Flow of matter from one region to another is determined by the potential energy of the system. Movement of water across a semipermeable membraneIcon_External_Link, in the absence of a hydraulic pressure difference e.g. a column of water, can result from three kinds of potential energy:
  • chemical-potential as a result of differences in solute concentration (dissolved chemicals)
  • electrical-potential as a result of a flow of electricity
  • thermal-potential as a result of heat differences

This non-hydraulic flow is called osmosis. Thus, it is called chemical osmosis when the potential was of chemical origin e.g. differences in salt concentration. Analoguesly, the others are called electro-osmosis and thermo-osmosis.

Osmosis depends on the existence of a semipermeable membrane. This is a membrane that restricts the passage of solutes while the solvent is not restricted. The most widely known semipermeable membrane is the a pig bladder. If such a membrane seperates solutions of different concentrations (also called activitiesIcon_External_Link) water will be transported from the lower concentration (=high activity) to the higher concentration (=lower activity) side. This water transport stops when the concentrations (activities) of the solutions on both sides are the same. This situation is reached if the concentration on both sides of the membrane are identical, or when a hydraulic pressure (water height difference, or hydraulic head) across the membrane is established that equals the osmotic pressure difference between the two solutions.

Schematically it looks like this:


Figure 1
Imaginary experiment using a U-tube showing the
principles of chemical osmosis (Keijzer, 2000).

In the begin situation the water levels at the salt and fresh water side are identical, the solutions are seperated by a semipermeable membrane (Figure 1). Due to the differences in concentration water will flow from the fresh to the salt water side. As a result of this water transport the water level at the salt water side will rise. The transport stops when the water level on the salt side, or
hydraulic headIcon_External_Link, equals the osmotic pressure.

coupled flow

Chemical osmosis is part of what is called coupled flow or coupled transport. In most cases simultaneous flows of different types are present, even when only one type of driving force is acting. For example, when pore water containing chemicals flows under the action of a hydraulic gradient, there is a concurrent flow of chemicals through the soil called advection. Or, in the case of chemical osmosis, a gradient in concentration will initiate a flow of water. Thus a gradient of one type can cause a flow of another type, according to:

Ji = Lij Xj

in which Ji is the flux of type i as a result of a driving force X of type j, Lij is called the coupling coefficient. This is a property of the soil which may or may not be of any significant magnitude.

In the table below the relation between the driving force or hydraulic, temperature, electrical or chemical gradient and the type of induced flow is given. For example: if a hydraulic gradient or hydraulic pressure is applied a hydraulic flow which can be described by
Darcy's Law will be the primairy result. Fluid will flow as a result of the applied hydraulic gradient, this is called the direct flow. But with the movement of the fluid also secondairy or coupled flow phenomena will occur. As a result of the fluid flow heat will be redistributed (so-called convective heat flow), a streaming current will be generated and as a result of the flow of disolved ions also a streaming current will be generated. The direct flows are shaded grey and the main law describing the flow is given. These direct flows are well known ... the coupled flows however are far more interesting. From the table it can be derived for example that as a result of a hydraulic gradient a current will be generated, or that as the result of a chemical gradient a flow of water will take place!

coupled flow

Interested readers might refer to Mitchell (1993) for a clear and thorough introduction into coupled flows. References are given at the bottom of this page.

clay as a semipermeable membrane

about clays ­­­— To understand why clay can act as a semipermeable membrane one needs to know something about clay mineralogy. Clay mineralsIcon_External_Link are made up of combinations of two simple structural units, the silica tetrahedronIcon_External_Link and the aluminium or magnesium octahedronIcon_External_Link. These units are assembled in sheets with the general formula (Si2O52-)n for the tetrahedron and (Al2(OH)6)n or (Mg3(OH)6)n for the octahedron sheet. When a clay mineral consists of one octahedral and one tetrahedral sheet a so–called 1:1 layer or platelet is formed as in the mineral kaoliniteIcon_External_Link. If an octahedral sheet is sandwiched between two tetrahedral sheets, a 2:1 platelet is formed as in montmorilloniteIcon_External_Link, a member of the smectiteIcon_External_Link group. The different clay minerals are thus characterised by the differences in stacking of these sheets and the manner in which the successive two– or three–sheet platelets are held together. In Figure 2 the way the various clay minerals are made is schematically given.

Synthesis of clays

Figure 2
Synthesis pattern of the various clay minerals (taken from Mitchell, 1993).

Differences between minerals within a clay mineral group result from differences within the crystal structure of the tetrahedral and octahedral sheet, known as isomorphic substitution. Isomorphic substitution is the presence of a
cationIcon_External_Link other than the Si4+ in the ideal tetrahedral and Al3+ in the ideal octahedral sheet. Common is the substitution of Al3+ for Si4+ in the tetrahedral sheet and Mg2+ or Fe2+ for Al3+ in the octahedral sheet. As a result of these substitutions, most clay surfaces have a net negative surface charge under natural conditions.

diffuse double layer — To preserve electrical neutrality the negative charge of the clay particle is balanced by the attraction of cations which are held between the layers, and on the surface of the particles. While electrostatically attracted the concentration of these cations or counter–ions diminishes with increasing distance from the clay particle surface (Figure 3). The charged clay surface together with the counter–ions in the pore water form the so-called diffuse double layerIcon_External_Link. The pore water outside the double layer region is referred to as the equilibrium or free solution. In the idealised form this is known as the Gouy–Chapman double layer. The cationsIcon_External_Link in the double layer are subjected to opposing forces. Electrostatic forces attract the cations towards the charged clay surface, whereas by diffusionIcon_External_Link they tend to move away from the surface. Simultaneously, the anionsIcon_External_Link or co–ions with the same charge as the clay surface are repelled from the surface. Diffusion from the equilibrium solution towards the surface counteracts the electric repulsion of anions. At equilibrium the average concentration of the ions at a known distance from the clay surface is a function of the concentration in the equilibrium concentration. Furthermore, the double layer is influenced by the valency of the counter–ions and the temperature.


