Theory capillaries

In this case, it is assumed that the rate of movement of water is proportional to a concentration gradient, and capillary and gravitational forces are neglected. Water may, however, flow from regions of low concentration to those of high concentration if the pore sizes are suitable, and for this and other reasons, Ceaglske and Hougen1 1415) have proposed a capillary theory which is now considered. 

The capillary theory of drying has been proposed in order to explain the movement of moisture in the bed during surface drying. The basic importance of the pore space between... 

Drying of a granular material according to the capillary theory... 

The rate of shrinkage dA/dt of the circular arc is given from standard capillary theory as... 

This analogy, as Buckingham pointed out, is only formal. In the flow of heat and electricity, conductivity is a constant quantity. In capillary theory, however, X will vary with distance and time. The capillary... 

Fig. 2.6. Comparison of strength of moist agglomerates with predictions from capillary theory (data of Newitt and Conway-Jones [10] from compression testing and of Pietsch et al. [11] from tensile testing).

In actual use for mobility control studies, the network might first be filled with oil and surfactant solution to give a porous medium with well-defined distributions of the fluids in the medium. This step can be performed according to well-developed procedures from network and percolation theory for nondispersion flow. The novel feature in the model, however, would be the presence of equations from single-capillary theory to describe the formation of lamellae at nodes where tubes of different radii meet and their subsequent flow, splitting at other pore throats, and destruction by film drainage. The result should be equations that meaningfully describe the droplet size population and flow rates as a function of pressure (both absolute and differential across the medium). 

There are three general theories for interpretation of moisture distribution and rate of moisture movement inside poroizs solids. These theories can be listed as (1) diffusion theory, (2) capillary theory, and (3) vaporization-condensation theory. 

Corben and Newitt (C8) showed that the drying characteristics of moist porous granular material are consistent with the capillary theory of moisture movement. The difference in the form of the drying curves are primarily due to the capillary action of the pores. The rate of drying during the constant-rate period is higher for porous than nonporous materials. 

A classical thermodynamic argument based on simple capillary theory determines the freezing temperature as the point at which the chemical potential of the solid core inside... 

An alternative explanation, which we refer to as pressure-inhibited charge, is that downward hydrocarbon migration from sealing source rocks ceases as the pressure of the underlying stratigraphically contiguous reservoir approaches the pore-pressure of the seal. This process is consistent with capillary theory. 

Historically, the calculation of pore size distributions in porous materials has been primarily based on various forms and modifications of capillary theory... 

Foster, A.G. (1932). Sorption of condensable vapors by porous solids. I. Applicability of the capillary theory. Trans. Faraday Soc., 28, 645-57. 

For non-hygroscopic materials, the equilibrium moisture content is essentially zero at all temperatures and humidities. Equilibrium moisture content is particularly important in drying because it represents the limiting moisture content for given conditions of humidity and temperature. The mechanisms of drying during this phase are not completely understood, but two ideas can be considered to explain the physical nature of this process— one is the diffusion theoiy and the other the capillary theory. 

This means that there are no contradictions between the kinetic theory of microflotation by Derjaguin Dukhin, in which the limiting stage is the overcoming of the electrostatic repulsion between bubble and particle, and the capillary theory of flotation by Scheludko in which a special attention is paid to t,p(. and the contact angle. Both models are identical in the... 

Using the concept of Rh has enabled a number of mathematical models to be derived for the permeability of a porous material based on its porosity (see Table 8.3). The models were derived from the following three differing theoretical approaches drag theory, cell theory, and capillary theory. 

Capillary theory uses the simplest model, whereby pores within a solid material are represented as parallel capillaries of equal diameters in the porous solid. The analogy is between the tortuous pore-system of the solid and the cylindrical pores of the capillaries. The equation for k is then derived from the Hagen-Poiseuille equation for streamline flow through straight circular capillaries taking account of the tortuosity of material s pores. The tortuosity is defined as the ratio of the actual length of the flow channel to the length of the porous medium. 

The capillary theory (PI) assumes that a packed bed of nonporous spheres contains a void space between the spheres called pores. As water is evaporated, capillary forces are set up by the interfacial tension between the water and solid. These forces provide the driving force for moving the water through the pores to the drying surface. 

Christensen and Livbjerg [35] Agglomerate model A, C Literature data [30, 31] Based on capillary theory [36]... 

Surface tension is a state variable in the collective representation of interfacial thermostatics. Its actual value depends on the chemical behaviour of the adjoining phases. Identical relationships can be obtained if instead of the collective variables the individual contributions of the phases are introduced. This is made possible by the individual representation of the capillary theory [1]. 

Thus, capillary theory can be extended with the transformation given in Eq. (1). Based on the set of tools involving also the material quantities, relationships showing up only in the individual representation can be defined. 

As the classical equations of capillary theory can also be applied to a vacuum, the factor q can be defined for the vacuum as well ... 

Abstract The quantities and relationships of capillary theory are summarized in a consistent formalism. Its constituents are the canonical thermo statics of the excess quantities, the interpretation of the surface tension according to deformation theory, and the formalism of parametric theory. A generalized concept of surface excess quantities is established by introducing the... 

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