Indicator Dispersal by Convection and Diffusion in Fluid Flow through a Tube.

• The problem of dispersion of an indicator by laminar flow in a cylindrical tube of radius, R, was recently examined by Taylor. Initially the tube may be filled with indicator-free solution, and then the indicator solution "washed in," or it may be filled with solution containing indicator, which is then "washed out" with indicator-free solution. Taylor obtained equations for the mean concentration of indicator in a cross section of tube as a function of time, t, and distance x along the tube. Hereafter this will be designated as mean areal concentration. These equations were obtained for two cases of interest: Case I: dispersion of indicator due to diffusion is negligible compared with dispersion resulting from convective transport; and Case II: though convective transport is still present, the pattern of indicator dispersion results mainly from radial variations of indicator concentration due to diffusion. According to Taylor this latter case obtains if