Surface of liquids

This rule is approximately obeyed by a large number of systems, although there are many exceptions see Refs. 15-18. The rule can be understood in terms of a simple physical picture. There should be an adsorbed film of substance B on the surface of liquid A. If we regard this film to be thick enough to have the properties of bulk liquid B, then 7a(B) is effectively the interfacial tension of a duplex surface and should be equal to 7ab + VB(A)- Equation IV-6 then follows. See also Refs. 14 and 18. 

Fig. 3.21 The effect of meniscus curvature on surface tension. Plot of /) against r . y is the surface tension of the meniscus having the mean radius of curvature and y that of a plane surface of liquid, according to Melrose. The value of y/y was calculated by the equation V = /x(l - with a . = 3 a.

Pitched-blade turbines (Fig, 18-3) are used on top-entering agitator shafts instead of propellers when a high axial circulation rate is desired and the power consumption is more than 2,2 kW (3 hp), A pitched-blade turbine near the upper surface of liquid in a essel is effecth e for rapid submergence of floating particulate solids,... 

Fig. 5. Sessile drop on a rough surface true contact angle BTA and apparent contact angle BTH. Thick curve = surface of solid (s) thin curve = surface of liquid (1) v = vapour. T is the triple point HTR a horizontal AT a tangent to the solid surface BT a tangent to the liquid surface.

The simulated free surface of liquid water is relatively stable for several nanoseconds [68-72] because of the strong hydrogen bonds formed by liquid water. The density decrease near the interface is smooth it is possible to describe it by a hyperbolic tangent function [70]. The width of the interface, measured by the distance between the positions where the density equals 90% and 10% of the bulk density, is about 5 A at room temperature [70,71]. The left side of Fig. 3 shows a typical density profile of the free interface for the TIP4P water model [73]. 

Spiegel, m. mirror, speculum, refiector polished surface surface (of liquids, fabrics,... 

Rotative speed, revolutions per minute = RPM = rpm P = Positive external pressure on surface of liquid ( + ) or partial vacuum on surface of liquid ( —)... 

In the diffusion-controlled domain (preferable in situations with large overpotentials) a diffusion layer is formed. This layer is found on the solution side of solid-state membranes it is located with in the membrane surface of liquid and glass membranes. 

Foam in the bioreactor is troublesome it can reduce the oxygen transfer rate (OTR). Antifoam is use to prevent foam formation. However, excess antifoam may cause growth inhibition in the course of fermentation. The simplest device is known as a foam breaker, which is mounted on the stirrer shaft located on the surface of liquid. It is a flat blade. 

TABLE 3.1. Parameter Sets for potential surfaces of liquid water3... 

Surface energy (associated with the surface of liquids and solids)... 

With a basket radius of b m, a radius of the inner surface of liquid of x m and h m the distance radially from the surface of the liquid, the equation of motion in the radial direction of a spherical particle of diameter d m under streamline conditions is ... 

Z 0 Vertical height of free surface of liquid (at radius ro) m L... 

The surface potential, x, is defined as the differential work done for a unit positive charge to transfer from the position of the outer potential into the condensed phase. This potential arises from surface electric dipoles, such as the dipole of water molecules at the surface of liquid water and the dipole due to the spread-out of electrons at the metal surface. The magnitude of x appears to remain constant whether the condensed phase is charged or uncharged. 

The Gibbs adsorption theory (Birdi, 1989,1999, 2002, 2008 Defay et al., 1966 Chattoraj and Birdi, 1984) considers the surface of liquids to be monolayer. The surface tension of water decreases appreciably on the addition of very small quantities of soaps and detergents. The Gibbs adsorption theory relates the change in surface tension to the change in soap concentration. The experiments that analyze the spread monolayers are also based on one molecular layer. The latter data indeed conclusively verifies the Gibbs assumption (as described later). Detergents (soaps, etc.) and other similar kind of molecules are found to exhibit self-assembly characteristics. The subject related to self-assembly monolayer (SAM) structures will be treated extensively (Birdi, 1999). However, no procedure exists that can provide information by direct measurement. The composition of the surface of a solution with two components or more would require additional comments. 

Most of the notions and physical laws of surfaces have been obtained by the studies of liquid-gas or liquid, iquid2 interfaces. The solid surfaces have been studied in more detail, but this has taken place more recently. The asymmetrical forces acting at the surfaces of liquids are much shorter than those expected on solid surfaces. This is due to the high energies that stabilize the solid structures. Therefore, when one examines a solid surface, the surface roughness will need to be considered. 

If condensation of liquid in the micropores of charcoal when brought into contact with a vapour should occur the equilibrium vapour pressure above these constricted liquid filled capillaries will be much less than above a plane surface of liquid (see Chap. ix). Under these conditions the liquid filling the pores will be included in the amount of vapour adsorbed by the charcoal and give an erroneous impression as to the true extent of adsorption. At the same time for actual condensation to occur it is necessary that a mobile free surface of liquid should first be formed at some point in the capillary, in order that the surface forces of the liquid may promote further condensation. The primary formation of a layer more than one molecule thick is thus an essential preliminary to the process of capillary condensation. 

We have noted that the evidence for orientation at a gas-liquid interface is very convincing. Iredale (Phil. Mag. XLV. 1088, 1923) has shown that the areas occupied by molecules on the surface of liquid mercury are sensibly the same as those occupied by the molecules on a water surface, thus the orientation of molecules condensing from a vapour on the surface of liquid mercury is identical with the orientation on water. There is no reason to suspect that if the liquid mercury surface were replaced by a solid metal surface the orientation of the adsorbed molecules would in any way be affected. Again the X-ray examination of the layers of fatty acids solidified on mica (Muller and Shearer, J.G.8. oxxiii. 156, 1923) has revealed the fact that the fatty acid molecules adsorbed on the mica are stratified in regular orientated molecules, the direction of orientation being perpendicular to the plane of the mica. 

Evidence of attachment of an organic molecule to a metal surface by a particular group in the molecule is not only provided from surface tension data on the surface of liquid mercury but is also to be noted in the phenomenon of displacement of one liquid by another from a surface. The hydrocarbons adhere to metals much less tenaciously than molecules containing polar groups such as —COOH and —OH. Thus we find that a hydrocarbon may be removed from a metal surface by displacement with alcohol and also that the lubricating properties of a hydrocarbon are materially affected by the addition of hydrocarbon compounds containing polar groups (Hardy, Proc. Roy. 8oc. A, c. 650, 1922, A, ci. 487, 1923). 

A. Frumkin and A. Gorodetzkaya, Electrocapillary Phenomena and Layer Formation on the Surface of Liquid Gallium, Z. Phys. Chem. (Leipzig) 136 215 (1928). 

Compared to the film model or the penetration model, the surface renewal approach seems closer to reality in such a case where the surface of liquid in an... 

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