Linear tension

The actual form of lenses of non-spreading liquids on the surface of another immiscible liquid has been recently studied by Lyons3 and Langmuir.4 Langmuir shows that, in addition to the surface tension, if the lens is not of very large size, the linear tension / at the curved line of contact between the two liquids makes an appreciable difference to the thickness of the lens. The actual shape of the lenses is dependent on a rather complicated balance between the spreading coefficient the densities of the liquids, and the linear tension / round the perimeter of the lens, whose radius is R. If Dlt Z>2 are the densities of the lower and the upper liquids, respectively, the thickness t of a lens so large that its upper surface may be taken as flat, in the centre, is... 

As Fa is a negative quantity for a non-spreading liquid which forms lenses, this expression is positive. The linear tension f can be calculated from measurements of stationary lenses Bradley5 has deduced its amount from measurements on oscillating lenses. It may amount to several dynes. 

The direct measurement of the various important parameters of foam films (thickness, capillary pressure, contact angles, etc.) makes it possible to derive information about the thermodynamic and kinetic properties of films (disjoining pressure isotherms, potential of the diffuse electric layer, molecular characteristics of foam bilayer, such as binding energy of molecules, linear tension, etc.). Along with it certain techniques employed to reveal foam film structure, being of particular importance for black foam films, are also considered here. These are FT-IR Spectroscopy, Fluorescence Recovery after Photobleaching (FRAP), X-ray reflectivity, measurement of the lateral electrical conductivity, measurement of foam film permeability, etc. 

Bubble of size of the order of tens of micrometers floating on the surfactant surface only little deviates from the spherical shape. This fact has been used in the method of diminishing bubble [128,129] which allows to measure the contact angle of the black film, the linear tension of the contact line film/meniscus and the coefficient of the gas permeability through the film. Fig. 2.24 presents the scheme of this device. 

The sign and magnitude of the linear tension, ae, are determined by peculiarities of the interaction between the phases in contact in the vicinity of the perimeter of wetting. 

The conditions of heterogeneous nucleation, as well as the work of formation and the curvature radius of the critical nucleus, may be significantly influenced by the linear tension of the perimeter of wetting, x if x<0, the formation of heterogeneous nuclei becomes easier... 

The linear tension of the side face ( the step ), k, is approximately equal to the product of the specific interfacial energy and the nucleus height (size of a molecule) k bo. The work of formation of the critical two-dimensional nucleus is given by ... 

Fig. 13.3 (a) Linear tension cut-off, (b) nonlinear tension softening, (c) constant shear retention factor... 

The stability of membrane is determined not only by macroscopic parameters, such as surface and linear tension, but also by the molecular geometry of lipids conic molecules of the broad head-narrow tail type are prone to forming inverted pores, and membranes made up of them have a short life-time. 

It is also worth emphasizing that the interatomic bonds are not fully compensated at the three-phase contact line. This results in a free energy excess and a linear tension, ae, acting along the perimeter of a three-phase boundary. This linear tension can be either positive or negative and does not exceed 10 dyn/cm. While the linear tension can in most cases be neglected, it plays an essential role in the case of very small droplets, particularly in nucleation. 

FIGURE 1.8 Interface between two liquids and a gas (a) linear tension, ae, (b) selective wetting 0 > 90°, hydrophilic (oleophobic) surface 0 > 90°, hydrophobic (oleophilic) surface (c). 

Measurements carried out in mercury indicated that the appearance of a cavity takes place immediately upon the approach of the sphere to the wall under the action of very small forces, not exceeding several pN, which is in line with the earlier conclusion regarding an activation-free formation of the cavity, that is, under these conditions, there is no action of positive linear tension. The perimeter of a contact is easily visible through the eyepiece of a microscope and has the shape of a perfect circle. The values of the measured adhesion forces PsLs nd of the meniscus diameters 2xq are reported in the two left-hand columns of Table 1.1. While confidence intervals for the 2xq values indicate primarily the accuracy of measurements, the confidence intervals for the p Ls charac-... 

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