Pattern selection in fingered growth phenomena

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

“…As a consequence of this the thininterface model is capable of giving quantitatively correct predictions for V and ρ during dendritic growth, from which a back-calculation of σ * may be undertaken in order to compare with earlier stability-based theories. Interestingly, where calculation of σ * has been undertaken away from the limit of vanishing Peclet number, both phase-field [15,16] and numerical solvability [17,18] models show that σ * has not only a materials dependence, through the anisotropy strength, ε, but also a dependence upon the growth conditions.…”

Atomistic and continuum modeling of dendritic solidification

“…The lack of a capillary length scale leads to a degeneracy of solutions in the Ivantsov approach such that the tip shape or velocity cannot be determined uniquely. The second major advancement in the theory of dendrite solidification is the advent of microscopic solvability theory [14,15], which seeks allowable solutions to the dendrite growth problem with the inclusion of interfacial free energy. In addition to the Invantsov constraint, solvability theory predicts a value for the product r 2 V and hence r and V are found independently.…”

Quantification of mesh induced anisotropy effects in the phase-field method

“…A rigorous approach to the problem of selecting the operating point of a needle crystal is provided by the theory of microscopic solvability [3,4]. The principal physical insight of solvability theory is that surface tension acts as a singular perturbation which resolves the degeneracy found in the macroscopic problem.…”