Crystal growth under non-equilibrium conditions can give rise to complex patterns which are generically similar to those found in processes such as viscous fingering, aggregation and electrochemical deposition. Recent theoretical understanding focuses on the interplay between the macroscopic driving force associated with the phase transition and the microscopic interfacial dynamics.

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The formation of patterns in non-equilibrium growth

In this work a mixed Eulerian–Lagrangian technique is devised, hereinafter abbreviated as ELAFINT (Eulerian–Lagrangian Algorithm For INterface Tracking). The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving/free phase boundaries. The position and shape of the boundary are tracked explicitly by the Lagrangian translation of marker particles. The field equations are solved on an underlying fixed grid as in Eulerian methods. The interface passes through the grid lay-out and details regarding the treatment of the cut cells so formed are provided. The issues involved in treating the internal boundaries are dealt with, with particular attention to conservation and consistency in the vicinity of the interface. The method is tested by comparing with solutions from well-tested body-fitted co-ordinate methods. Test cases pertaining to forced and natural convection in irregular geometries and moving phase boundaries with melt convection are presented. The capability developed here can be beneficial in solving difficult flow problems involving moving and geometrically complex boundaries.

Elafint: a Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries

Phase-field simulation of dendritic growth in a shear flow

This is the first account of the history of our understanding of, and ability to model, solidification microstructures. Its objective is to retrace the scientific steps made, from the earliest obse...

Shakeel H. Tirmizi

Papers

Effect of natural convection on growth velocity and morphology of dendritic ice crystals

Experimental investigation of the dynamics of spontaneous pattern formation during dendritic ice crystal growth