6 December 2020
Briggs (1897) deduced capillary flow from deviation of the equilibrium between capillarity and gravity. Richards (1931) raised capillary flow to an unproven soil hydrological dogma. Attempts to correct the dogma led to concepts of non-equilibrium flow, macropore flow, and preferential flow during infiltration. Viscous film flow is proposed as an alternative approach to capillarity-driven flow during unsaturated infiltration.
The paper that follows was submitted to
Peter and I had been good friends since we first met and started doing fieldwork together at the Institute of Hydrology at Wallingford in 1979, where he spent a year as a postdoc, and we found we had a common interest in preferential flows. Beven and Germann (2013) include some information and a photograph of the tracing experiment we did at Grendon Underwood in 1979. This was instructive in that it was done at the end of the winter on well-wetted clay soil when all the cracks in the clay should have been closed. In fact, it took the Rhodamine dye we added at the surface some 45 s to reach a mole drain at a depth of 60 cm, and destructive sampling after the trace showed that the cracks were still transmitting water (and that the grass roots were mostly on the surface of the peds).
Peter was born in St. Gallen, Switzerland, in 1944. He grew up in Bischofszell and later completed his schooling in St. Gallen. In 1963–1969 he studied to obtain a degree in forestry at ETH Zurich, and then he stayed with Professor Felix E. Richard to carry out research towards a PhD at the Eidgenössische Forschungsanstalt für Wald, Schnee und Landschaft (WSL) from 1969 to 1976. He continued his work in the Laboratories of Hydraulics, Glaciology and Hydrology (VAW) during the period 1976–1980. His PhD work was a study of the water relations on a forested slope in the Rietholzbach catchment based on maintaining a network of 35 nests of tensiometers at 10 different depths down to 3 m, set out on a triangular grid amongst the trees. At this time these were still manual tensiometers coupled to mercury manometers that were read every 2–3 d for 3 years. One of the features that this remarkable data set revealed was that during infiltration wetting could occur at depth in some cases, apparently bypassing the tensiometers above. Another was the large heterogeneity in responses between sites and between wetting events.
Peter returned to Switzerland from Wallingford, and then in 1980 he took up a post as assistant professor in the Department of Environmental Sciences at the University of Virginia (UVA) in Charlottesville, where we overlapped again for 2 years. Peter stayed at UVA until 1986. He then took a position as an associate professor in the Department of Soils and Crops at Rutgers University. In 1989 he was offered a professorship at the Institute of Geography, University of Bern, back in Switzerland, where he stayed until he retired in 2009. He held an emeritus position at Bern until 2015.
For the major part of his research career, Peter was a strong advocate for a reconsideration of the physics of water flow through soils and, in particular, for the limitations of the Darcy–Buckingham–Richards flow theory that is based on an assumption of the equilibration of capillary potentials in some (not clearly defined) “representative elementary volume” of soil pores. The paper that follows is a continuation of that theme.
Our common interest resulted in the highly cited review paper in
Peter later developed the kinematic wave approach into a theory of viscosity
(rather than capillarity)-dominated film flows subject to Stokes' law during
infiltration. This is still somewhat contentious (see the comment on the
paper by John Nimmo at
Beven, K. J. and Germann, P. F.: Water flow in soil macropores, II. A combined flow model, J. Soil Sci., 32, 15–29, 1981.
Beven, K. J. and Germann, P.: Macropores and water flow in soils, Water Resour. Res., 18, 1311–1325, 1982.
Beven, K. J. and Germann, P. F.: A distribution function model of channelling flow in soils based on kinematic wave theory, Proceedings of the International Symposium on Water and Solute Movement in Heavy Clay Soils, Wageningen, Neth. ILR Pubn. 37, 89–100, 1985.
Beven, K. J. and Germann, P. F.: Macropores and water flow in soils
revisited, Water Resour. Res., 49, 3071–3092,
Germann, P. F. and Beven, K. J.: Water flow in soil macropores, I. An experimental approach, J. Soil Sci., 32, 1–13, 1981a.
