Surface tension origin

The quantities yi and y2 refer to the surface tensions of the corresponding homopolymers, and )/ =kBTIa acts as a reference surface tension. Originally, this equation was applied to the surface tension of miscible polymers with A = 1 [Belton and Evens, 1945 Kammer, 1994]. We want to discuss two limiting cases of Eq. (8.42) ... 

This principle applies to all the alcohols tested. They display high surface activity, and surface tension of their solutions decreases as much as 2.5-fold relative to water (72 mN/m). Due to the dispersion of homologues and ethoxymers, it is hard to determine the CMC values on the basis of surface tension. One may say, however, that after exceeding the concentration of 0.01 wt%, micelles appear in the solution, and their concentration is significant. The differences in surface tension originate from changes in the structure of the molecule, namely, the length of the ethylene oxide and alkyl chains and the presence of an unsaturated bond (oleyl alcohol). 

Surface tension originates in intermolecular forces of cohesion. These forces are short-range but nonlocal. The equilibrium density should minimize the free energy. Near the interphase boundary, the density varies in space, and the interfacial energy can be computed as an excess energy of this inhomogeneous layer. 

It is argued by Armitstead and Goldbeck-Wood (1992) that Ah and As are not true bulk properties, but that they instead both include effects of the chain ends. They therefore vary with crystal thickness. The surface free energy factor (other part of the fold surface free energy is included in Ah TJi0, jr)) and As(TJ0, x)). 

Based on this low surface tension feature and the commonly observed insolubiUty of defoamers, two related antifoam mechanisms have been introduced (29) (/) The agent dispersed in the form of fine drops enters the Hquid film between bubbles and spreads as a duplex film. The tensions created by this Spreading lead to the mpture of the original Hquid film. (2) A droplet of the agent enters the Hquid film between bubbles, but rather than spreading produces a mixed monolayer on the surface. This monolayer, if of less coherence than the original film-stabilizing monolayer, causes destabilization of the film. 

The Good-Girifalco theory [77-82] was originally formulated to make an attempt to correlate the solid-liquid interfacial tension to the solid surface energy and the liquid surface tension through an interaction parameter, basic formulation of the theory is ... 

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

The reduction of the C— Br and C—1 group moments from 1.10 and 0.90 in bromo- and iodo-benzene to about 0.80 and 0.50 in 2-bromo- and 2-iodo-thiophene has been ascribed to the larger weight of resonance forms such as (8) and (9) in the thiophene series. The chlorine, nuclear, quadrupole, resonance frequencies of chloro-substituted thiophenes are much higher than those of the corresponding benzene derivatives. This has been ascribed to a relayed inductive effect originating in the polarity of the C—S o-bond in thiophenes. The refractive indices, densities, and surface tension of thiophene, alkyl- and halo-thiophenes, and of some other derivatives have been... 

In all cases it is known from experiment that the surface tension diminishes with increase of temperature of the surface. (Bede has shown that this is the case even when the fluids in bulk preserve their original temperature.)... 

In another study of the physical behavior of soap-LSDA blends, Weil and Linfield [35] showed that the mechanism of action of such mixtures is based on a close association between the two components. In deionized water this association is mixed micellar. Surface tension curves confirm the presence of mixed micelles in deionized water and show a combination of optimum surface active properties, such as low CMC, high surface concentration, and low surface concentration above the CMC. Solubilization of high Krafft point soap by an LSDA and of a difficulty soluble LSDA by soap are related results of this association. Analysis of dispersions of soap-LSDA mixtures in hard water shows that the dispersed particles are mixtures of soap and LSDA in the same proportion as they were originally added. These findings are inconsistent with the view that soap reacts separately with hard water ions and that the resulting lime soap is suspended by surface adsorption of LSDA. The suspended particles are responsible for surface-active properties and detergency and do not permit deposits on washed fabric unlike those found after washing with soap alone. 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

The values of some properties will be dependent on the method of measurement for example, surface tension and flash point, and the method used should be checked, by reference to the original paper if necessary, if an accurate value is required. 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

Enantiomeric discrimination and its relation to film component reorganization upon compression can also be observed in dynamic surface tension hysteresis loops. Figure 26 shows the WjA isotherms generated upon five successive compression/expansion cycles (from II = 0 to lOdyncm-1) of racemic and enantiomeric films containing 17 mole percent palmitic acid. The hysteresis loops, obtained on the apparatus described in Section 2 (p. 63), show that the first compression/expansion cycle of the racemic system is repeated in each successive cycle. Upon expansion of the film from the maximum surface pressure back to Odyncm-1, the racemic film returns to its original state without detectable reorganization of the components. However, the... 

Subjected to steady acceleration, a droplet is flattened gradually. When a critical relative velocity is reached, the flattened droplet is blown out into a hollow bag anchored to a nearly circular rim which contains at least 70% of the mass of the original droplet. Surface tension force is sufficient to allow the bag shape to develop. The bag, with a concave surface to the gas flow, is stretched and swept off in the downstream direction. The rupture of the bag produces a cloud of very fine droplets presumably via a perforation mode, and the rim breaks up into relatively larger droplets, although all droplets are at least an order of magnitude smaller than the initial droplet size. This is referred to as bag breakup (Fig. 3.10)T2861... 

Droplet Formation in Water Atomization. In water atomization of melts, liquid metal stream may be shattered by impact of water droplets, rather than by shear mechanism. When water droplets at high velocities strike the liquid metal stream, some liquid metal fragments are knocked out by the exploding steam packets originated from the water droplets and subsequently contract into spheroidal droplets under the effect of surface tension if spheroidization time is less than solidification time. It is assumed that each water droplet may be able to knock out one or more metal droplet. However, the actual number of metal droplets produced by each water droplet may vary, depending on operation conditions, material properties, and atomizer designs. 

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