The newly developed Particle Interlayer Directed Wetting and Spreading (PIDWAS) technique is a promising new technique used in the joining process with ceramic substrates. A sintered metal powder layer is formed on the ceramic substrate, and liquid silver imbibes into the porous layer by capillary action. This technique has many applications, notably in electronics and electrical storage/conversion devices. The manufacturing of PIDWAS layers relies heavily on the sintering process and spontaneous imbibition. This dissertation seeks to develop numerical methods to introduce tools to aid in the optimization of the manufacturing process. These tools can be used more broadly to simulate and model these processes to further our understanding.First, a sintering simulation accounting for rigid-body motion of grains induced by densification is implemented. During sintering, atoms migrate to decrease the energy of the system via two main mechanisms: coarsening and densification. The phase-field method has been broadly utilized to simulate sintering dynamics because of its convenience in tracking morphology evolution. When a large number of grains is involved, it is common to use the same order parameter to describe multiple grains that are not in direct contact with one another. However, with this treatment it is difficult to handle the rigid-body motion of individual grains during densification. In this work, an implementation scheme is introduced to overcome the challenge of calculating individual particle motion in the existing equations. It uses a grouping algorithm and sets a cutoff radius on each grain for calculating the particle velocity during densification. This method allows for the incorporation of the densification mechanism, which has been commonly ignored in previous work, into phase- field sintering models in three-dimensional simulations with a large number of particles/grains. Moreover, combined with Smoothed Boundary Method (SBM), material properties of sintered microstructures can be calculated during the sintering processes. A single-phase flow simulation is then developed. Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this dissertation, a diffuse interface embedded boundary method known as the Smoothed Boundary Method is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier-Stokes equations in terms of this domain parameter, using only algebraic identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Results from the SBM-formulated Navier-Stokes equations are compared with results generated using a conventional sharp-interface description. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient. Next, an improved macroscopic model for imbibition velocity is developed and the imbibition velocity of molten silver into a porous nickel interlayer on a non-wetting sapphire substrate is investigated. Several imbibition models for porous media that use bulk characteristics and material properties are employed to predict the imbibition front location as a function of time. The model predictions are compared to experimental observations. It is found that pore size distribution is a better predictor of imbibition velocity than correlations based on permeability and porosity. The tortuosity of the microstructure is also found to have a significant effect and should be considered. A new model accounting for the different liquid contact angles on the underlying substrate and the porous interlayer material is proposed and achieves better agreement with the experimental observations. Finally, a two-phase fluid flow simulation is developed, combining the Smoothed Boundary Method with the Navier-Stokes equations for fluid flow and the Cahn-Hilliard equations to track the separate phases. This is implemented with the simplification of phases with equal viscosity and density. While comparison with realistic systems is limited, preliminary results are analyzed.
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