A theory has been developed for heat or mass transfer between phases which may have unsteady time dependent velocity fields. The configuration analyzed involves two concentric tubes, but the analysis can be extended to more than two phases, or streams, and to noncylindrical cross sections. For the configuration considered, the dispersion coefficient is found from first principles.
It is noteworthy that the dispersion model given by Equation (15) or (63) and (64), which is consistent with the basic continuum model of Equations (8) and (9), is based on the superficial velocity rather than the interstitial velocity. This strongly suggests that experimental observations on packed beds, or other multiphase systems, should be interpreted on the basis of um, the superficial velocity, rather than the interstitial velocity which has been used often in the past.