Does exist ink bottle effect ? A little survey on hydraulic hysteresis

Soil physics textbooks often illustrate hysteresis with a simple diagram of a pore shaped like an old ink bottle: a wide body connected to a narrow neck. The story is familiar: during drainage, water is trapped in the wide body because the narrow neck controls the suction at which the pore can empty; during wetting, the pore fills at a lower suction than it empties. The ink-bottle model has been the standard pedagogical explanation for soil water hysteresis for more than half a century.

There is, however, a flaw in this reasoning. In the original version of this post I asked the reader to find it. The answer, which I develop below, is that the ink-bottle model explains Haines jumps but not macroscopic hysteresis — and the distinction matters profoundly for how we think about unsaturated flow.

The ink-bottle mechanism describes what happens at a single pore: a meniscus passing through a constriction undergoes an abrupt rearrangement — a Haines jump (Haines, 1930). These jumps are real, experimentally observable, and dissipate energy at the pore scale. But they are microscopic events. A single pore filling or emptying in a jump tells us nothing about the macroscopic retention curve.

Macroscopic hysteresis — the fact that the drying curve sits above the wetting curve in the θ(ψ) plane — requires that the entire filling distribution (which pores are full and which are empty) differ between wetting and drying at the same total water content. That is a network-scale phenomenon, not a single-pore phenomenon. The ink bottle, being a local geometric feature, cannot explain it.The most compelling evidence comes from lattice Boltzmann simulations by Hosseini, Kumar, and Delenne (2024; arXiv preprint 2022). They systematically eliminated every mechanism that has traditionally been proposed to explain hysteresis: 

• Contact angle hysteresis kept constant throughout wetting and drying
• The ink-bottle effect — eliminated by using simultaneous drainage/injection throughout the domain rather than boundary flow, preventing water from flowing in opposite directions
• Air entrapment — eliminated by the same scheme
• Soil fabric changes — grain positions fixed

Despite eliminating all of these, hysteresis persisted. What they found instead was a fundamental asymmetry in how the two fluid phases expand within the pore network:

• During wetting, new liquid zones appear throughout the gas phase in the form of capillary bridges. Many bridges expand simultaneously and coalesce, filling pores from smallest to largest. This is a multi-site nucleation process.
• During drying, new gas zones cannot spontaneously nucleate within the liquid phase — that would require cavitation. Only the existing gas cluster connected to the boundary can expand, and it is constrained by the pore openings surrounding it. This is a single-cluster expansion process.

The asymmetry is not local geometry (bottle necks) but global topology (many simultaneous nucleation sites versus single connected cluster). It is a property of the network, not of individual pores.I f hysteresis comes from topological asymmetry rather than local geometry, then several foundational questions in soil physics need rethinking:

The classical view treats the drying and wetting retention curves as two distinct equilibrium relationships. But if the asymmetry is topological — if it is about which pores the system can reach rather than about multiple thermodynamic minima — then perhaps there is only one equilibrium at each water content, and what we call “hysteresis” is the inability of the system to reach that equilibrium along certain paths. If so, the water retention curve is not a constitutive law but a trajectory through a configuration space, and hysteresis is a kinematic phenomenon, not a thermodynamic one.This distinction has consequences. If there is a unique equilibrium, then the relevant question is not “what is the equilibrium pressure at this water content?” but rather “how does the system approach equilibrium, and what prevents it from getting there?”
The ink-bottle picture treats wetting and drying as the same process run in opposite directions. But the Hosseini result shows they are qualitatively different: multi-site nucleation versus single-cluster expansion. This asymmetry suggests that wetting and drying should be described by different operators — not by a single reversible process with a sign change. And if we go further: in the field, drying is not a single process at all. At least four distinct mechanisms remove water from soil:

• Capillary drainage: gas invades from the boundary through the connected gas cluster, emptying the largest accessible pores first.
• Stage I evaporation (atmosphere-limited): removes water from small surface pores, where the vapor pressure is highest.
• Stage II evaporation (diffusion-limited): vapor diffusion through a dry surface layer can empty pores that are hydraulically disconnected from the gas-phase boundary — it bypasses the topological constraint.
• Root uptake: plants extract water through the root–soil interface, accessing a pore topology entirely unrelated to the gas-phase connectivity.

Each mechanism creates a different pore-emptying sequence. A soil dried by evaporation and then subjected to root uptake reaches a different internal configuration than one dried by roots first and then by evaporation. This suggests a richer non-commutativity than just “wetting versus drying” — the different drying mechanisms themselves may not commute. 

The Hosseini result already changes how we should think about several practical questions:

The body/throat distinction is unnecessary. If hysteresis does not come from the ink-bottle geometry, then the elaborate pore network models that distinguish “pore bodies” from “pore throats” are solving the wrong problem. What matters is the connectivity structure C(r, r’) — which pore classes are connected — not whether a given pore segment is a “body” or a “throat.”

Laboratory retention curves are insufficient for field predictions. Lab curves are measured under quasi-static capillary drainage — a single drying mechanism, at near-zero forcing rate. They capture none of the kinetic effects, none of the multiple drying mechanisms, and none of the rate dependence that dominate under field conditions. The gap between lab and field measurements may not be experimental error but a genuine physical discrepancy that no amount of careful laboratory work can eliminate.

Scanning curves require new models. The Mualem (1974) independent domain model — still the standard for predicting scanning curves — assumes that each pore class fills and empties independently. The topological asymmetry found by Hosseini implies that accessibility is history-dependent: which pores can participate in the current filling/emptying step depends on which pores are already full. This correlation is precisely what the independent domain assumption neglects.

Related posts: Minkowski functionals (a way to track water movement) | Five Paradoxes of Soil Hydrology | Minkowski functionals: Critical Limitations

References for further reading:

• Celia, M. A., Reeves, P. C., & Ferrand, L. A. (1995). Recent advances in pore scale models for multiphase flow in porous media. *Reviews of Geophysics*, 33(S2), 1049-1057.
• Haines, W. B. (1930). Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith. J. Agric. Sci., 20(1), 97–116.
• Hassanizadeh, S. M., & Gray, W. G. (1993). Thermodynamic basis of capillary pressure in porous media. *Water Resources Research*, 29(10), 3389-3405.
• Hosseini, R., Kumar, K., and Delenne, J.-Y. (2024). Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method. Acta Geotechnica, 19, 7577–7601.
• Lehmann, P., Assouline, S., and Or, D. (2008). Characteristic lengths affecting evaporative drying of porous media. Phys. Rev. E, 77, 056309.
• Lu, N., & Likos, W. J. (2004). Unsaturated Soil Mechanics. Wiley.
• Mualem, Y. (1974). A conceptual model of hysteresis. Water Resour. Res., 10, 514–520.
• Or, D., & Tuller, M. (1999). Liquid retention and interfacial area in variably saturated porous media: Upscaling from single-pore to sample-scale model. Water Resources Research, 35(12), 3591-3606.
• Tuller, M., Or, D., & Dudley, L. M. (1999). Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores. Water Resources Research, 35(7), 1949-1964.
• Tuller, M., Or, D., & Hillel, D. (2004). Retention of water in soil and the soil water characteristic curve. Encyclopedia of Soils in the Environment, 4, 278-289.
• Mualem, Y. (1984). A modified dependent-domain theory of hysteresis. Soil Science, 137(5), 283-291.