Capillary equilibrium

Fig. 13. Capillary equilibrium of a drop 2 floating on an immiscible liquid 3 1 is the vapor...

It is difficult to believe that capillary equilibrium, which is not needed for the stability of this crystal, becomes all poverful in a system of Fig. 12. 

This method is based on the principle of capillary equilibrium, providing a nondestructive technique in which the total porosity and capillary pressure-saturation data are measured [198,199]. The idea is that when two partially saturated porous materials are in contact, the system moves toward an equilibrium state in which the capillary pressure of a liquid in one of fhe samples is the same for fhe ofher material. 

The subsequently presented model of water sorption in PEMs reconciles vapor sorption and porosity data. At sufficiently large water contents exceeding the amount of surface water, T > equilibrium water uptake is controlled by capillary forces. Deviations from capillary equilibrium arising at A < can be investigated by explicit ab initio calculations of water at dense interfacial arrays of protogenic surface groups. ° In the presented model, the problem of Schroeder s paradox does not arise and there is no need to invoke vapor in pores or hydrophobicity of internal channels. Here, we will present a general outline... 

The method of standard porosimetry (MSP)41-43 was one of the first approaches used to obtain air-water capillary pressure curves for GDMs.16 In this test, a GDM sample is initially saturated with water and contacted with a water-saturated porous disc, which is a standard with known Pc(Sw) behavior. The capillary pressure of the sample-standard system is varied by allowing the liquid to evaporate from the standard and sample while in contact. If the two media can be assumed to be in capillary equilibrium, their capillary pressures are equal. Saturation is determined by measuring the weights of the sample and standard periodically. The capillary pressure of the system is found by reference to the known capillary pressure curve of the standard. This method is limited to scanning... 

Gallagher et al.50 have reported a method that is somewhat similar to MSP. As with MSP, the GDM is initially saturated with water and placed on a porous plate that is also water-saturated. Instead of changing the GDM saturation by drying, as in MSP, the capillary pressure is controlled directly by applying suction to the porous plate. Capillary equilibrium is established between the GDM and the plate as water flows from the GDM into the plate and vice versa. 

Moisture-Equivalent—Briggs and McLane (1907) made extensive physical studies on what has been termed moisture-equivalent — that is, the percentage of water retained by a soil, when the moisture content is reduced by means of a constant centrifugal force until it is brought into a state of capillary equilibrium. While King s procedure yields specific information on the relative retentiveness of various soils only after considerable time, the method of Briggs and McLane is rapid,... 

The situation shown in Figure lb is a coordinated evaporation from wide entrances A and B. Under continuous evaporation both menisci move inside the capillary having the same curvature. When one of the meniscus passes the narrowest section (rA > rB), the capillary equilibrium infringes, and mass transfer from A to B occurs spontaneously until the meniscus radii equalize. Such spontaneous mass transfer, known as jumps of Haines, occur when... 

Assuming that the mobility of the triple line (expressed by the velocity of the line in the corresponding non-reactive system for the same instantaneous contact angle) is high compared to the rate of interfacial transfer and to the diffusion rate in the bulk liquid, capillary equilibrium at the triple line is readily maintained, so that fd(t) = 0 and the instantaneous contact angle is given by ... 

A Section is devoted to wetting of a substrate by solid particles. This is particularly important in processing of nanomaterials for which capillary equilibrium is expected in short times because of the reduced size of the particles. 

At high temperatures, there is always some dissolution of the oxide in the liquid metal but to what extent can this reactivity affect wettability Useful insight can be obtained by studying spreading kinetics the time for millimetre size droplets to reach capillary equilibrium is less than I0-1 second for non-reactive systems (see Section 2.1.1), so much slower spreading kinetics are a strong indication of control by interfacial reactions. 

IMarkin (Ml) made an extensive study of capillary equilibrium in porous solids, and formulated a model of a porous medium in which the... 

A close set of equations was formulated in Ref. 16, related to the capillary pressure isotherms determined by the method of standard porosimetry [60], In the latter procedure, the equilibrium amount of the wetting liquid is measured in the porous sample under study. Simultaneously, the amount of the wetting liquid is measured in the standard specimen with a genuine porous structure, in which the capillary equilibrium is established. The standards are kept in thermodynamic equilibrium with the sample. The comparison of the amount of wetting liquid in the membrane with the pore-radius distribution in the standards, enables one to record (with a minimum of theoretical assumptions), the volume-size and surface-size distribution curves, specific pore-space surface area, and absorption isotherm in the membrane of interest, for various wetting liquids. 

