Capillary potential

Surface Tension and Capillary Potential Affecting Underground... 

Gardner and Widstoe (1921) made attempts to develop a general equation. They assumed an ideal soil to be one in which the capillary potential was a linear function of the reciprocal of the moisture-content (after Buckingham, 1907), and that the inherent moisture conductivity is independent of the moisture-content. These assumptions are necessary for mathematical reasons. For downward flow through sand, whose surface is kept saturated, the equation connecting the time t and distance from the surface L was as follows ... 

Buckingham showed that the relation between p and the moisture-content Mc could be ascertained from measurement of the equilibrium moisture distribution (which is very slowly attained and never certain) in a vertical column of soil, whose lower end was in water and upper end protected from evaporation. Consider the work required to move a small mass of water from x to x + dx, the capillary potentials being and ( p + (b p/bx)dx), respectively. The total work done against capillary potential is therefore... 

The dependence of capillary potential on moisture-content, as we have seen in King s (1899) experiments, is a function of x, so that... 

Thus, a change of capillary potential with moisture-content is equal to a constant divided by the rate of moisture change with height. Integrating, we obtain... 

For conditions of steady flow, Richards developed an equation relating the conductivity XB and capillary potential p... 

Richards has given some experimental data relating to the conductivity and capillary potential. These are shown plotted on semi-... 

Figure 84. Relationship of Soil Conductivity to Capillary Potential for Two Types of Soils. Data from L. A. Richards (1931).

The usefulness of capillary potential to soil-moisture and plant investigators. J. Agr. Res., 37 719-742. 

Streaming potential pressure gradient liquid plug or capillary potential difference streaming potential (difference) per unit of pressure difference s(r Vm N- ... 

Buckingham (B4), Gardner (G2, G3), and Wilsdon (W5) attempted the difficult problem of applying variable diffusivities to the diffusion equations by employing a capillary potential instead of a concentration potential. 

Effects of the fractal nature of soil on water and solute transport can be further complicated by the differences among fractal dimensions in soils at different scales. Avnir et al. (1986) found at least two ranges of radii with different surface fractal dimensions in studied soils. Dependence of fractal dimension on pore radii was demonstrated (Wu et al., 1993 Perfect et al., 1993). Pachepsky et al.( 1995a) found three or four distinct scaling intervals with different fractal dimensions in the range of pore radii from 4 nm to 5 pm. Fractal scaling of soil water retention is usually well pronounced at capillary potentials lower than -30 kPa. 

When specific design of the LHP allows assumption that all hydraulic resistances (excluding are much smaller than capillary potential... 

According to Eq. [4], the electrochemical potential of a macroscopic or planar electrode, for which k is either small or zero, is independent of surface orientation because addition or removal of material changes only the quantity of metal in the bulk and not the surface shape or area. For sufficiently small crystals or surface features, the curvature is appreciable, and the equilibrium potential is shifted from the bulk value by a capillary potential represented by the second term on the right hand side of Eq. [4]. 

The discussion above suggests that a single suction field is not enough to interpret the behaviour of expansive materials with a marked bi-modal porosity distribution. Therefore, in addition to the net stress, two additional water potential fields are considered Sm and s, . Sm may be interpreted as a capillary potential, but the concept of water potential, linked to the physico-chemical mechanisms of water bounding to the clay minerals, is more appropriate for s. For the purposes of discussing the experimental behaviour observed it is convenient to work with two stress spaces which integrate the net stress field and the two independent water potential variables The space (Oq,SM) associated with the macrostructure and the space (ajj,s, ) associated with the microstructural level. (A reference zero air pressure will be considered, for simplicity). 

The moisture content in road shoulders is governed by climatologic factors such as rainfall, temperature and evaporation and typically show a large variation in comparison with the body of the road. Depending of the moisture contents in the shoulders the capillary potential may drive moisture either in or out of the road body. Moisture is typically transported downwards out of the pavement structure as vapor in the summer and upward, into the structure, during winter [15]. Wallace [16] demonstrated the significance of the shoulders as water entries to the unbound material layers during transient conditions in a theoretical study. The rate of lateral intrusion in the unbound layers will be dependent on ... 

Rainwater that is carried away as surface runoff infiltrates in the unsealed shoulders of the road and may also move laterally into the road body driven by the capillary potential, hydraulic pressure [16,23-25], vapor pressure and temperature gradients [ 13]. Pressure gradients in porous media, also referred to as hydraulic non-equilibrium, typically arise when the flow field is transient and non-uniform. 

IV. USING MIP IN CAPILLARIES—POTENTIAL PROBLEMS A. Detection of Analytes... 

In the hterature, several methods such as the neutral marker method, the current monitoring method [5], etc. have been introduced to indirectly determine the average liquid velocity of the EOF in a tnicrocapillary so that the capillary -potential can be determined using Eq. 3. However, in practice, there exist difficulties in identifying a real, electrically neutral marker and in locating the cutoff of the asymptotic current vs. time curve. 

Detector MS Finnigan LCQ, quadrupolar ion trap, capillary electrospray, needle voltage 4 kV nebulizer gas flow at 60% of maximum capillary temperature 250° capillary potential 20 V lens potential 10 V, positive ion MS-MS mode, m/z 140-350... 

Figure 10 depicts the mechanistic interpretation of equilibrium in the partly saturated state in the absence of further available fluid input. On first wetting by the contaminant leachate, the higher potential difference in the clay peds will ensure saturation of the peds and contaminants transported to the peds will be more strongly held than in the macropores. At equilibrium, the osmotic potential V tt in the clay peds is balanced by the matric (micro-capillary) potential V m in the inter-ped structure. Because further fluid input will only begin to fill the macropores, and because the potential difference in the inter-ped structure is considerably smaller than that exhibited within the clay peds, desorption of sorbed contaminants will occur primarily within the macropores that characterize the inter-ped structure. Retention of contaminants can be visualized as being the dominant accumulation process in the peds. Transport of con-... 

We have just described the linearized theory of capillarity. In the electrostatic analogy the field M(r ) is identified with a 2D electrostatic potential ( capillary potential ) and Il(r ) with a charge density ( capillary charge ) Equation 2.8 reduces to the Poisson equation of electrostatics and Equation 2.9 relates the tensor Tn, which has the form of Maxwell s stress tensor, with the electric force exerted on the capillary charge n(rn) (also the usual boundary conditions imposed on the interface have a close electrostatic analogy [34,35]). 

Here we recall briefly some results pertaining electrostatics in two dimensions. A distribution Il(r) of capillary charge creates a capillary potential u r) that can be written, provided rt(r) vanishes fast enongh at infinity, as... 

Hydraulic conductivity, which is one of the important soil parameters for seepage analysis, is estimated from the pore-size distributions measured by a mercury intrusion porosimeter. Two different relations are indispensable for analysis of partial saturation soil because hydraulic conductivity depends on the capillary potential, which is usually characterized by soil-water retention. 

Soil mechanics is the application of the laws of Mechanics and Hydraulics to problems dealing with soiKref. 1). The seepage flow through the unsaturated soil is an important problem because the soil mass behavior depends on the interactions between the soil grains and pore water. The parameters for the seepage analysis require moisture retention as well as hydraulic conductivity, since hydraulic conductivity depends on water saturation which also relates to capillary suction. The moisture retention is usually described by the relation between the water saturation and capillary potential. 

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