maximum entropy production rate (MEPR) postulate is also reviewed as to its ability to predict patterns, especially those that form during positive temperature gradient solidification. The principle of MEPR states that if there are sufficient degrees of freedom within a system, it will adopt a stable state at which the entropy generation rate is maximized in an open thermodynamic system. In the context of steady state solidification, pathway selections are reflected in the overall steady-state morphological features and shape-bifurcations that are noted with a change in the rate of solidification.