Find your next learning step
Preferential flow can deliver part of a solute pulse quickly while another part exchanges slowly with less mobile soil water. Two-domain models make that split explicit. Dual-porosity, mobile-immobile and dual-permeability are not interchangeable labels: they make different claims about where water flows, how solute is stored and how mass crosses the interface.
Open the chapter contents · Soil Science root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Choose the two-domain model before fitting parameters
A mobile-immobile or dual-porosity transport model often lets advection occur mainly in a mobile region while an immobile region stores solute and exchanges mass. A dual-permeability model allows water and solute flow in both a faster domain and a slower matrix domain.
Name the domains physically—macropores and matrix, inter- and intra-aggregate pores, fractures and blocks—only when measurements support that interpretation. Mathematically fitted fast and slow domains can be effective representations rather than directly observed pore classes.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Write the water and solute bookkeeping
Let θf and θm be volumetric water contents in fast and matrix domains, with θ=θf+θm under the stated volume convention. Each solute balance includes storage, advective-dispersive flux where allowed, reactions and an inter-domain exchange term with opposite signs.
Exchange must conserve mass: what leaves one domain enters the other unless degradation, sorption or an external boundary removes it. A fitted first-order coefficient combines geometry, diffusion distance, interface conductivity and unresolved variability.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a pulse-and-tail mass ledger
Inject a conservative 100 mg tracer pulse. Suppose 30 mg follows connected fast paths and exits early, while 70 mg enters matrix-associated storage. If 10 percent of the remaining stored mass exchanges into the mobile outflow per interval, the first three delayed releases are 7.00, 6.30 and 5.67 mg.
| Stage | Fast-path exit | Matrix mass before release | Delayed release | Matrix mass after |
|---|---|---|---|---|
| Arrival | 30.00 mg | 70.00 mg | 0.00 mg | 70.00 mg |
| Interval 1 | 0 | 70.00 mg | 7.00 mg | 63.00 mg |
| Interval 2 | 0 | 63.00 mg | 6.30 mg | 56.70 mg |
| Interval 3 | 0 | 56.70 mg | 5.67 mg | 51.03 mg |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Read early breakthrough and late tailing together
A connected fast domain can create arrival earlier than a single-domain advection-dispersion model predicts. Slow release from matrix or immobile regions can then sustain concentrations after the main mobile pulse has passed.
Either feature alone is not diagnostic. A broad input pulse, spatially variable velocity, rate-limited sorption, diffusion into aggregates, sampling volume or detection limits can also shape breakthrough and tailing.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change the exchange rate and preserve total mass
Keep the same 70 mg stored mass but change the per-interval release fraction from 0.10 to 0.25. The first delayed release becomes 17.5 mg and only 52.5 mg remains; the tail is shorter even though the eventual conservative recovery can still approach the same total.
| Release fraction | First delayed release | Mass remaining | Expected tail |
|---|---|---|---|
| 0.05 | 3.50 mg | 66.50 mg | Longer and flatter |
| 0.10 | 7.00 mg | 63.00 mg | Reference case |
| 0.25 | 17.50 mg | 52.50 mg | Shorter and steeper |
| 0.50 | 35.00 mg | 35.00 mg | Rapid exchange |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Separate dual porosity from dual permeability
In a dual-porosity flow idealisation, one region may be hydraulically mobile while the other is effectively stagnant for advection. In dual permeability, both regions have their own flow equations and exchange water as well as solute.
The distinction matters during infiltration, drainage and changing saturation. A matrix that is slow during a storm is not necessarily immobile over seasonal time. Model structure should follow the process and observation window.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect the established soil-water routes
The preferential-flow guide identifies bypass evidence. The hydraulic-conductivity guide separates flux capacity from water storage.
Use the Richards-equation guide for boundary and storage accounting and the pedotransfer guide when hydraulic parameters are predicted rather than measured.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Design observations that can separate mechanisms
Combine flux concentrations with resident concentrations, water contents, pressure heads and cumulative drainage. Use several pulse lengths or flow rates when possible; one breakthrough curve may not identify mobile fraction, dispersion and exchange rate separately.
Continue sampling far enough into the tail to close mass balance. Compare disturbed and intact cores, dye or imaging evidence, depth profiles and repeated wetting states. Parameter identifiability is an experimental property, not only an optimiser setting.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
Two fitted domains do not prove exactly two pore populations. Exchange coefficients can compensate for dispersion, sorption kinetics or boundary errors. Parameters estimated at one water content, column length or flow rate may not transfer.
An early peak does not mean most mass used macropores, and a long tail does not mean contamination is harmlessly stored. Low concentrations sustained for long periods can dominate exposure and delayed leaching.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record domain definitions, volume fractions, water-flow equations, solute equations, exchange law, boundary conditions, input pulse, resident and flux sampling, recovery duration, mass closure, sorption and degradation assumptions, parameter correlations, uncertainty and transfer tests.
The USDA Agricultural Research Service groundwater modelling chapter distinguishes uniform, mobile-immobile, dual-porosity and dual-permeability concepts. The USDA-hosted dual-porosity solute-transport model develops water and solute exchange between fracture and matrix regions.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is immobile water completely disconnected?
Not necessarily. It is immobile with respect to the modelled advective time scale but may exchange solute by diffusion or mass transfer.
Why can recovered mass appear too low?
Sampling may stop before the tail ends, mass may remain resident, or unmodelled sorption, degradation and boundary losses may occur. Close the full ledger before assigning a mechanism.
Does a better curve fit justify more domains?
No. Added flexibility needs identifiable parameters, independent evidence and improved prediction in changed conditions.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a flow-rate transfer check
Repeat a tracer experiment at twice the mobile water flux. Predict how the advective arrival time, apparent mobile fraction and exchange opportunity might change. State which observations would distinguish a fixed exchange coefficient from a water-state-dependent one.
Continue through the Soil Science root, the Gold Standard of Education and the How X Works hub.
Top · Contents · Previous · How X Works