Interfacial pressure definition

In line with the Gibbs adsorption equation (equation 3.33 in chapter 3), the presence of thermodynamically unfavourable interactions causes an increase in protein surface activity at the planar oil-water interface (or air-water interface). As illustrated in Figure 7.5 for the case of legumin adsorption at the n-decane-water interface (Antipova et al., 1997), there is observed to be an increase in the rate of protein adsorption, and also in the value of the steady-state interfacial pressure n. (For the definition of this latter quantity, the reader is referred to the footnote on p. 96.)... 

The interfacial pressure difference effect and the combined interfacial shear and time fraction gradient effect are treated in the same manner as suggested discussing the analogous terms in (3.161). The modified definition of the generalized drag force follows naturally from an analogy to (3.163). 

The molecules of liquids are separated by relatively small distances so the attractive forces between molecules tend to hold firm within a definite volume at fixed temperature. Molecular forces also result in tlie phenomenon of interfacial tension. The repulsive forces between molecules exert a sufficiently powerful influence that volume changes caused by pressure changes can be neglected i.e. liquids are incompressible. 

The material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

Equation D3.5.13 illustrated that the free energy of an interfacial system can be expressed in terms of the interfacial tension and chemical potential of the overall system. A simple differentiation or alternatively the reutilization of the definition of the interfacial tension used in Equation D3.5.7 at constant pressure and temperature yields ... 

Thus far, the discussion of reaction rate has been confined to homogeneous reactions taking place in a closed system of uniform composition, temperature, and pressure. However, many reactions are heterogeneous they occur at the interface between phases, for example, the interface between two fluid phases (gas-liquid, liquid-liquid), the interface between a fluid and solid phase, and the interface between two solid phases. In order to obtain a convenient, specific rate of reaction it is necessary to normalize the reaction rate by the interfacial surface area available for the reaction. The interfacial area must be of uniform composition, temperature, and pressure. Frequently, the interfacial area is not known and alternative definitions of the specific rate are useful. Some examples of these types of rates are ... 

In this paper, we now report measurements of heat transfer coefficients for three systems at a variety of compositions near their lower consolute points. The first two, n-pentane--CO2 and n-decane--C02 are supercritical. The third is a liquid--liquid mixture, triethylamine (TEA)--H20, at atmospheric pressure. It seems to be quite analogous and exhibits similar behavior. All measurements were made using an electrically heated, horizontal copper cylinder in free convection. An attempt to interpret the results is given based on a scale analysis. This leads us to the conclusion that no attempt at modeling the observed condensation behavior will be possible without taking into account the possibility of interfacial tension-driven flows. However, other factors, which have so far eluded definition, appear to be involved. 

Nc)ow and (Nc)ow are not differentiated, simply calculating the single form of Nc. This is more obvious when the definition Nc = k(Ap/L)/a is used to calculate capillary number then we use the same absolute permeability (k), the pressure drop (Ap) along the core with the length L, and the interfacial tension... 

Eq. (2.18) is the exact definition of the experimental relationship for the determination of surface tension by measuring the corresponding pressure differences and radii of curvature. This relationship is the basis of many experimental surface and interfacial tension methods measuring for example the volume of detaching drops (Section 5.2), the pressure inside bubbles (Section 5.3) or drops (Section 5.5), and the shape of sessile or pendent drops (Section 5.4). 

Any extensive property can be made intensive by dividing it by the total amount of material in the system however, not all extensive properties are proportional to the amount of material. For example, the interfacial area between the system and its boundary satisfies our definition of an extensive property, but this area changes not only when we change the amount of material but also when we merely change the shape of the system. Further, although some intensive properties can be made extensive by multiplying by the amount of material, temperature and pressure carmot be made extensive. 

The interfacial area entering in this definition must, of course, be of uniform composition, temperature and pressure. The rate will then be expressed for instance in g-mole/cm -sec. In particular when the locus of reaction is an interface between a solid phase and a liquid phase, if the interfacial area, as frequently happens, is not known, alternative definitions of the specific rate are useful ... 

In ordinary drying, the liquid in a specimen evaporates, and the resulting surface (interfacial) tension can distort the structure. In critical point drying [425], heating a specimen in a fluid above the critical temperature to above the critical pressure permits the specimen to pass through the critical point (that temperature and pressure where the densities of the liquid and vapor phases are the same and they coexist and thus there is no surface tension). By definition, a gas cannot condense to a liquid at any pressure above the critical temperature. The critical pressure is the minimum pressure required to condense a liquid from the gas phase at just... 

As the whole of a surfactant micelle has the intrinsic nature of an interfacial complex, we must assume, of course, that the pressure within the hydrocarbon core varies from point to point, and is generally anisotropic, except at the very center, implying that the pressure tensor components Py and Pn in the tangential and normal directions, respectively, are, as a rule, different. Thus, there is no natural definition of P. Nonetheless, it turns out to be convenient to put P equal to the average tangential pressure within the micelle core, that is. 

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