HR: 0830h
AN: H51C-1051    [PDF]
TI: A Mathematical Formulation for the Effects of Nonlinear Chemical Reactions upon Taylor Dispersive Phenomena
AU: * Wright, E S
EM: ewright@uakron.edu
AF: University of Akron, Dept. Theoretical & Applied Math, Akron, OH 44325-4002 United States
AU: Aleem, T
EM: ta11@uakron.edu
AF: University of Akron, Dept. Theoretical & Applied Math, Akron, OH 44325-4002 United States
AB: In 1953, G.I.~Taylor published his landmark paper concerning the transport of a contaminant dissolved in a fluid flowing through a pipe of narrow diameter. He demonstrated that an interaction between the transverse variations in the fluid's velocity field and the transverse diffusion of the solute yielded an effective downstream mixing mechanism for the transverse average of the solute. This mechanism has since been dubbed ``Taylor Dispersion.'' Since his original publication, many related studies have surfaced. These include generalizations of channel geometry, generalizations of the velocity field (including turbulent field), applications to sedimentation problems, etc. However, much less attention has been given to the effects of nonlinear chemical reactions upon a {\sl system} of solutes undergoing Taylor Dispersion. We present a rigorous mathematical model for the evolution of the transverse averages of reacting solutes that travel within a fluid flowing down a pipe of arbitrary cross-section. The technique for deriving this model is a generalization of a multiple scales perturbation approach described by P.C.~Fife for linear (reactionless) problems. The key outcome is that while one still finds an effective mechanism for downstream mixing, but also there is also a effective mechanism for nonlinear advection.
DE: 1806 Chemistry of fresh water
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
SC: Hydrology [H]
MN: 2003 Fall Meeting