Dispersion in flow through small tubes

A new method is presented for obtaining asymptotic solutions of the now classical problem of the dispersion of a solute in a medium flowing through a tube of small diameter. Features of the method (a non-standard twotiming technique) are: (1) it is capable of treating arbitrary time-dependent flow fields and tubes of arbitrary cross-section; (2) the approximate solutions constructed are valid immediately after the initial time rather than after a time lag; (3) approximations to any desired order may be readily obtained; (4) their asymptotic validity may be proved rigorously. ‘Transient’ terms as well as ‘developed’ terms arise naturally in the treatment; the former decay rapidly in time.