Surface tension equilibrium

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]. 

The results were obtained at heat flux = 10 kW/m. For both liquids at f = 1 ms the contact angle is approximately of 0 = 60°, which is very close to the equilibrium surface tension of water. Throughout bubble growth this value decreases approxi-... 

Luo K, Shi Z, Varesi J, Majumdar A (1997) Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy. J Vac Sci Technol B 15 349-360 Majumdar A (1999) Scanning thermal microscopy. Annu Rev Mater Sci 29 505-585 Manghk RM, Wasekar VM, Zhang J (2001) Dynamic and equilibrium surface tension of aqueous surfactant and polymeric solutions. Exp Thermal Fluid Sd 25 55-64... 

The stability of a foam can be explained by the Gibbs elasticity (E). The Gibbs elasticity results from reducing the surface concentration of the active molecules in equilibrium when the film is extended. This causes an increase in the equilibrium surface tension o, which acts as a restoring force. 

Newtonian liquid viscosity, U is the bubble velocity, and aQ is the equilibrium surface tension), where surface tension and viscous forces dominate the bubble shape (15). Using a lubrication analysis, Bretherton established that the bubble slides over a stationary, constant-thickness film whose thickness divided by the radius of the tube, h R., varies as the... 

Two important parameters, a and pf arise which depend on the equilibrium and kinetic properties of the surfactant. First, a measures the fractional change in equilibrium surface tension with a fractional change in surfactant adsorption ... 

Some of the compounds described in this chapter were studied for specific physical properties. Surface tension measurements with solutions of 9-16 in 0.01 M hydrochloric acid demonstrated that these zwitterionic X5Si-silicates are highly efficient surfactants.21 These compounds contain a polar (zwitterionic) hydrophilic moiety and a long lipophilic z-alkyl group. Increase of the n-alkyl chain length (9-15) was found to result in an increase of surface activity. The equilibrium surface tension vs concentration isotherms for 9 and 16 were analyzed quantitatively and the surface thermodynamics of these surfactants interpreted on the molecular level. Furthermore, preliminary studies demonstrated that aqueous solutions of 9-16 lead to a hydrophobizing of glass surfaces.21... 

Figure D3.5.5 Equilibrium surface tension of sodium dodecyl sulfate (SDS) at the air-water interface as a function of surfactant concentration. The corresponding surface coverage was calculated using the Gibbs absorption equation (Eq. D3.5.26).

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. 

The formation of an adsorbed surface layer is not an instantaneous process but is governed by the rate of diffusion of the surfactant through the solution to the interface. It might take several seconds for a surfactant solution to attain its equilibrium surface tension, especially if the solution is dilute and the solute molecules are large and unsymmetrical. Much slower ageing effects have been reported, but these are now known to be due to traces of impurities. The time factor in adsorption can be demonstrated by measuring the surface tensions of freshly formed surfaces by a dynamic method for example, the surface tensions of sodium oleate solutions measured by... 

Many surfactant solutions show dynamic surface tension behaviour. That is, some time is required to establish the equilibrium surface tension. If the surface area ofthe solution is suddenly increased or decreased (locally), the adsorbed surfac-... 

It can be considered from the scheme that one has to distinguish between the foam kinetics, i.e. the rate of generation of foam under well defined conditions (air input and mechanical treatment) and the stability and lifetime of a foam once generated. The foam kinetics is also sometimes termed foamability in the literature. These quantities can be related to interfacial parameters such as dynamic surface tension, i.e. the non-equilibrium surface tension of a newly generated surface, interfacial rheology, dynamic surface elasticity and interfacial potential. In the case of the presence of oily droplets (e.g. an antifoam, a... 

Fig. 3.31. Equilibrium surface tension <7 vs. copolymer concentration C, (Wilhelmy plate method,...

