This tutorial explains the controls and features of the Multiple Solutes, Equilibrium Sorption with Sequential Decay applet. The applet implements the analytical solution of van Genuchten (1985) for one-dimensional transport of up to four sequentially decaying solute species, with equilibrium linear sorption, advection, and dispersion in a semi-infinite porous medium with a finite-pulse source.
For the mathematical background see the Solution Tutorial.
The applet is organized into three panels. A species-selection dropdown sits above the panels in a model row:
Both plot panels can be displayed simultaneously. The top canvas always shows the C vs Time (breakthrough curve) result; the bottom canvas shows the C vs Distance (concentration profile) result. Move the cursor over either canvas to activate the crosshair slider.
The dropdown at the top of the screen selects how many sequentially decaying species to include. The decay chain always starts from the parent compound C1:
| Selection | Decay Chain |
|---|---|
| 1 — Single Solute | C1 only (standard ADE with sorption and decay) |
| 2 — Chain C1 → C2 | C1 → C2 |
| 3 — Chain C1 → C2 → C3 | C1 → C2 → C3 |
| 4 — Chain C1 → C2 → C3 → C4 | C1 → C2 → C3 → C4 |
Only the rows for the selected number of species are shown in the Species Parameters table. Species are color-coded consistently across all plots and tables.
These parameters describe the physical domain and apply equally to all species:
| Parameter | Symbol | Units | Default | Description |
|---|---|---|---|---|
| Velocity | v | L/T | 1.0 | Average pore-water velocity (seepage velocity) in the longitudinal direction |
| Dispersion | D | L²/T | 0.5 | Longitudinal hydrodynamic dispersion coefficient |
| Pulse Length | tp | T | 200.0 | Duration of the source concentration pulse at x = 0. After tp, the inlet concentration of the parent (C1) drops to zero; daughters already in the domain continue to decay and transport. |
Each active species has three parameters entered in the species table. Species are identified by their color:
C1 C2 C3 C4
| Column | Symbol | Units | Description |
|---|---|---|---|
| Input Concentration | C0 | M/L³ | Source concentration at x = 0 during the pulse. Set to 0 for daughter species that are produced only by decay of the parent; they are not present in the source zone. |
| Retardation Factor | R | — | Accounts for linear equilibrium sorption: R = 1 + ρKd/θ. Must be ≥ 1. R = 1 means no sorption. |
| Aqueous Decay | μ | 1/T | First-order decay rate in the aqueous phase. Decay only applies to the dissolved phase, not the sorbed phase. Set to 0 for a conservative (non-decaying) species. |
Choose how to view the solution at each compute:
| Option | x-axis | Description |
|---|---|---|
| Fixed Position | Time [T] | Plot concentration vs time at a fixed spatial location x. This is a breakthrough curve (BTC). Enter the observation distance in the adjacent field. |
| Fixed Time | Distance [L] | Plot concentration vs position at a fixed time snapshot t. This is a concentration profile. Enter the time in the adjacent field. |
When Show Both Plots is enabled (see Options), each compute generates both solution types simultaneously. The Fixed Position result appears in the top canvas; the Fixed Time result in the bottom canvas. The two panels have independent scale bars.
| Option | Description |
|---|---|
| Show Both Plots | When checked, both C vs Time and C vs Distance are computed and displayed simultaneously in the two canvas panels. When unchecked, only the selected solution type is plotted. |
| Multiple Runs | When checked, each click of Compute overlays a new set of curves on top of the existing ones. Each successive run is drawn with a different line-dash pattern (solid, dashed, dotted, dash-dot, …) so overlapping runs remain distinguishable even for the same species colors. Uncheck to replace all existing curves on the next compute. |
Compute evaluates the van Genuchten (1985) analytical solution with the current parameter set and adds it to the active plot(s). Each species is drawn in its assigned color. In Multiple Runs mode, each successive run uses a distinct line-dash pattern, and an Active Runs list appears below the buttons showing all runs with delete controls.
Clear All removes all runs and curves and resets both canvases.
Move the mouse cursor over either plot canvas to activate the crosshair slider. A vertical dashed line appears at the cursor position. The Cursor Data table in the right panel updates live, showing one row per species per run with:
- A color swatch identifying the species and run dash-pattern
- A curve label (e.g., Run 1 C1)
- The x (distance) or t (time) coordinate at the cursor
- The interpolated concentration at that position
All runs and species are shown simultaneously, making it easy to compare breakthrough times and peak concentrations.
Clicking Show Data Table (right panel) opens a modal window with the full numerical dataset for all computed curves. The modal is organized with:
- Run tabs at the top — one per computed run
- Within each run: columns for the x or t coordinate and the concentration of each species (C1, C2, …)
- Download CSV — exports the currently selected run's data as a comma-separated file for use in spreadsheets or other analysis tools
Each canvas panel has an independent scale bar placed directly above it. The min and max fields set the x-axis range (time or distance):
| Field | Default | Description |
|---|---|---|
| min | 0.0 | Left edge of the x-axis. Usually left at 0. |
| max | 200 | Right edge of the x-axis. Increase to see long-term behavior; decrease to zoom in on the breakthrough front. |