Numerical analysis of particle transport during solidification using models based on stochastic differential equation

Abstract

In the present work, a comprehensive theoretical model is developed to describe the particle transport mechanisms in a solidifying binary melt in the presence of random thermofluidic fluctuations offered by the surrounding fluid medium. The detailed transport phenomena in the particle and bulk phases are coupled together through a stochastic formalism, capturing the physical mechanisms and consequences of complex interparticle interactions and the associated growth and/or dissolution of the crystals. The equation of the motion of the particles is modelled using the theory of stochastic differential equations. Numerical simulation study reveals the statistically randomised nature of the evolution of particle phase, which otherwise cannot be captured from a purely deterministic viewpoint. The mathematical model is also tested by comparing present numerical results with reported experimental observations; a very good agreement can be observed in this regard, thereby establishing the authenticity of the proposed formulation.