Germann, P. F. and Beven, K. J.: Water flow in soil macropores, III. A statistical approach, J. Soil Sci., 32, 29–31, 1981b.
Germann, P. F.: Preferential Flow: Stokes approach to infiltration and
drainage, University of Bern Press, available at:
Why does water know/where to flow?/Is the strongest force/dictating
the course?/Is the weakest resistance/controlling the distance?/Or is
soil hydrology nothing but mental strength/fiddling with mass, time, and
length? (Germann, 2014)
The success of terrestrial plants relies, among other phenomena, on the
simultaneous supply of oxygen and water to the root tips in the size range
of
Briggs also provides a qualitative description for flow when there is any deviation from this static equilibrium in terms of a capillary gradient and further postulated a variable permeability concept in partially water-saturated soils. He certainly introduced these concepts to Edgar Buckingham, who joined the Bureau of Soils to work under Briggs in 1902. Buckingham further developed these concepts, and his reports on the movement of soil moisture are frequently viewed as the origin of modern concepts of capillary flow (Buckingham, 1904, 1907): he extended a first-order gradient flux law to unsaturated soils as analogous to thermal and electrical fluxes (though does not explicitly mention Darcy's law), and he proposed hydraulic conductivity, diffusivity and the water capacity as quantitative functions of soil moisture. However, “Buckingham did not manage to formulate a clear-cut physical-mathematical flow theory that quickly inspired other soil physicists” (Raats and Knight, 2018, p. 11).
This seminal work at the Bureau of Soils was set back by the Chief of the
Bureau, Milton Whitney (who was chief from 1860 to his retirement in 1927).
Whitney dismissed King in 1904 because of his belief that soil nutrient
status was more important to crop growth than the soil physical properties
favoured by Whitney. He also encouraged Briggs to leave in 1905 because his
training as a physicist was resulting in the application of “rigid mathematical demonstration” to soil
physics that Whitney felt could not be justified (see Landa and Nimmo,
2003). After the departure of Briggs, Buckingham worked under Frank Kenneth
Cameron, who was not totally convinced by Buckingham's developments,
suggesting that there might be inconsistencies in Buckingham's approach to
water and vapour transport. Buckingham's response was not totally
convincing, but Cameron decided not to hold back the publication as “you seem to be convinced that it is all sound and safe”
(quoted in Nimmo and Landa, 2005). Buckingham's 1907 report was delayed as a
consequence until after he had also left the Bureau of Soils to join the
National Bureau of Standards in August 1906. He never returned to the study
of soil physics. He became much better known as the author of the
It was more than two decades before there was further significant progress with Lorenzo K. Richards' (1931) paper “Capillary Conduction of Liquids Through Porous Mediums”, where he presented the three-dimensional form of the second-order convection–diffusion equation, which bears his name. Note that, despite the comment of Raats and Knight (2018) quoted above, all the elements of the Richards equation were already present in the report of Buckingham (1907), but there he did not combine them into a single flow equation. In fact, Richardson (1922) had already done so before Richards but outside the context of the soil physics community (see Raats and Knight, 2018). Richards did, however, also present an experimental procedure for the determination of the parameters of his equation, including a demonstration of hysteresis in the soil water characteristics. This combination of theory and experiment based on that experiment made the approach attractive for practical applications.