Another pore filling model based upon capillary equilibrium in cylindrical pores has recently been proposed in which the condition of thermodynamic equilibrium is modified to include the effects of surface layering and adsorbate-adsorbent interactions [135-137]. Assuming that the vapor-liquid interface is represented by a cylindrical meniscus during adsorption and by a hemispherical meniscus during desorption, and invoking the Defay-Prigogene expression for a curvature-dependent surface tension [21], the equilibrium condition for capillary coexistence in a cylindrical pore is obtained as... 

Ksenzhek, O.S. (1963). Capillary equilibrium in porous media with intenecting pores. Russ.f. Phys. Chem., 37, 691-4. 

Unlike conventional hydrocarbon reservoirs, however, a BCGS develops as a result of unique temporal and spatial interactions among these various petroleum system elements. The dynamic processes responsible for fiuid distribution in a conventional gas accumulation are characteristically in static capillary equilibrium, whereas most BCGSs are not currently in an equilibrium state. This disequilibrium state is most often a result of ongoing hydrocarbon generation. 

Unlike conventional oil and gas reservoirs, structure and stratigraphy often play a secondary role in the accumulation of hydrocarbons within a BCGS, primarily because of the dynamics associated with the abnormal pressure generation (Law 1984a,b, 1985, 1995 Masters 1979, 1984 Nuccio et al. 1992). BCGSs are often not in static capillary equilibrium which is usually manifested by capillary pressure transitions that are more a function of two-phase capillary seals than from structural closure (Iverson 1994 ... 

Newsham, K. E. Rushing, J. A. 2002. Laboratory and field observations of an apparent sub capillary-equilibrium water saturation distribution in a tight gas sand reservoir. In Proceedings, 2002 Gas Technology Symposium Society of Petroleum Engineers. 

Model psds with varying values of and Xm are shown in Figure 2.2. At zero eurrent and other operating eonditions as speeified in the figure, capillary equilibrium exists in pores with radius = 5.5 nm. 

With the psd in Eq. (2.79), the continuum of possible wetting states collapses into three distinct states in which the CCL could exist locally, shown in Figure 2.10 a dry state with Sr = 0, an optimum wetting state with Sr = U /Up, and a fully flooded state with S = 1. In the dry and the fully flooded states, the CCL operates poorly due to impaired exchange eurrent density or impaired reaetant diffusion, respectively. In the optimum wetting state, local capillary equilibrium between liquid and gas phase is established in primary pores ( 3 10 nm radius), favoring large evaporation rates. At the... 

On the cathode side of a PEFC under normal operating conditions, one is concerned about excessive amounts of liquid water and flooding of gaseous supply charmels due to a net electroosmotic flux through the PEM and the production of water. Under these conditions, it is reasonable to assume full hydration of the ionomer phase in the CCL. Proton conductivity of the layer is, thus, eonsidered constant. Due to the assumption of capillary equilibrium in pores, pore-filling is... 

In addition to the conservation laws, a locally valid condition of mechanical equilibrium is needed. Here it is assumed that local pore filling is controlled by capillary equilibrium corresponding to the Laplace equation. 

Fig. 5.44 Pore-scale representation ofdrying gel with conditions for capillary equilibrium, capillary forces on the gel network and the use of phase functions in discretization.

In a first model version, the liquid distribution on the network of primary particles is assumed to be in capillary equilibrium. This allows interpretation of the fluid dynamics problem as a shape transformation problem. Cormected liquid patches have uniform curvature K of the liquid/gas phase boundary additionally, at three-phase boundaries, the contact angle 6 to the solid surface must be fulfilled (see Fig. 5.44). 

Another method that should be shortly mentioned here is the standard porosimetry developed by Volfkovich. Based on a well-characterized reference material the pore size distribution of a sample can be determined by making use of a capillary equilibrium between the sample and the reference. This variant of porosimetry is very sensitive and, like capillary flow, a non-destructive method. 

MSCP is based on the laws of capillary equilibrium. If two (or more) porous bodies partially filled with a wetting liquid are in capillary equilibrium, the values of the liquid s capillary pressure in these bodies are equal. In this method the amount of wetting liquid in the test sample (V ) is measured, and simultaneously, the same amount of wetting liquid is measured in a standard specimen of known porous structure (Vy). The liquids in both porous samples are kept in contact. After some time a thermodynamic equilibrium is reached. The measurements are performed for different overall amounts of the liquid Vo = Vj + V,. During the experiment this overall amount is changed by gradual evaporation of the liquid. 

Writing the capillary radius Rc in terms of the swelling variable qc, the liquid pressure at capillary equilibrium is given by... 

The solution of this equation can be written as an explicit relation between the wall charge density in a pore, in which capillary equilibrium exists, a c and the swelling... 

Equation 2.43 uses a notation, for the wall charge density, obtained as the solution of Equation 2.42. It is necessary to distinguish ao characteristic of pores, in which capillary equilibrium is established, from cro(water uptake at a given crQ c- The swelling variable r) is SL two variable function of ao andcro c-... 

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