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5. Results

5.1. Model Sensitivity Analysis

[11] We examined the sensitivity of particle breakthrough at the sampling positions to changes in the parameters that govern advection, dispersion, and particle immobilization kinetics. This involved comparing a simulation generated with a base-case set of parameter values to modeled results obtained by individually adjusting , D_V, and v₂ from their base-case values of 2 h^-1, 0.005 m² h^-1, and 0 m h^-1, respectively.

[12] Model calculations made with the base-case parameters reveal that particle concentrations for the sampling-site positions on the left side of the channel (i.e., LS, LM, LD) are identical to those computed for corresponding depths on the right side (i.e., RS, RM, RD) (Figure 2a). Three conditions combine to produce this symmetry in particle breakthrough: the left- and right-side sampling sites are spaced equal distances from the channel center, the injection source is centered laterally within the channel, and the flow field parallels the channel walls (i.e., V = v₁ and = 0°). Peak breakthrough concentrations at the mid-depth samplers are greatest at the central sampling point (CM) and decrease towards the left (LM) and right (RM) owing to dilution by lateral dispersion. On both the left and right sides of the channel, breakthrough concentrations decline with vertical distance away from the injection source (see Figure 1B for sampler depths); that is, concentrations at the mid-depth samplers (LM and RM) are higher than concentrations at the shallow samplers (LS and RS), which, in turn, are higher than those at the deep samplers (LD and RD) (Figure 2a).

[13] Variation in the value of controls the magnitude of the breakthrough concentrations. An increase in from 2 h^-1 to 3 h^-1 leads to a 3-fold decline in peak breakthrough (compare Figures 2a and 2b). Changes in do not affect the apparent dispersion or travel time of the suspended particles, however. Because the immobilization rate varies linearly with C, increases in promote proportionate reductions in breakthrough concentrations at all sampling positions.

Figure 2. Model-calculated TiO2 breakthrough curves for (a) base-case parameter values, (b) = 3 h-1, (c) DV = 0.001 m2 h-1, and (d) v2 = -2 m h-1. (The y-axis scaling varies between plots.) The breakthrough curves are referenced by the lateral and vertical positions of the samplers (see Figure 1b). In D, only breakthrough curves calculated for the mid-depth samplers are shown. [larger image]

[14] The vertical dispersion coefficient (D_V) regulates the distribution in particle concentrations between the mid-depth sampling sites and the shallow and deep sampling sites. Vertical mixing decreases as D_V declines from its base-case value to 0.001 m² h^-1, so the particles (which were injected near mid depth) do not spread in appreciable concentrations to the shallow and deep sampling sites, and particle transport is relegated to the middle of the water column, resulting in comparatively higher breakthrough concentrations at the mid-depth samplers (compare Figures 2a and 2c).

[15] We adjusted v₂ from its base-case value of zero in order to explore the effects of cross-channel flow on particle breakthrough. For v₂ = -2 m h^-1 (the negative sign signifies that cross-channel component of flow is from right to left), symmetry in particle breakthrough between the left and right sampling sites disappears and concentrations on the left side of the channel grow at the expense of concentrations on the right side of the channel (compare Figures 2a and 2d). Cross-channel flow also lowers peak breakthrough concentrations because particles exit the channel before being detected at the monitoring points.

5.2. Comparison of Field Observations and Model Calculations

[17] Although deviations between experimental and calculated results exist, the model matches the range in observed breakthrough behavior reasonably well (Figure 3). The best-fit values of v₁ and v₂ are 5.1 and -1.5 m h^-1, respectively, which corresponds to a mean surface-water velocity (V) of 5.3 m h^-1. The cross-channel component of flow ( = -16.4°) leads to the asymmetry in breakthrough concentrations between the left and right sides of the channel.

[18] Dispersion of the TiO₂ particles was small. Best-fit estimates of D_Lon and D_Lat are nearly equal at 0.16 and 0.15 m² h^-1, respectively, and 150 times greater than D_V (= 0.001 m² h^-1). The small D_V is consistent with our observations that the TiO₂ plume traveled through the center of the water column and did not spread in substantial levels to the shallow and deep samplers.

[19] The optimal value of is 3.55 h^-1. Based on this estimate, the time scale for immobilization (^-1) is 0.3 h, or 4.5 fold less than the time required for particles to be transported by advection from the injection source to the sampler array. The absence of tailing on the experimental breakthrough curves suggests that captured particles were not remobilized during the course of the experiment.

Figure 3. Measured (symbols) and modeled (lines) breakthrough concentrations of TiO2. Measured and modeled TiO2 concentrations at LD, RS, and RD remained at baseline levels during the injection and are not shown. [larger image]