Interfacial tension precision

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

Non-equilibrium liquid films formed in the process of spreading have been considered in some early works, especially in the test of the theory of interfacial tension and the rule of Antonov [204], A review on the rule of Antonov and its interpretation on the basis of isotherms of disjoining pressure in wetting films is presented in [532]. However, these works do not deal with precise measurement of film thickness and the studies confined only the kinetics of spreading and lens formation. 

However, for precise absolute measurements [1.6.1] is Inadequate. When the droplet falls down, part of the liquid remains on the capillary and the counteracting surface force is not vertical. The breakaway phenomenon is rather com-plicated and may rather look like fig. 1.17. Using high speed cinematography, details of the detachment phenomena can be seen. As the expansion of the interface is a dynamic process, the rate at which the interfacial tension can adjust. 

For measurement of the interfacial tension between two liquids the equation changes in that p is replaced by [ p(plate) - p b )] and Ap by [ p(plate) - p(L ) if is the heavier of the two liquids Lj and. Generally these measurements tend to be less precise because usually < y. ... 

The weak point in the method is that is a sensitive, though esoteric quantity. We discussed its value for fluid interfaces in sec. 2.8, where we concluded that the order of magnitude is well established but that a precise vedue is difficult to assign. For SG interfaces we did not develop a theory in those systems represents the depth over which the atoms near the surface assume mutual positions differing from those in the bulk of the solid. However, we shall show below that for contact angles the choice of is less critical than it is for interfacial tensions. 

The value of Sp depends on several parameters, including the hydrodynamic properties of the channels, the centrifugal force (Sp increases to reach a maximum with the centrifugal force), the mobile-phase flow rate (Sp decreases linearly with the mobile-phase flow rate), the physical properties of the solvent system (such as viscosity, density, interfacial tension), the sample volume, the sample concentration, and the tensioactive properties of solutes to separate [2,3]. It is necessary to precisely monitor Sp because various chromatographic parameters depend on it, in particular the efficiency, the retention factor, and the resolution. Foucault proposed an explanation for the variation of Sp with the various parameters previously described. He modeled the mobile phase in a channel as a droplet and applied the Stokes law which relies on the density difference between the two phases, the viscosity of the stationary phase, and the centrifugal force. Then, he applied the Bond number, derived from the capillary wavelength which was formerly introduced for the hydrodynamic mode [4] and which relies on the density difference between the two phases the interfacial tension and the centrifugal force [3]. 

Static capillary phenomena lead to precisely determined geometrical shapes like sessile menisci, pendent menisci, minimal surfaces, which can be used for the physical determination and measurement of the surface tension or the interfacial tensions between fluids. In addition to the simple forms considered herein, more complex forms (e.g., sessile lenticular drops) can be studied. Mathematical resolution of these shapes is a combination of the (numerical) solution of the highly nonlinear Young-Laplace equation together with an appropriate set of boundary conditions. For practical purposes, only axisymmetric forms are readily amenable to mathematical analysis. 

The precise relation between the surface tensions of the two liquids separately against theory vapor and the interfacial tension between the two liquids depends on the chemical constitution and orientation of the molecules at the surfaces. In many cases, a rule proposed by Antonow holds true with considerable success. 

Thus the normal-stress balance is precisely satisfied with fo = 0. The capillary (or interfacial-tension) contribution is simply to produce a jump in pressure equal to n = 2/Ca across the drop surface. This pressure jump is, in fact, precisely the result (2 138) that was derived earlier, simply written in dimensionless terms based on a characteristic pressure,... 

Measurement of the surface or interfacial tension of liquid systems is accomplished readily by a number of methods of which the most useful and precise for solutions of surfactants are probably the drop-weight and Wilhelmy plate methods. An excellent discussion of the various methods for determining surface and interfacial tension is included in the monograph on emulsions by Becher (1965). 