Figure 3
Distribution of cations and anions adjacent to a clay
platelet according to the difuse double layer theory (Keijzer, 2000).

clay as a semipermeable membrane — The ability of a clay to act as a semipermeable membrane arises when the double layers of adjacent clay platelets overlap (Figure 4). This overlap can be the result of compaction of the clay under an overburden load. It results in an even higher concentration of cations and lower concentration of anions in the double layer with respect to the equilibrium solution. The water film present in the narrow pore between the clay layers is thus completely dominated by the overlapping double layers, and the electrical restrictions they impose. Anions attempting to migrate through the narrow aqueous film are repelled by the negative charge of the clay platelets. This effect is known as ‘negative adsorption’ or Donnan ExclusionIcon_External_Link. In order to maintain electrical neutrality in the external solution cations will tend to remain with their co–ions. Thus, their movement across the clay will also be restricted.


Figure 4
Distribution of cations and anions adjacent to a clay platelet;
top when there is no overlap, and bottom with overlapping double layers
as a result of compaction (Keijzer, 2000).

ideality of a semipermeable membrane

The osmotic pressure difference across a semipermeable membrane can be calculated using:

Δπ0 = (RT/Vw) ln(afresh/asalt)

In which Δπ0 is the osmotic pressure in kPa, R is the gasconstant 8.31451 J/mol K, T the absolute temperature, Vw the molar volume of water (= 0.01802 L/mol at 25°C) and afresh the activity of the fresh water and asalt the activity or potential of the salt water. This equation will yield the theoretical osmotic pressure between two solutions. If the semipermeable membrane is an ideal membrane the theoretical osmotic pressure will equal the induced hydraulic head, as shown in Figure 1.
The semipermeable membranes in nature such as clays are often not so ideal, or so-called non-ideal membranes. The hydraulic head that will be induced by a concentration differences across the membrane will be lower than might be expected from the above equation. Non-ideality means that the membrane is a 'leaky' one (Figure 5). The solutes (dissolved chemicals) at both sides of the semipermeable membrane are not completely restricted from entering the membrane and thus will diffuse from the high to the low solute concentration side.


Figure 5
The development of a hydraulic head across an ideal
and non-ideal or 'leaky' semipermeable membrane (Keijzer, 2000).

This non-ideality is expressed as a reflection coefficient σ which is defined as the ratio of the observed hydraulic head (Δp) over the theoretical osmotic pressure (Δπ0) when there is no water transport, thus:


An ideal membrane will have a reflection coefficient of 1, all solutes are 'reflected' by the membrane. Non-ideal membranes will have a value for σ, somewhere between 0 and 1. If a layer, e.g. a sand layer, doesn't exhibit semipermeable properties the reflection coefficioent will be 0. There are several models to calculate a reflection coefficient for natural clayey materials but it can get rather complicated, interested readers should refer to more specialised literature like my Ph.D.-thesis (Keijzer, 2000), see also a list at the end of this page.

Ideality of a natural clayey material depends on several factors. The most important are:

  • the type of clay; clays with a high negative charge such as montmorilloniteIcon_External_Link are inherent better semipermeable membranes than clays like kaoliniteIcon_External_Link as there double layer is thicker.
  • porosityIcon_External_Link of the clay layer; the more compact the layer the better the double layers overlap
  • concentration within the pore water of the clay layer; the lower the concentration in the pore water the thicker the double layer, hence the clay is a more ideal membrane

In Figure 6 the ideality of three clays are given according to one of the models describing chemical osmosis in geological meterials ­­—the Fritz-Marine Membrane Model (Fritz, 1986)— as a function of the porosity.
MontmorilloniteIcon_External_Link is a clay with a high negative charge, illiteIcon_External_Link has a lower charge. The AWy is a commercially available montmorillonite used during my research.


Figure 6
The reflection coefficient, σ, of AWy as a function of the porosity;
top for a typical montmorillonite with capacity of 100 meq/100g and an illite
with a capacity of 20 meq/100g, using a mean salt concentration of 0.35 mol/L
NaCl, and
bottom the ideality of AWy at two different pore water
concentrations (Keijzer, 2000).


For those who are interested in a more fundamental discussion on (chemical) osmosis and coupled transport can refer to:

  • Fritz SJ (1986), Ideality of clay membranes in osmotic processes: a review, Clays Clay Miner 34, 214-223
  • Groenevelt PH & Bolt GH (1969), Non-equilibrium thermodynamics of the soil-water system, Journal of Hydrology 7,
  • Katchalsky A & Curran PF (1965), Nonequilibrium thermodynamics in biophysics, Harvard University Press, Cambridge 1965
  • Keijzer ThJS (2000), Chemical osmosis in natural clayey materials, Geologica Ultraiectum 196, Ph.D.-thesis, Universiteit Utrecht, Utrecht, the Netherlands
  • Mitchell JK (1993), Fundamentals of soil behavior, Wiley, New York 19932, chapter 12
  • Yeung AT & Mitchell JK (1993), Coupled fluid, electrical and chemical flows in soil, Geotechnique 43, p 121-134