Dye Dispersion Studies

The partial differential equation for the dispersion of dye from a point source in an infinite fluid is presented and the general solution for the one, two and three dimension cases is derived. The characteristics of the dye dispersion curve is determined as well as, the rate of diminution of the peak concentration of dye. Practical methods for determining the longitudinal, lateral, and vertical diffusion coefficients that govern the dye dispersion rates are given and some of the methods are demonstrated with numerical examples of actual studies. Data pertaining to the magnitude of diffusion coefficients is presented. The wide range of diffusion coefficients is explained by noting that the different diffusion coefficients may have different significant periods of time associated with each distinct coefficient. The data and theory presented enable a realistic design and interpretation of dye dispersion studies in fresh and tidal streams, lakes, bays, and oceans.