Computational studies are conducted on two multiphase systems using a front-tracking/finite-difference method developed for direct numerical simulations of time-dependent systems. The two problems are selected to demonstrate the ability of this numerical method to accommodate problems with differing degrees of complexity. In this work, both electrohydrodynamic effects on suspended droplets and the solidification of multiple, molten-metal droplets impinging on a cold wall are investigated.;In part I of this work, electrohydrodynamic effects on uncharged, dielectric droplets suspended in an ambient fluid are examined. Most of the previous work on electrohydrodynamic effects of leaky dielectric droplets have been computed under Stokes flow conditions. Finite Reynolds number simulations are conducted to study the interaction of leaky-dielectric droplet pairs. Computational results show that inertial effects decrease the rate of droplet motion induced by viscous circulatory motion associated with leaky-dielectric response in an external electric field. The electrohydrodynamic study also examines the interaction of multiple deformable droplets suspended in a Poiseuille flow as a possible means of manipulating global flow characteristics in a channel. The effects of electric field strength, number of droplets, and droplet volume fraction on droplet distribution within the channel are discussed.;In part II of this work, the deformation and solidification of multiple, molten-metal droplets impinging on a cold surface are examined. Numerical simulations are performed in axisymmetric coordinates to determine the effects of Weber number, Peclet number, and droplet deposition frequency on the final shape of towers made from stacked droplets. A parameter space is determined which allows for the construction of towers with a uniform diameter. The investigations of the droplet deposition and solidification also include fully three-dimensional simulations which are necessary to observe the more complex interactions that cannot be captured in axisymmetric calculations. These three-dimensional and axisymmetric numerical results are compared to one another in order to validate the accuracy of the numerical method.
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