In chapter 3 of our paper we present equations of motion for continuous mass distribution subject to hydrodynamic forces in their most general form. We start with equations for discrete mass particles and then transform the equations so that it is appropriate for a continuous mass distribution. As we do that, new forms of interactions are generated and we successfully include these interactions, using the propagator theory, in the general form of our hydrodynamic equations for continuous mass distributions. We also took a deeper mathematical description of rotational flows. We were able to explain many physical phenomena successfully by our treatment of rotational flows in a more concrete and simple way, for example, the phenomenon of ripples that appear on ocean beaches and in desert sands. In chapter 4 we study the behavior of water surfaces. A liquid drop of water takes on a spherical shape because of the phenomenon of surface tension. A physical model based on the arrangement which the water molecules have on the surface is introduced to explain the above phenomenon. A mathematical model, as well as the physical model mentioned above, is introduced to describe the kind of forces involved on a wavy surface. The equations obtained describe the phenomenon of surface tension on a microscopic level very successfully. In chapter 5 we apply the results of chapters 3 and 4 to get an equation that gives a critical dynamical value which govern the interactions between the moving fluid and the dust particles residing on the ground. / Graduation date: 1996

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Cyrus K. Aidun; Committee Member: Marc K. Smith; Committee Member: S. Mostafa Ghiaasiaan. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This thesis focuses on the lattice-Boltzmann method (LBM) and its ability to simulate immiscible two-phase flow. We introduce the main lattice-Boltzmann-based approaches for analyzing two-phase flow: the color-fluid model by Gunstensen, the interparticle-potential model by Shan and Chen, the free-energy model by Swift and Orlandini, and the mean-field model by He. The first objective is to assess the ability of these methods to maintain continuity at the interface of two fluids, especially when the two fluids have different viscosities or densities. Continuity issues have been mentioned in the literature but have never been quantified. This study presents a critical comparison of the four lattice-Boltzmann-based approaches for analyzing two-phase flow by analyzing the results of the two-phase Poiseuille flow for different viscosity ratios and density ratios. The second objective is to present the capability of the most recent version of the color-fluid model for simulating 3D flows. This model allows direct control over the surface tension at the interface. We demonstrate the ability of this model to simulate surface tension effects at the interface (Laplace bubble test), stratified two-phase flows Poiseuille two-phase flow), and bubble dynamics (the free rise of a bubble in a quiescent viscous fluid).