The extensive research on microemulsions was prompted by two oil crises in 1973 and 1979, respectively. To optimise oil recovery, the oil reservoirs were flooded with a water-surfactant mixture. Oil entrapped in the rock pores can thus be removed easily as a microemulsion with an ultra-low interfacial tension is formed in the pores (see Section 10.2 in Chapter 10). Obviously, this method of tertiary oil recovery requires some understanding of the phase behaviour and interfacial tensions of mixtures of water/salt, crude oil and surfactant [4]. These in-depth studies were carried out in the 1970s and 1980s, yielding very precise insights into the phase behaviour of microemulsions stabilised by non-ionic [5, 6] and ionic surfactants [7-9] and mixtures thereof [10]. The influence of additives, like hydro- and lyotropic salts [11], short- and medium-chain alcohols (co-surfactant) [12] on both non-ionic [13] and ionic microemulsions [14] was also studied in detail. The most striking and relevant property of micro emulsions in technical applications is the low or even ultra-low interfacial tension between the water excess phase and the oil excess phase in the presence of a microemulsion phase. The dependence of the interfacial tension on salt [15], the alcohol concentration [16] and temperature [17] as well as its interrelation with the phase behaviour [18, 19] can be regarded as well understood. 

When compared with the other methods, the capillary rise method is the ultimate standard method in terms of the degree of theoretical exactitude, and, although it is the oldest method, it still gives the most precise liquid surface tension results if carefully applied, and when the time of measurement is allowed to be sufficiently long. However, with the improvement in computer-controlled electronic equipment, other methods now also have a very high precision. Some of the surface tension results are summarized in Table 6.1, and the interfacial tension between pure liquids in Table 6.2. 

Equation (515) is known as Vonnegut s equation and it is valid on the assumption that the drop is in equilibrium and its length is larger than four times its diameter (/ > 4r ). The spinning drop tensiometer method is widely used for measuring liquid-liquid interfacial tension, and is especially successful for examination of ultra-low interfacial tensions down to l(T6mNnr1. In addition, it can also be used to measure interfacial tensions of high viscosity liquids when precise temperature control is maintained. 

Adsorption. Some substances tend to adsorb onto an interface, thereby lowering the interfacial tension the amount by which it is lowered is called the surface pressure. The Gibbs equation gives the relation between three variables surface pressure, surface excess (i.e., the excess amount of surfactant in the interface per unit area), and concentration—or, more precisely, thermodynamic activity—of the surfactant in solution. This relation only holds for thermodynamic equilibrium, and the interfacial tension in the Gibbs equation is thus an equilibrium property. Nevertheless, also under nonequilibrium conditions, a tension can be measured at a liquid interface. 

Precision of Measurements. Aliquots from a stock solution of 0.1 M sodium oleate (five months old) were used to prepare aqueous test solutions that were 0.01 M in sodium oleate and 0.1 M in sodium chloride pH 9 5 Interfacial tensions were measured against n-undecane without pre-equilibration. The second solution was made and measured one week after the first and the third solution two weeks after the first. The results in Table I... 

Precision of Interfacial Tension Measurements 0.01 M Sodium Oleate, 0.1 M Sodium Chloride pH 9 5 vs n-Undecane... 

Mayonnaise, on the other hand, is a relatively stable emulsion due mostly to high viscosity (more precisely, viscoelasticity), though surfactants are also present. The oil and water in mayonnaise cannot separate into phases because the emulsion droplets do not have enough energy for much movement. In less viscous emulsions, surfactants are responsible for stability. They reduce interfacial tension for the formation of small particles that either repel or very weakly attract each other. Brownian motion must be able to counter the effects of interparticle attraction, sedimentation, or creaming, which is floatation. Micellar suspensions could also be considered microemulsions, although this is debatable. 

Such a knowledge is particularly valuable for the study of the additives known as dopes. The action of the dopes is precisely that of modifying, by surface adsorption, not only the absolute values of adhesion tensions and of interfacial tensions, but also the signs of these forces, which are indicated by a change of the contact angles. 

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