Tension Variation

Experiments demonstrate that intrafacial tension varies with both interfacial composition and temperature. At equilibrium, both these quantities are uniform along an interface and hence so is inteifacial traision. If transport processes (e.g., diffusion of surfactant to a newly created interface) cause interfadal tension to be time dependrait while remaining uniform at each time, changes in intrafacial shape may occur. Such processes may be followed by, for instance, monitoring the dimensions of a sessile or pendant drop as a function of time. 

Flow or transport may also produce spatial variations in interfadal tempraa-ture or concraitration and hence in intrafadal tension. Indeed, we have already seen in Chapter 5 that flow assodated with surface wave motion causes surfactant concentration gradients to develop at an interface with an insoluble monolayer. The resulting inteifacial tension gradiraits were found to significantly enhance the damping of wave motion at hquid-gas interfaces, with resulting adverse effects on transfer of heat or mass across the interface. 

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Cord tension variation 250 N per total width both in calendering direction and across... 

The work currently being conducted by Satyanarayan, Kumar, and Kuloor (S3) indicates that the effect of surface tension is more involved than hitherto appreciated. Some of their data are presented in Figs. 6. and 7. They find that at very small orifice diameters or at very large flow rates, the surface tension variation has negligible influence on the bubble volume. For higher orifice diameters, the influence is more pronounced at small flow rates, as is evident from Fig. 7. 

The low interfacial tensions between two liquids have been measured for different systems by using the pendant drop method. In the case of the quaternary system Ci2ll25S 3 tNa+H20+n-Butanol+Toluene, the interfacial data as measured by pendant drop method are compared with reported literature data, using other methods (with varying NaCl concentration). In order to understand the role of co-surfactant, ternary systems were also investigated. The pendant drop method was also used for measuring the interfacial tension between surfactant-H20/n-alcohol (with number of carbon atoms in alcohol varying from 4-10). The interfacial tension variation was dependent on both the surfactant and alcohol. 

Princen [64] discovered that the yield stress, xQ, was strongly dependent on <(>, increasing sharply with increasing phase volume. x was also found to depend linearly on the surface tension. Variation with the mean droplet radius, however, did not match theoretical predictions this was reportedly due to the presence of a finite film thickness between adjacent droplets. 

In figure 9A, a typical power time curve and the simultaneous oxygen tension variation are shown with the microheterotrophic cell numeration (N cells/ml). Consequently to the initial organic enrichment (in the microcosm), the heat production increased exponentially... 

The amount of pigment utilized depends on the color and the hiding power required of the coating. The flow additive often is introduced to relieve surface tension variations between the coating and substrate, to eliminate pinholes or crater formation. Solvents are added as necessary to achieve flow under application conditions. 

Drance SM.The significance of the diurnal tension variations in normal and glaucomatous eyes. Arch Ophthalmol 1960 64 494-501. 

Some questions remain unanswered about the values of the prefactor measured in our experiments (table III). The value of the prefactor y of the interfacial tension variations is very small ... 

Surface tension variations of surface tension from one liquid to another. 

An estimate of the total desorption flow from the surface of a strongly retarded region in the neighbourhood of the rear pole of the bubble is derived as follows. When electrostatic retardation of adsorption-desorption kinetics does not exists, the results of Chapter 8 [Eq. (8.145)] can be applied. For ionic surfactant, the equation for surface tension variation somewhat differs from that for non-ionic surfactant. With regard to these differences, the following estimate of desorption flow results. 

Clearly, then, we must know the concentration, temperature, and charge distributions at the interface in order to define the surface tension variation required to solve the hydrodynamic problem. However, these distributions are themselves coupled to the equations of conservation of mass, energy, and charge through the appropriate interfacial boundary conditions. The boundary conditions are obtained from the requirement that the forces at the interface must balance. This implies that the tangential shear stress must be continuous across the interface, and the net normal force component must balance the interfacial pressure difference due to surface tension. 

In the preceding section, we have examined a variety of steady thermocapillary and diffusocapillary flows. Not all such flows are stable and in fact surface tension variations at an interface can be sufficient to cause an instability. We consider here the cellular patterns that arise with liquid layers where one boundary is a free surface along which there is a variation in surface tension. It is well known that an unstable buoyancy driven cellular convective motion can result when a density gradient is parallel to but opposite in direction to a body force, such as gravity. An example of this type of instability was discussed in Section 5.5 in connection with density gradient centrifugation. 

