Simulating transport phenomena in interfacial systems

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The governing equations for the surface phase, in the form established by BAM are developed in the second chapter. These equations are unique in that the surface is treated as a separate entity, with it's own differential equations and surface variables, the bulk phases entering primarily as boundary conditions. In the third chapter the surface equations are used to describe the surface instability of a system first investigated experimentally and theoretically by Linde. Our linear stability analysis, based on the surface balance equations, can extract the stability relations among the surface variables and the rate of energy input, whereas earlier studies had been less successful. In the fourth chapter, the patterns formed in the well-known Benard system are studied using a "finite-difference" representation of coupled nonlinear hydrodynamic equations, representing the system. Surface dynamics play a very significant role in the behavior of this system and when incorporated in the finite difference description of the bulk, one can readily demonstrate the complex interplay of surface and bulk effects. In chapter five we investigate the flow of a gas "bubble" which leaves a thin film as it displaces the liquid between two parallel plates. The finite difference representation of the hydrodynamic equations is restricted to two dimensions but provides not only a description of the movement of the curved gas-liquid interface, but also yields flow patterns in the bulk and at the surface. The interfacial conditions can be varied very quickly within the numerical program and the bubble behavior is studied systematically under a wide range of physical constraints. The thesis concludes, in chapter six, with a discussion of the significance of our results and comments on applications of the equations and computer code developed.
Wassmuth, F. (1990). Simulating transport phenomena in interfacial systems (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from doi:10.11575/PRISM/19129