Mobile, Immobile, and Multiflow Domain Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 269

process was far removed from equilibrium after short flow interruption
durations, and that a significant time period was required to alleviate the
concentration gradient that was established between large and small pore
domains during flowing conditions. In addition, one value of the param-
eter α was used to obtain these simulations for the different columns having
increasing stop flow duration. This finding is significant and lends credence
to physical nonequilibria in soils.
The concentration perturbations that result from flow interruptions place
a constraint on the model simulations such that a limited range in certain
parameter values was acceptable for matching the observed data. As shown
in Figure 8.7, model simulations are highly dependent on the parameter F
where the solid curve represents best simulation of the experimental data.
Large values of F described the rapid breakthrough of the bromide tracer
as well as the ascending and descending limbs of the BTC. However, the
concentration perturbation at the stop flow was completely absent. Smaller
values of F well described the influence of flow interruption. However, the
model grossly overestimated the rapid breakthrough of the tracer. Likewise,
only a limited range of α values could satisfactorily describe the experimen-
tal BTC.
Model sensitivity to a range of the mass transfer coefficient α in describing
Br breakthrough results is illustrated in Figure 8.8. The solid curve repre-
sents best simulation of the experimental data. Small values of α overpre-
dicted the rapid breakthrough of tracer and the concentration perturbation
that resulted from flow interruption. Large values of α described a majority
of the BTCs; however, the simulated concentration perturbation was absent.
If stop flow interruption was not accounted for in the model to describe the
experimental data, the resulting simulations would be less than optimum.
Flow interruption places a constraint on the modeling effort that is advanta-
geous for predictions of observed transport data.
8.4 A Second-Order Approach
In the previous chapter, the second-order reactions associated with sites 1
and 2 were considered as kinetically controlled, heterogeneous chemical
retention reactions (Rubin, 1983). One can assume that these processes are
predominantly controlled by surface reactions of adsorption and exchange.
In this sense, the second-order model is along the same lines as the earlier
two-site model of Selim et al. (1976) and Cameron and Klute (1977). Another
type of two-site model is that of Villermaux (1974), which is capable of describ-
ing BTCs from chromatography columns having two concentration maxima.
In this section, the second-order concept is invoked where processes of sol-
ute retention were controlled by two types of reactions; namely, chemically