Development of Squeeze Flow models for Thermal Interface Materials contained between planar and non-planar geometries

The goal of this thesis is to analytically model the Squeeze Flow behavior of particle-filled Thermal Interface Materials (TIMs) contained between planar and non-planar geometries. The fluid models studied in this thesis are both Newtonian and non-Newtonian in nature. Specifically, the Newtonian behavior is modeled as a power- law fluid, which is a more general representation of Newtonian fluid. For power-law fluids, different index values are used to address shear thickening and shear thinning fluid behavior. The non-Newtonian behavior is modeled as a Bingham fluid, which includes an yield strength beyond which flow begins (viscoplastic fluid). The parallel plate geometries between which the fluids are squeezed are of circular, rectangular, and square shapes. The non-planar geometry considered involves a cylindrical post at the center of one of the two circular disks. The velocity, pressure, and force solutions are obtained for each model. In an effort to model real TIMs that contain a particle phase, the homogenized, effective viscosity of the fluids are incorporated into the developed analytical models. The three models used to homogenize particle- filled fluids are: Einstein\u27s model, Bruggeman\u27s model, and Maxwell-Garnett\u27s model. These models are constructed on bases of a well separated approximation, which means particles are far enough from each other to influence others. These models are valid only for low volume fraction of particles. In reality, these TIMs have high volume of particles in them, which can\u27t be captured by analytical models. For these highly particle-filled TIMs, numerical models are required. The developed analytical solutions to Newtonian behavior of the fluids are validated using squeeze flow models created in a commercial finite element code (COM- SOL). From the non-planar geometries, it is confirmed that as the post size is reduced to zero, the derived results reduce to parallel plate solutions. The influence of the size of the post on the force is systematically analyzed from which it is observed that the force required to compress the fluid increases with the post size, and that the force solution deviates by a greater amount from the parallel plate solution. From planar plate geometry, it is inferred that, for the same type fluid present within the plates of different shapes, circular plates require the most force to squeeze the material, whereas the rectangular plates require the least force. A detailed analysis is carried out on the fluid contained within rectangular plates to determine the squeezing force as a function of back pressure, fluid yield strength, and fluid viscosity. A comprehensive study is carried out to determine the Bond-Line Thickness (BLT) of Newtonian and Bingham fluids contained within circular plates. It is demonstrated that finite BLT is achieved in-case of fluids with yield stress. It is shown that materials with greater yield strength, produce higher BLTs. From viscous effects, it is inferred that greater the viscosity of the fluid, the greater the time it takes to reach the final state. The effect of back pressure is shown to increase the BLT. Lastly, it is shown that as particles are added into the fluid, the effective viscosity increases and as a result a greater force is required to squeeze the fluid material