On the dispersion of a solute in a fluid flowing through a tube

Sir Geoffrey Taylor has recently discussed the dispersion of a solute under the simultaneous action of molecular diffusion and variation of the velocity of the solvent. A new basis for his analysis is presented here which removes the restrictions imposed on some of the para­meters at the expense of describing the distribution of solute in terms of its moments in the direction of flow. It is shown that the rate of growth of the variance is proportional to the sum of the molecular diffusion coefficient, D, and the Taylor diffusion coefficient Ka2U2/D, where U is the mean velocity and a is a dimension characteristic of the cross-section of the tube. An expression for k is given in the most general case, and it is shown that a finite distribution of solute tends to become normally distributed.