Mathematics Commons^™

Flame Dynamics In Steady Strained Flows, Zili Huang

Dissertations

In this dissertation, the response of a premixed flame to time-dependent strained flow fields is investigated. Because of the potential application to turbulent combustion modeling, the main focus is on the particular case of a flame in stagnation point flow with an imposed oscillatory strain rate. The flame is modeled as a hydrodynamic discontinuity separating burned from unburned gasses. To complete the formulation of the problem, conditions relating the fluid variables across the flame front are needed, as is a flame speed equation that determines the evolution of the discontinuity. These conditions are derived through asymptotic analysis of the flame …

A Theoretical Study Of Bubble Motion In Surfactant Solutions, Yanping Wang

Dissertations

We examine the effect of surfactants on a spherical gas bubble rising steadily in an infinite fluid at low and order one Reynolds number with order one and larger Peclet numbers. Our mathematical model is based on the Navier-Stokes equations coupled with a convection-diffusion equation together with appropriate interfacial conditions. The nonlinearity of the equations and boundary conditions, and the coupling between hydrodynamics and surfactant transport make the problem very challenging.

When a bubble rises in a fluid containing surface-active agents, surfactant adsorbs onto the bubble surface at the leading edge, convects to the trailing edge by the surface flow …