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A soil pore can be spacious in its body and narrow at its throat. That simple geometry makes entry and retreat follow different thresholds. During imbibition, wetting films can reconnect through corners and pinch a continuous gas thread into isolated clusters. The remaining ganglia are not merely “air left over”: their shape, connectivity, pressure and mobility record the pore geometry and 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. Name the phases and the path
Imbibition is the increase of the wetting phase, often water, into pores occupied by a non-wetting phase such as air. Drainage is the reverse displacement. Wettability must be stated because the same geometry behaves differently when contact angle or surface chemistry changes.
A ganglion is a connected cluster of the non-wetting phase. After snap-off, one thread may become several disconnected ganglia even though total gas volume changes little at that instant.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Recognise an ink-bottle pore
An ink-bottle geometry has a large pore body connected through a narrower throat. The throat controls entry or escape while the body stores volume, so filling and emptying do not retrace the same capillary-pressure path.
Pore networks contain many such constrictions and loops. Cooperative filling, corner films and access from multiple throats make real thresholds more complex than a single cylindrical capillary.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work an ideal capillary-pressure ledger
For an ideal cylindrical scale, |Pc|≈2γ|cosθ|/r. With water–air surface tension γ=0.072 N/m and cosθ=1, a 100 μm pore body gives 1.44 kPa while a 20 μm throat gives 7.20 kPa. The smaller throat sets a much larger pressure scale.
| Element | Radius | Ideal |Pc| | Interpretation |
|---|---|---|---|
| Pore body | 100 μm | 1.44 kPa | Large storage volume |
| Narrow throat | 20 μm | 7.20 kPa | Entry or exit bottleneck |
| Ratio | 5:1 | 5:1 pressure scale | Geometry creates hysteresis |
| Reality check | Irregular | Curvature-dependent | Use as scale, not exact threshold |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. See how snap-off disconnects gas
During imbibition, wetting films advance along grain corners and roughness while a non-wetting thread remains in the pore centre. When the films meet across a throat, the central thread can pinch off rapidly and isolate gas in the neighbouring body.
Snap-off competes with piston-like displacement and cooperative pore filling. Which event occurs depends on geometry, contact angle, pressure history, rate and neighbouring interfaces.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change rate and wettability
At low capillary number, capillary thresholds and pore geometry strongly organise invasion. Raising viscous forces can mobilise or fragment clusters and alter the residual saturation. A wettability shift changes film stability and the contact angles that enter the pressure thresholds.
| Change | Likely pore-scale effect | Possible outcome | Check |
|---|---|---|---|
| Higher flow rate | Larger viscous gradients | Mobilisation or fragmentation | Pressure and imaging |
| More water-wet | Stronger wetting films | Earlier snap-off | Contact angle history |
| Wider throats | Lower entry scale | Less severe bottleneck | Pore geometry |
| Reversed path | Different access sequence | Scanning hysteresis | Cycle history |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Distinguish trapped from permanently immobile
A disconnected ganglion is capillary-trapped when the imposed pressure gradient cannot overcome its entry barriers. Increase the gradient and it may move, split or reconnect. Over longer times it may also shrink by dissolution and diffusive exchange.
Therefore “trapped” needs a pressure range and time scale. A cluster immobile during one image sequence need not be permanent in a field wetting cycle.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect the established soil-water routes
The air-entrapment guide tracks gas left during infiltration. The hysteresis guide places these pore events inside path-dependent retention curves.
Use the dynamic-capillarity guide when pressure and saturation lag during rapid change, and the pressure-overshoot guide for unstable wetting fronts.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Measure topology as well as saturation
Two samples can have the same gas saturation but different ganglion-size distributions, interfacial areas and connectivity. Those structures affect relative permeability, dissolution and remobilisation.
Time-resolved X-ray or confocal imaging can identify pore filling, snap-off and cluster evolution. Segmentation resolution and partial-volume error should be reported because thin wetting films may fall below the voxel size.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
The Young–Laplace calculation above is a scale estimate, not a full pore-network solution. Contact-angle hysteresis, angular pores, surface roughness and dynamic curvature can shift thresholds.
Ink-bottle hysteresis does not explain every loop in a bulk retention curve. Entrapment, film flow, swelling, contact-angle change and measurement equilibration can contribute simultaneously.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record pore geometry, fluid pair, surface tension, advancing and receding contact angles, initial saturation, drainage–imbibition path, flow rate, capillary number, pressure convention, image resolution, event definition, cluster connectivity and mass balance.
Singh and colleagues resolve snap-off and pore-filling dynamics. A Water Resources Research study measures pore-by-pore capillary pressure and residual-cluster formation. Three-dimensional confocal observations show wetting-fluid pinch-off and disconnected non-wetting ganglia during imbibition.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is snap-off the same as air entrapment?
Snap-off is one pore-scale mechanism that can create disconnected gas; entrapment is the broader outcome and can also arise through bypass and enclosure.
Does smaller pore radius always mean a measured 2γ/r threshold?
No. That expression is an ideal scale; real curvature, contact angles and access geometry determine the event.
Can residual ganglia disappear without flowing out?
Yes. Gas can dissolve and diffuse into surrounding water, especially under changed pressure or undersaturation.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a geometry transfer check
Repeat the ideal ledger for a 50 μm body and 10 μm throat with the same γ and cosθ. Then reduce |cosθ| to 0.5 and recompute both pressure scales. Explain why equal radius ratios preserve the ideal pressure ratio while wettability changes the absolute thresholds.
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