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A disconnected gas or non-wetting-liquid ganglion can remain immobile while water flows around it. Mobilisation begins when the viscous pressure difference acting across the cluster can overcome the capillary barriers at its leading and trailing menisci. Because pores, clusters and wettability vary, a sample does not switch at one magic pressure. It desaturates across a range that must be tied to a capillary-number definition and a flow history.
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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. Define the trapped cluster and driving force
A ganglion is a disconnected non-wetting-phase cluster spanning one or more pores. It is trapped when the imposed pressure field cannot move both bounding interfaces through their next constrictions.
The relevant driving force is a pressure difference across the ganglion, not simply the inlet pressure. Cluster length, pathway permeability and local pressure gradients control how much viscous drop reaches the interfaces.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Write a threshold pressure balance
A simple mobilisation test compares the viscous drop ΔPv across a cluster with the difference between downstream and upstream capillary entry pressures. Mobilisation becomes possible when ΔPv exceeds that capillary barrier.
The Young–Laplace scale 2γ cosθ/r helps estimate each throat pressure, but irregular curvature, advancing and receding angles, cooperative filling and dynamic contact lines shift the threshold.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a critical-gradient ledger
Take water–air surface tension γ=0.072 N/m and cosθ=1. Suppose the downstream throat radius is 10 μm and the upstream release throat is 20 μm. Their ideal capillary scales are 14.4 and 7.2 kPa, so the barrier is 7.2 kPa. Across a 2 mm ganglion, the illustrative critical gradient is 7.2 kPa/0.002 m=3.6 MPa/m.
| Element | Radius or length | Ideal pressure | Role |
|---|---|---|---|
| Upstream throat | 20 μm | 7.2 kPa | Release side |
| Downstream throat | 10 μm | 14.4 kPa | Entry side |
| Barrier | — | 7.2 kPa | Difference to overcome |
| Ganglion length | 2 mm | 3.6 MPa/m | Illustrative gradient |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Build a capillary desaturation curve
A capillary desaturation curve plots residual non-wetting saturation against a dimensionless measure of viscous-to-capillary forcing. Saturation may remain near a plateau at low forcing, then decline as progressively harder clusters mobilise.
The transition is broad because ganglia differ in length, throat sequence, orientation and connectivity. Fragmentation, coalescence and bypass can change the population while desaturation proceeds.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change the capillary-number definition
One common form is Ca=μu/γ, using viscosity μ, Darcy velocity u and interfacial tension γ. Other studies use phase mobility, pressure gradient, permeability or contact-angle terms. Numerical thresholds cannot be compared until definitions and characteristic quantities match.
| Change | Effect on forcing | Possible response | Required record |
|---|---|---|---|
| Increase velocity | Raises viscous drop | More clusters mobilise | Darcy or pore velocity |
| Lower γ | Lowers capillary barriers | Earlier desaturation | Fluid composition |
| Higher viscosity | Raises Ca at same u | Larger pressure loss | Which phase viscosity |
| Change wettability | Changes thresholds and films | Different pathway | Advancing/receding angles |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Connect mobilisation to snap-off
The snap-off guide explains how wetting films and ink-bottle pores create disconnected ganglia. Mobilisation is the later question: what pressure field changes that topology again?
A mobilised cluster may not leave intact. It can split at a downstream throat, reconnect with another cluster or become trapped in a new pore body.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect the established soil-water routes
The air-entrapment guide tracks residual gas during infiltration. The hysteresis guide places mobilisation inside path-dependent retention.
Use the dynamic-capillarity guide when pressure and saturation lag, and the pressure-overshoot guide when fronts become unstable.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Design a defensible mobilisation experiment
Increase forcing in controlled steps, allow declared equilibration, and image the same volume. Track individual clusters, total saturation, pressure drop, flow redistribution and effluent phase volume.
Run the path downward as well as upward when safe. Hysteresis reveals whether the observed desaturation is reversible motion, permanent production, dissolution or a changed ganglion population.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
A bulk pressure gradient does not equal the local gradient across every cluster. Preferential channels can carry flow while shielded ganglia remain trapped.
A decline in measured saturation is not proof of advective mobilisation. Dissolution, compression, segmentation error and temperature or pressure corrections can change apparent phase volume.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record pore geometry, permeability, fluids, γ, viscosities, wettability, initial path, capillary-number formula, velocity definition, pressure taps, cluster length, threshold rule, imaging resolution, saturation correction and production balance.
Helland and colleagues examine trapping and mobilisation of residual ganglia in pore networks. Guo and colleagues review capillary-number definitions used in desaturation curves. Liu and colleagues analyse how wettability changes ganglion mobilisation thresholds.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is there one critical pressure gradient for a soil?
No. A specimen contains a distribution of cluster barriers and local pressure pathways.
Does a higher capillary number always mean more removal?
Often it promotes mobilisation, but the definition, flow history, fragmentation and bypass determine the measured curve.
Can a cluster move and remain residual?
Yes. It may relocate and become trapped again without leaving the specimen.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a pressure-transfer check
Repeat the ideal ledger if both throat radii double while ganglion length remains 2 mm. Compute the new capillary pressures, barrier and critical gradient. Then halve γ and explain why the ideal threshold halves even though the pore geometry is unchanged.
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