Surface tension, gases

The thickness of the layer of the adsorbed molecules is the characteristic distance scale for fractal surface. (3) Van der Waals attraction forces between solid/gas interactions and the liquid/gas surface tension forces are contributed to the grand potential of the system. 

For higher coverage, the interface is controlled by the liquid-gas surface tension forces (capillary condensation) and van der Waals forces between solid/gas interactions are negligible. Then, the relationship between C and dv sl, changes to the following... 

If s < 0, the liquid/gas surface tension forces are dominant, while the van der Waals forces are dominant if > 0. 

Ap is the difference between the densities of liquid and vapor g is the gravitational constant h is the meniscus height a is the liquid-gas surface tension of water. 

Other physical properties required are viscosities, especially the viscosity of the liquid densities of the liquid and gas surface tension of the liquid, including the influence of surfactants (e.g. on bubble coalescence behaviour) and, if the gas is a mixture, the gas-phase diffusivity of the reactant A. These physical properties are needed in order to evaluate the equipment characteristics as follows. 

For higher coverage, the interface is controlled by the liquid-gas surface tension forces (capillary condensation) and van der... 

Van der Waals forces between solid/gas interactions and the liquid/gas surface tension forces represent the limiting cases, but in general both the forces competitively affect the adsorption process. Therefore, in determining the surface fractal dimension by using the SP method, it is very important to use appropriate relation between CSP and <4n-r,sp- According to Ismail and Pfeifer,60 the threshold for the dominant forces between van der Waals forces and the liquid/gas surface tension forces is given as... 

Waals forces and the liquid/gas surface tension forces in the multilayer gas adsorption EDLC Electric double-layer capacitor... 

Surface tensions arise from the unbalance of molecular attractive (and repulsive) forces that result at an interface from the different nature of the materials that come in contact. Surface tensions are more readily observed in liquids—between immiscible liquids or between a liquid and a gas. Surface tensions are also present on the surface of solids, but the rigidity of the solid structure prevents their manifestation in an observable way, except in combination with the surface of a liquid in contact with the solid surface. Thus, while the surface tension and the surface free energy in a liquid are the same, this is not the case on solid surfaces. 

MASS TRANSFER TO DROPS AND BUBBLES. When small drops of liquid are falling through a gas, surface tension tends to make the drops nearly spherical, and the coefiBcients for mass transfer to the drop surface are often quite close to those for solid spheres. The shear caused by the fluid moving past the drop surface, however, sets up toroidal circulation currents in the drop that decrease the resistance to mass transfer both inside and outside the drop. The extent of the change depends on the ratio of the viscosities of the internal and external fluids and on the presence or absence of substances such as surfactants that concentrate at the interface. ... 

Fig. 10.1.4. The liquid may spread freely over the surface, or it may remain as a drop with a specific angle of contact with the solid surface. Denote this static contact angle by 6. There must be a force component associated with the liquid-gas surface tension (t that acts parallel to the surface and whose magnitude is a cos 0. If the drop is to remain in static equilibrium without moving along the surface, it has to be balanced by other forces that act at the contact line, which is the line delimiting the portion of the surface wetted by the liquid, for example, a circle. It is assumed that the surface forces can be represented by surface tensions associated with the solid-gas and solid-liquid interfaces that act along the surface, and tr i, respectively. Setting the sum of the forces in the plane of the surface equal to zero, we have...

Waals forces and the liquid/gas surface tension forces... 

Holdup volume fraction liquid 0.05-0.25. Static liquid holdup is constant for low Eotvos number, o < 4 (Eo = density liquid X gravitational constant X particle diameter squared/liquid-gas surface tension). Liquid holdup increases with Eo for Eo > 4. Dynamic liquid holdup increases with liquid flow-rate but is independent of gas flowrate. 

The critical liquid surface tension, yc, is defined as the point where the plotted line intersects the cos 0 line, i.e. the line representing complete wetting. In theory, all liquids with a liquid-gas surface tension (/lg) equal to or lower than the yc will spread on that surface. In practice, however, yc is not a constant for any given solid, but varies somewhat with the liquid type. 

III. Wherever the meniscus is concave toward the gas, surface tension exerts a pull on the liquid. The result of this pull is the rise of the liquid in the capillary. A corresponding and opposite pressure is exerted on the capillary. Wliere the capillary is vertical this pressure is equal to the weight of the liquid raised. 

Harkins and Jura [20] describe a method to obtain the absolute surface area of a solid by the following method. Firstly, the powder is exposed to a high vapor pressure of water. Indeed it is best to expose it in a high-sensitivity calorimeter over a reservoir of water. The powder is then allowed to fall into the reservoir and the amount of heat produced is measured. By doing so, one eliminates the outer surface of the adsorbed film releasing the energy associated with the liquid-gas interface surface tension. Since the liquid-gas surface tension energy is known one may then calculate from the amount of heat released the area of the powder (or at least the outer surface area of the adsorbed film before immersion). 

The component theories, which are presented in Chapter 3, are useful for estimating the interfacial tensions of solid-interfaces (solid-liquid, solid-solid) and for characterizing solid surfaces using the experimental data for the few properties that can be measiued (liquid-gas surface tension, liquid-liquid interfacial tension, contact angle). Important equations in this context arc the Young equation... 

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