This tutorial describes the Mass Transfer Sorption with Solute Decay applet. The applet implements the two-site non-equilibrium sorption model (CXTFIT-1, Toride et al. 1993), which partitions sorption sites into an instantaneous equilibrium fraction and a kinetically limited fraction, combined with optional first-order decay in the liquid and sorbed phases.
For the mathematical background, see the Solution Tutorial.
The applet is divided into three panels:
Move the mouse cursor over either plot to activate the crosshair slider. The right panel updates with the liquid and sorbed concentrations for each plotted curve at the cursor position.
| Parameter | Symbol | Units | Default | Description |
|---|---|---|---|---|
| Dispersion Coef. | D | L²/T | 0.0005 | Hydrodynamic dispersion coefficient |
| Pore Water Vel. | v | L/T | 0.0100 | Average linear (seepage) velocity of the pore water |
| Porosity | θ | — | 1.0 | Effective volumetric water content (0 < θ ≤ 1). For fully saturated media, θ equals the porosity. |
| Bulk Density | ρ | M/L³ | 1.0 | Dry bulk density of the porous medium |
| Input Conc. | Cf | M/L³ | 1.0 | Source concentration at the inlet boundary during the pulse |
| Pulse Duration | tf | T | 1000 | Duration of the finite concentration pulse at the inlet. After tf, the inlet concentration drops to zero. |
The two-site model splits sorption sites into two types: a fraction f that is at instantaneous equilibrium with the dissolved phase, and a fraction (1−f) that exchanges solute kinetically at rate α.
| Parameter | Symbol | Units | Default | Description |
|---|---|---|---|---|
| Fraction Equil. | f | — | 0.5 | Fraction of sorption sites at instantaneous equilibrium (0 ≤ f ≤ 1). f = 1 gives pure equilibrium retardation only; f = 0 gives pure kinetic sorption. |
| Sorption Coef. | Kd | L³/M | 0.1 | Linear distribution (partition) coefficient between dissolved and sorbed phases |
| Mass Transfer Rate | α | 1/T | 1.0 | First-order mass transfer rate between mobile water and kinetic sorption sites. Must be > 0. |
First-order decay can be applied independently to the dissolved phase, the equilibrium sorbed phase, and the kinetic sorbed phase. Set all rates to zero for a conservative (non-decaying) solute.
| Parameter | Symbol | Units | Default | Description |
|---|---|---|---|---|
| Liquid Decay | μl | 1/T | 0.0 | First-order decay rate in the dissolved (liquid) phase |
| Equil. Sorbed Decay | μse | 1/T | 0.0 | First-order decay rate on the equilibrium sorption sites |
| Kinetic Sorbed Decay | μsk | 1/T | 0.0 | First-order decay rate on the kinetic sorption sites |
Choose whether to observe the concentration as a function of time at a fixed location, or as a function of space at a fixed time:
| Option | x-axis | Description |
|---|---|---|
| Fixed Distance | Time [T] | Plot concentration vs time at a fixed observation location x. Produces a breakthrough curve (BTC). Enter the distance in the adjacent field. |
| Fixed Time | Distance [L] | Plot concentration vs position at a fixed time snapshot t. Produces a concentration profile. Enter the time in the adjacent field. |
Both the top panel (liquid phase) and the bottom panel (sorbed phase) always update simultaneously. The sorbed concentration shown is the total sorbed concentration: s = se + sk.
| Mode | Description |
|---|---|
| Auto | The x-axis range (time or distance) is computed automatically based on transport parameters. This is the recommended starting point. |
| Manual | Enter explicit minimum and maximum values for the horizontal axis. Use this to zoom in on a region of interest or to compare curves over the same range. |
Compute Curve runs the CXTFIT-1 solver and plots the result on both panels. With Multiple Curves checked, each compute overlays a new curve in a different color — up to five curves. This is useful for comparing the effect of varying a single parameter (e.g., different f values).
Clear Curves removes all plotted curves and resets both panels. Show Data Table opens a tabbed modal showing the numerical output for each curve; use the CSV button inside to download the data.
Move the mouse over either plot canvas to activate the crosshair slider. A dashed vertical line appears on both panels at the cursor position. The right panel updates live, showing:
- Slider Position — the x/t coordinate of the cursor
- Curve Values — a row per curve with a color swatch, the interpolated liquid-phase concentration, and the interpolated sorbed-phase concentration at that position
Move the cursor off the plot area to hide the slider.