Phase-field investigation of non-isothermal solidification coupled with melt flow dynamics
Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to model and simulate these dynamics. However, most existing models neglect essential thermodynamic couplings, particularly the capillary (Korteweg) stress in the momentum equation. This stress, which arises from the coupling between the phase field and the melt flow, accounts for thermal capillary effects during non-isothermal solidification. Neglecting it leads to models inconsistent with non-equilibrium thermodynamics and incapable of capturing capillarity-driven melt flow. In this work, we present a thermodynamically consistent, non-isothermal phase-field model for solidification coupled with melt flow, incorporating cross-coupling terms and explicitly including the Korteweg stress in the momentum equation. Model validation is performed for solidification-only cases, followed by simulations of dendritic growth under melt flow. The results show that thermal capillary effects induce flow near the interface, influencing dendrite tip velocity and morphology. Simulations under forced convection further demonstrate asymmetric dendrite growth due to the imposed flow field. Additionally, we numerically demonstrate the influence of viscosity interpolation schemes on enforcing the no-slip boundary condition in phase-field models with melt flow.