The theory of miscible dispersion is extended to interphase transport systems. As a specific example miscible dispersion in laminar flow in a tube in the presence of interfacial transport due to an irreversible first-order reaction at the wall is analysed by an exact procedure. A new exact dispersion model which accounts for dispersion with interphase transport is derived from first principles. The new concept of an ‘exchange coefficient’ arises naturally. This coefficient depends strongly on the rate of interfacial transport. Such transport also affects the convection and dispersion coefficients significantly. A general expression is derived which shows clearly the time-dependent nature of the coefficients in the dispersion model. The complete time-dependent expression for the exchange coefficient is obtained explicitly and is independent of the velocity distribution in the flow; however, it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large-time evaluations are made for the convection and dispersion coefficients, but these are sufficient to give useful physical insight into the nature of the problem. When the rate of the wall reaction approaches zero the exchange coefficient also approaches zero and the other two coefficients approach their proper values in the absence of interfacial transport. At the other extreme of rapid wall reaction rates, the convection coefficient is more than 50 %
larger
than its value in the absence of interfacial transport and the dispersion coefficient is an
order of magnitude smaller
than that for zero interphase transport.
Dispersion of a non-uniform slug in time variable fully developed laminar flow is studied by an exact method which in principle is valid for all values of time. A generalized dispersion model, which involves an infinite set of time-dependent coefficients
K
i
(
T
), arises naturally as a consequence of the analysis. Expressions are obtained from first principles for the convective coefficient
K
1
(
T
), the apparent diffusion coefficient
K
2
(
T
), and the rest of the coefficients
K
i
(
T
). The convective coefficient
K
1
(
T
) is a new quantity which is time dependent, even if the velocity field is steady, because the initial distribution of solute is non-uniform. The general method of analysis proposed is applied to the particular case of a slug of material of length
x
s
and radius
aR
which is initially symmetrically located in a tube of radius
R
, and then is dispersed in steady laminar flow. Breakthrough curves for various downstream positions show that the mean velocity of the material in the slug is greater than the average velocity of flow for small residence times and, as one would expect intuitively, approaches this value as the distance between the injection and observation points increases. It also is shown that for
T
≲ 0.5,
K
2
, the axial dispersion coefficient, decreases as the initial slug radius decreases. However, for all values of '
a
', both
K
1
and
K
2
approach the asymptotic values of —½ and
(Pe)
-2
+ 1/192 respectively for values of dimensionless time
T
≳ 0.5. Since the initial concentration distribution of solute in the slug affects the time of arrival of the peak mean concentration at a downstream location, this may cause errors in the estimation of mean flow rates by tracer techniques. For example, if one injects a quantity of material into a stream and assumes it is uniformly distributed across the tube, when in reality it occupies only a part of the tube, this leads to overestimating the average flow velocity. This may be of practical importance in a variety of applications.
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