i,„9d>p=oh+gr; pI>P\ Fig. 2.2. Diagram of wedging action of thin films of bound water.

In the case when the absolute value of Pwed is greater than the interaction forces between two mineral particles Pcoh and the external load on them, g, the particles will move away from each other due to the wedging effect of the film water accumulating under the action of the surface forces of the mineral

,bwi is particles (Fig. 2.2). In this case, the condition n7a > HhJ with < , always met. This is what ensures water migration into the intersurface gap between particles until the potentials are equalized and a new equilibrium established in the system. In the case of Pwed < Pcoh + g, even if> the particles fail to move apart. With the external load being greater than the wedging pressure Pwed and the repulsive force Pt between particles (d > -Pwed + pr)>the particles will draw closer and water will flow out of the intersurface gap. From this standpoint the pressure of swelling clayey soils should be regarded as resulting from the wedging effect of the thin films of bound water.

Water migration can occur in soils in the capillary form (capillary water proper) and in the film form (weakly bound water). Capillary water migration occurs mainly in the molar (volumetric) way due to meniscus (Laplace) forces. In frozen soils migration of bound water, occurring usually in the film form, is very important. In the case of the portion of the film transfer being comparable with that of the capillary water transfer in soil micropores, a mixed capillary-film transfer mechanism can be said to occur. The film mechanism of water migration becomes increasingly important with diminishing soil water content. Characteristically, soil water migrates in the films not as a compact mass (volume migration), but from particle to particle (molecular diffusion migration). Naturally, the film water migration velocity and, consequently, the water migration flow density, prove substantially lower than for the capillary water transfer.

Molecular-kinetic bound water migration in a dispersed soil is due, in the presence of an inhomogeneous force field, to the difference between the jumps of water molecules in forward and in backward directions along the force gradients. Migration by jumps is self-diffusion and is called transla-tory. For translatory jumps from node to node in the lattice to occur, it is necessary that the kinetic (vibrational-rotational) energy of the particle Ek be greater than that of its bonding energy (interaction) with other particles Eh, i.e. Ek > Eh. Note that heating increases the kinetic energy of particles and reduces the bond energy between them.

Calculated data have shown that each water molecule, at a temperature of25°C,for example, makes some 6 x 108 jumps per second. The jumps are separated from each other by time intervals of 1.7 x 10" 9 s, i.e. the time of a molecule staying near the equilibrium centre. A water molecule makes in its equilibrium stay time (between jumps) some 1000 vibrations. Generally the frequency,), of molecular jumps per second, is defined by the formula:

where j0 is some coefficient relating to the vibration frequency of particles near the equilibrium state; T is the absolute temperature in Kelvin; e is the natural logarithm base.

The mean time of a particle vibration near one equilibrium centre is the reciprocal of j, i.e. x = 1 /j. In addition to the migration form of individual molecules in liquids and gases discussed above, there are also group molecule migrations pushed by surrounding particles. Such associations of molecules perform Brownian movement adding to the translatory migration of separate H20 molecules.

The above concepts about the translatory movement of H20 molecules and groups of molecules relate to chemically pure, bound water. They failed to take into account either the ion hydration, i.e. interaction of electrolyte ions with water molecules, or the effect of the binding of water molecules to active centres of mineral soil particle surfaces. Consequently, the bond energy of each water molecule should be increased by the energy of bonding of the H20 molecule (AE{) with an ion, on the one hand, and by the energy of binding a molecule with the mineral surface (AEm), on the other. Thus, bound water, containing ions of the electric double layer, has the frequency of translatory H20 molecule jumps reduced and this is expressed as:

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