A numerical study of diffusion of nanoparticles in a viscous medium during solidification

In the field of additive manufacturing process, laser cladding is widely considered due to its cost effectiveness, small localized heat generation and full fusion to metals. Introducing nanoparticles with cladding metals produces metal matrix nanocomposites which in turn improves the material characteristics of the clad layer. The strength of the laser cladded reinforced metal matrix composite are dependent on the location and concentration of the nanoparticles infused in metals. The governing equations that control the fluid flow are standard incompressible Navier-Stokes and heat diffusion equation whereas the Euler-Lagrange approach has been considered for particle tracking. The mathematical formulation for solidification is adopted based on enthalpy porosity method. Liquid titanium has been considered as the initial condition where particle distribution has been assumed uniform throughout the geometry. During the solidification process of liquid titanium, particle flow and distribution has been observed until the entire geometry solidified. A numerical model implemented in a commercial software based on control volume method has been developed that allows to simulate the fluid flow during solidification as well as tracking nanoparticles during this process. The influence of the free surface of the melt pool has a high importance on the fluid flow as well as the influence of pure natural convection. Thus both buoyancy and Marangoni convection have been considered in terms of fluid flow in the molten region. A detailed parametric study has been conducted by changing the Marangoni number, convection heat transfer coefficient, constant temperature below the melting point of titanium and insulated boundary conditions to analyze the behavior of the nanoparticle movement. With the change in Marangoni number and solidification time, a significant change in particle distribution has been observed. The influence of increase in Marangoni number results in a higher concentration of nanoparticles in some portions of the geometry and lack of nanoparticles in rest of the geometry. The high concentration of nanoparticles decrease with a decrease in Marangoni number. Furthermore, an increase in the rate of solidification time limits the nanoparticle movement from its original position which results in different distribution patterns with respect to the solidification time.