Collections > UNC Chapel Hill Undergraduate Honors Theses Collection > Enhanced Diffusion of a Passive Scalar in Taylor Pipe Flow
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In 1953 and 1954, Sir Geoffrey Taylor worked on several papers quantitatively describing how a soluble substance could spread out along with a steady flow through the pipe. This phenomenon was due to a combination of advection and molecular diffusion. After Taylor, various mathematicians have proposed new thoughts on this topic. Rutherford Aris proposed a moment-based method on analyzing the dispersion of the solute. Later on in 1982, N.G Barton adopted the Aris method of moments and solved analytically for the asymptotic of the second moment of the mean of dispersing solute. In 2010, Camassa, Lin and McLaughlin reconsidered the problem and modeled it with a pair of stochastic differential equations. [for equation see paper] in which W1 is an unbounded Brownian motion and W2 is a bounded Brownian motion. From this pair of SDEs, Camassa, Lin and McLaughlin derived an analytic solution for the concentration, as well as an analytic representation of the second moment. This project is to use an experimental setup to verify this analytic solution to the enhanced diffusion of a passive scalar in pipe flow; and this thesis is to provide a mathematical basis of the validity of the experimental setup.