This brings up the question of how this scheme has to be modified when equilibrium is not attained. The answer is that the identity of thermod3mamical and mechanical measurement persists, but that the value obtained for y differs from y (eq.) in fact, often y (non-eq.) > y (eq.). Suppose a given interface is created very rapidly and then starts to relax with a time scale r. At any time t equilibrium state, characterized by the pertaining y (non-eq.). Even then, this non-equilibrium surface tension can be measured, provided the time-scale of our measurement is short in comparison with t. When different methods of measurement, either thermodynamical or mechanical, do not yield the same y this may either mean that there have been errors in the measurement or that they apply to different moments (or time intervals) of the relaxation period. The downward tendency of y(f) reflects the general trend of F(V,T,n) and G(p,T, n) to become minimal at equilibrium (sec. 1.2.12). When only relaxation of the interface takes place, y must decrease. However, when the bulk phases also relax slowly or when the relaxation is determined by adsorption-desorption processes, y may also increase. For instance, this would be observed if... 

In this section we address the measurement of interfacial tensions that are time dependent because the interface is not at equilibrium. Sometimes such tensions are called dynamic surface tensions but we prefer non-equilibrium surface tensions. Their measurement will be discussed in this section, particularly against the background of the techniques described so far. Most of the interpretation (in terms of surface rearrangements, transport to and from interfaces, etc.) and additional monolayer techniques (wave damping, for instance) will be deferred to chapters 3 and 4. 

From the viscosity, as well as the phase equilibrium, surface tension, and density measurements it is evident that the system KF-K2M0O4-B2O3 is very complex. Beside the chemical reactions, the polymerization tendency of the melts, especially in the region of higher contents of boron oxide, makes this system difficult to study. 

Equilibrium surface pressure (TTg) values were calculated as TTg = ct-q — (Te, where (a-g) is the equilibrium surface tension and oq is the solvent surface tension. They were measured by the Wilhelmy plate method, using a platinum plate attached to a Sigma digital tensiometer. The range of concentrations studied were 5 X 10 to 2% wt. 

The long-time portions of the curves in Figure 5.5, plotted as o vs. comply very well with straight lines, whose slopes, S are plotted in Figure 5.6a — the points. The theoretical curve for Si is calculated using the procedure given after Equation 5.85. The curve is obtained using only the parameters of the equilibrium surface tension isotherm and the diffusion coefficients of the ionic... 

FIGURE 5.6 (a) Plot of the slope coefficient 5, vs. the surfactant (DDBS) concentration the points are the values of 5, for the curves in Figure 5.5 the fine is the theoretical curve obtained using the procedure described after Equation 5.85 (no adjustable parameters), (b) Plots of the relaxation time and the Gibbs elasticity vs. the DDBS concentration is computed from the equilibrium surface tension isotherm = n (S, /Eq) is calculated using the above values of 5,. 

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. 

The isotherms (2-151) or (2-153) can now be combined with the Gibbs expression, (2-148), to obtain the relationship between the equilibrium surface tension and the equilibrium interfacial concentration ... 

On the other hand, if the solution is too dilute, then the surface tension of the solution will approach that of the pure solvent, and then the restoring force, which is the difference between the surface tension of the clean surface (than of the pure solvent) and the equilibrium surface tension of the solution, will be too small to withstand the usual thermal and mechanical shocks. Thus, according to this mechanism, there should be an optimum concentration for maximum foaming in any solution producing transient foams. (In these solutions the foam stabilization effects are much less important than the foam-producing effects, and therefore the latter can be measured more or less independently of the former.) This maximum in the foam valume-concentration curve of solution producing transient foams has been well verified experimentally. 

From the discussion of dynamic surface tension (Chapter 5, Section IV), the maximum rate of reduction of surface tension occurs when t = t, the time required for the surface tension to reach half of the value between that of the solvent, y , and the meso-equilibrium surface tension value, ym. From equation 5.3, it has been shown (Rosen, 1991) that... 

In summary then, the factors promoting foaming in aqueous surfactant solutions are (1) low equilibrium surface tension, (2) moderate rate of attaining equilibrium surface tension, (3) large surface concentration of surfactant, (4) high bulk viscosity, (5) moderate surface viscosity, and (6) electrical repulsion between the two sides of the foam lamella. The first three promote film elasticity the last three promote foam persistence. 

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