Surface tension time

Equations D3.5.30 and D3.5.32 are both very valuable. They state that the rate of adsorption can be obtained from plots of the interfacial tension versus either tA- (for t—>0) or lth (for the long-term solution f— >). With these two equations the tool to extract the adsorption rate from experimentally obtained surface tension-time curves is at hand. It should be noted that instead of the Gibbs model, one could use one of the previously mentioned adsorption isotherms such as the Langmuir adsorption isotherm to convert interfacial tension to interfacial coverage data. The adsorption isotherms may be obtained by fitting equilibrium surface tension data versus surfactant concentration. 

Certainly, equilibrium surface tension (or surface pressure) is of basic importance. However, as regards interfacial processes in the marine environment, dynamic surface tension (time domain), y(t), or the surface dila-tional modulus (frequency domain), s (i(o), is far more important than the static quantity. It is now firmly established that the existence of the dynamic quantity significantly modifies various interfacial phenomena. 

This example emphasizes the danger of using the ideal Langmuir-Szyszkowski equation of state in converting surface tension-time data into adsorption—time data even for very dilute monolayers. Also it clearly shows that any conclusion about the existence or non-existence of an... 

The surface tension-time curves obtained are shown in Figures 16, 17, 18, 19, and 20. For the ST-l-PS and ST-3-PS blends, surface tensions first fall... 

There are a number of techniques available to measure the surface or interfacial tension of liquid systems, which together cover a wide range of time. In many cases, several methods are required in order to receive the complete surface tension time dependence of a surfactant system. One of the important points in this respect is that the data obtained from different experimental techniques have to be recalculated such that a common time scale results, i.e. one has to calculate the effective surface age from the experimental time, which is typically determined by the condition of the methods. For example, the maximum bubble pressure... 

Figure2.2 Evolution ofthe homogeneous reaction time, diffusion time, conduction time, surface tension time and gravity time with respect to the characteristic dimension from the microscale up to the pilot scale (properties of aqueous solutions and water/air surface tension).

We start by supplying a thermodynamic definition of line tension [3]. Consider the three-phase system as shown in Fig. 13. Around the line of three-phase contact a cylinder is drawn with length L and radius R, and implicitly we assume that R and L approach infinity. The total free energy inside the cylinder comprises terms of the form pressure times volume, surface tension times surface area, and, finally, line tension times line length... 

The room temperature reseal diameters from Section 3.9 can be updated based on inclusion of room temperature data from Chapter 4 into the historical set of data. To determine the reseal diameter, the value was essentially back calculated from the plot of reseal pressure versus the product of surface tension times the cosine of the receding contact angle for all fluids. Uncertainties for reseal diameters were estimated in the same way as effective pore diameters as outiined in Section 10.3.1. 

The adhesion tension, cos 6, is defined as the surface tension times the cosine of the contact angle made by a liquid drop on the solid surface considered. It relates to solid-... 

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

An empirically determined relationship between drop weight and drop time does allow surface tensions to be determined for small surface ages [41],... 

As an example of the application of the method, Neumann and Tanner [54] followed the variation with time of the surface tension of aqueous sodium dode-cyl sulfate solutions. Their results are shown in Fig. 11-15, and it is seen that a slow but considerable change occurred. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

About this time Miss Pockelsf [3] showed how films could be confined by means of barriers thus she found little change in the surface tension of fatty-acid films until they were confined to an area corresponding to about 20 per molecule (the Pockels point). In 1899, Rayleigh [5] commented that a reasonable interpretation of the Pockels point was that at this area the molecules of the surface material were just touching each other. The picture of a surface film... 

Microcrystals of SrS04 of 30 A diameter have a solubility product at 25°C which is 6.4 times that for large crystals. Calculate the surface tension of the SrS04-H20 interface. Equating surface tension and surface energy, calculate the increase in heat of solution of this SrS04 powder in joules per mole. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

In figure A3.3.9 the early-time results of the interface fonnation are shown for = 0.48. The classical spinodal corresponds to 0.58. Interface motion can be simply monitored by defining the domain boundary as the location where i = 0. Surface tension smooths the domain boundaries as time increases. Large interconnected clusters begin to break apart into small circular droplets around t = 160. This is because the quadratic nonlinearity eventually outpaces the cubic one when off-criticality is large, as is the case here. 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

Surface Tension. Interfacial surface tension between fluid and filter media is considered to play a role in the adhesion of blood cells to synthetic fibers. Interfacial tension is a result of the interaction between the surface tension of the fluid and the filter media. Direct experimental evidence has shown that varying this interfacial tension influences the adhesion of blood cells to biomaterials. The viscosity of the blood product is important in the shear forces of the fluid to the attached cells viscosity of a red cell concentrate is at least 500 times that of a platelet concentrate. This has a considerable effect on the shear and flow rates through the filter. The surface stickiness plays a role in the critical shear force for detachment of adhered blood cells. 

A low melting (5°C) gallium—indium—tin alloy has been the choice for small spiral-groove bearings in vacuum for x-ray tubes at speeds up to 7000 rpm (71). Surface tension 30 times that of oil avoids leakage of the gallium alloy from the ends of the bearings. 

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