Experimental Analysis of the Diffusion of a Passive Scalar Subject to Steady Flow in a Circular Pipe*

The Taylor Pipe Flow experiment at UNC's Joint Fluids Lab was designed to be a continuation of the research on the dispersion of soluble matter through a tube conducted by G.I. Taylor in the '50s. We explore analytically, numerically and experimentally the evolution of the dispersion of a solute, focusing primarily on computing and measuring the first four moments (mean, variance, skewness and kurtosis) of solute concentration in two-dimensional channel models and three-dimensional glass pipes with circular or square cross-sections. Our experimental setup allows us to observe the effects of Poiseuille flow as either advection or diffusion dominates in different regimes and timescales set by the Taylor time scale $ t_T \propto a^2/\kappa$, depending on the cross-sectional characteristic length $a$ and the diffusion coefficient $\kappa$. We conduct experiments to illustrate these regimes, characterized by the dimensionless P\'{e}clet number, $Pe = u \,a /\kappa$, where $u$ is the characteristic velocity. Experimentally, we take the intensity of a fluorescein-dyed portion of distilled water and find its corresponding concentration by solving an inverse problem of intensity to concentration. The experimental results validate the theoretical approach.