However, Richards was also instrumental in introducing some misconceptions
into soil physics. He authoritatively stated the following: If there is a steady flow of liquid through a porous medium which is only partially saturated, then the larger pore space containing air and the effective cross-sectional area of the water conducting region is reduced. If these air spaces could in some way be filled with solid, the condition of the flow would be unchanged and the proportionality between the flow and the water-moving force would still hold because Darcey's [sic] law is independent of the size of particles or the state of packing. (Richards, 1931, p. 323)
A reconsideration of the ubiquity of Richards' (1931) capillary approach to
infiltration and drainage demands a concept that replaces this assumption of
dominance by capillarity. In early attempts, Germann and Beven (1981), Beven
and Germann (1981), and Germann (1985) successfully approached transient
infiltration/drainage with kinematic wave theory that can be applied when
gravity is the dominant driving force rather than the gradient of capillary
potential, which will be the strongest driver under drier conditions. More
recently, Germann and al Hagrey (2008) summarize the features of
gravity-dominated viscous film flow John Nimmo in his comments on
this paper (see
Infiltration expresses how water arriving from above the ground, usually in the shape of drops, transitions to water flow in the soil below the ground surface. Drops have internal pressures higher than atmospheric pressure. According to Laplace–Young theory, pressures against the atmosphere in drops increase from about 15 to 750 Pa as their diameters reduce from 5 to 0.1 mm. When drops hit the ground surface, depending on their size and Bond number, they will often burst. The remnants then join and form local films at atmospheric pressure. There are two ways for water to continue. Either water has to follow the strongest gradient, as in capillary flow. Richards' (1931) forceful conjecture of the dominance of capillarity during infiltration in unsaturated porous media works well under steady-state conditions. However, increasing the flow rate causes the well-known phenomena of non-equilibrium flow, macropore flow, and preferential flow. Water then follows the way of least resistance, as a viscous film flow. This type of flow occurs under atmospheric pressure, regardless of the thickness and path widths of the films, as Flammer et al. (2001) have demonstrated with acoustic velocity measurements across soil columns. Germann (2018b) also demonstrates how acoustic velocity experiments suggest that preferential flows can proceed faster than capillary gradient-driven fluxes in unsaturated soils.
On the one hand, the Richards' (1931) capillary gradient flow (and implied local equilibration of potentials) continues to be taught and used in models of soil hydrology in a rather dogmatic way. There have been modifications suggested to allow for dual permeability functions near saturation, but these are not really convincing (Beven and Germann, 2013; Beven, 2018). On the other hand, there are a plethora of review articles that discuss the hydro-mechanical inconsistencies with the Richards equation and observations of preferential, non-equilibrium, and macropore flows in both unsaturated and saturated soils (see again Beven, 2018, and references therein). This conflict remains to be resolved but is clearly important for the understanding of both flow and transport. It is, however, the case that there are few ongoing research efforts, either theoretical and experimental, on developing coherent descriptions of preferential flow in soil physics. The author's application of viscous film flow concepts to infiltration in unsaturated soils has been one such effort, and it is hoped that it will be taken on and further developed by others (see, for example, the recent papers of Germann, 2017, 2018a, b; Germann and Prasuhn, 2018; Germann and Karlen, 2016).
In conclusion, Briggs' (1897) convenient and, within his concept, correct definition of capillary flow led, via the work of Buckingham, to Richards' (1931) dogma of the unproven dominance of capillary gradient-driven fluxes during infiltration that is still widely used today. However, as it turns out, while capillary flow relies on the strongest force exerted on water in an unsaturated soil, the weaker force of viscosity can dominate during infiltration as a result of the formation of film flows at and near the soil surface.
I was shocked and deeply saddened to learn, after I had written my review of
his paper, that Peter Germann had died. When Erwin Zehe last fall invited me
to review this paper for
The missed opportunity for discussion of this paper is a small part of the loss I feel in Peter's death. He was a tremendous inspiration to me, ever since he warmly befriended me at an AGU meeting years ago. Peter enlightened me with his profound insights. Moreover, he encouraged and energized me by his bold example in putting forth innovative, even revolutionary, ideas into a scientific realm where they were needed and fruitful. Though in person he is no longer with us, his many written works will continue to enlighten and inspire scientists into the future.
No data sets were used in this article.
This article is part of the special issue “History of hydrology” (HESS/HGSS inter-journal SI). It is not associated with a conference.
This paper was edited by Erwin Zehe and reviewed by John R. Nimmo.