YIH, C-S. 1968. Fluid motion induced by surface tension variation. Phys. Fluids 11, 477-480. 

During the 1870 s, Carlo Marangoni, who was apparently aware of Carra-dori s work but not of Thompson s, formulated a rather complete theory of surface tension driven flow (M2, M3). He noted that flow could result from surface tension variations as they are caused by differences in temperature and superficial concentration, and that, conversely, variations in temperature and concentration could be induced by an imposed surface flow. Marangoni ascribed several new rheological properties to the surface (notably surface viscosity, surface elasticity, and even surface plasticity), while remarking that perhaps some of these properties could be associated only with surface contamination. Most present-day authors ascribe the first explanation of surface tension driven flow to Marangoni, and term such flow a Maragoni effect. ... 

Testing for elastomeric fabrics is not similar to that used for rigid fabrics because the slight tension variation of elastomeric yams affects the final fabric properties. Normally, an ahysteresis curve is produced when a force is applied to an elastomeric fabric... 

The occurrence of these two minima may be interpreted by analyzing the variation of the interfacial tension (Fig. 14, left) and emulsion stability (Fig. 14, center) along the same formulation scan (81,82). The difference between the two variations is essentially due to the fact that the tension variation takes place over a much wider temperature interval than the -stabiiity change. The combination of these two factors that have opposite effects on the drop size generates the shown variation. When optimum formulation is approached (from any side), the first effect to be fell is the tension reduction, which makes breakup easier with a resulting drop size decrease. Then, when the rapid reduction in emulsion stability takes place, the coalescence rate increases very quickly and the trend is reversed to produce larger drops. Consequently, the minimum size drop is not attained at optimum formulation, where the tension exhibits its lowest value, but at some distance" from it, where the best compromise between low tension and not too... 

For an air/liquid system a measure of the surface-tension variation resulting from the imposed periodic area variation in the Langmuir trough is performed. If both dilational viscous = (f) and dilational elastic j = e (f) data are needed, and if a Langmuir-type trough is used, then one barrier can be oscillated and another barrier can be used to adjust the extent of the interfacial area. The calculation of the complex modulus, , requires complete scans at different frequencies. 

Faidley, R. W. Panton, R. L. Measurement of liquid jet instability induced by surface tension variations. Exp. Therm. Fluid Sci. 3, 383-387 (1990). 

The presence of surfactants in the mass transfer systems presented has been shown to affect the mass transfer process by inducing, reducing or suppressing interfacial convection. Since interfacial convection is caused by interfacial tension variations and the addition of a surfactant to a system alters interfacial tension, an examination of the effect surfactants have on the interfacial tension of the systems is of interest. 

At short times (f 0), the second term may be neglected and F(f) increases simply by diffusion from the bulk. The surface tension variation at those times can be written as... 

Surface tension variations can also be produced by adding surfactants on the interface. These surface active materials (e.g., soap) typically consist of a hydrophilic head group and a hydrophobic tail. Therefore, the presence of surfactants in solution is energetically unfavorable and one gains in free energy if the molecules align along the free surface, which is the equilibrium situation. The creation of a layer of surfactant molecules on the interface then lowers the surface tension of the system. 

The pattern of tension variation within the contact line is shown in Figure 2. It can be shown that there is a zone of no-slip (A-B) followed by a zone of shp (B-C). The rope tension... 

Having established the pattern of tension variation within the slip zone, the variation in torque traction in the transverse direction can be demonstrated. The incremental torque traction changes dMIr are related to the contact force P by... 

For a single-component liquid-vapor interface, it is not possible to vary temperature and pressure independendy while maintaining the phases in equihbrium. Flowever, measurement of interfacial tension variation with pressure at constant temperature is possible in a binary system. Good (1976) has shown that such data can be used to obtain useful information about interfacial characteristics in this case. 

The interfadal tension y in this equation is that of the initial stagnant layer, with interfacial tension variations providing a second-order correction that is neglected in our linear analysis. With the pressure given by Equations 5.39 and 5.26, z given by and A3, A5, and Ag eliminated by Equations 6.21 through 6.23, Equation 6.24 becomes... 

The coefficient dy/dT of interfacial tension variation with tranpraatuie is assumed to have a constant valne. It is virtually always negative, a typical value being abont -0.1 mN/m K. According to Equation 6.26, developmrait of a temperature gradient along an interface causes flow to arise having shear stresses that balance the lateral force produced by the interfadal tension gradirait. In terms of the coeffidents A, Equation 6.26 becomes... 

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