Interfacial tension calculation

A schematic of change in the type of microemulsion with the salinity is shown in Figure 7.8, and a volume fraction diagram of the data presented in Table 7.2 is shown in Figure 7.9. The volume fraction information can also be represented by a solubility plot, as shown in Figure 7.10 (see page 254). We will see later that the solubilization ratio is a very important parameter in interfacial tension calculation. 

In order to confirm that the bulk viscosity has no appreciable effect, a paraffin oil of viscosity 10 cp was used. The shape of the I.D.T. pressure trace was of the standard form and the interfacial tension calculated from the pressure jump was in agreement with the pendant drop value. The I.D.T. traces were independent of displacement velocity for the displacement rates used (0.03 to 0.3 mm s ). 

Fig. 8.24 Interfacial tension calculated by the real-time FPGA approach and a software reference implementation applying the Young-Laplace equation and a fourth order Runge-Kutta solver for 800 captured frames [68]...

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

Another oscillatory method makes use of a drop acoustically levitated in a liquid. The drop is made to oscillate in shape, and the interfacial tension can be calculated from the resonance frequency [113]. 

The theoretical treatments of Section III-2B have been used to calculate interfacial tensions of solutions using suitable interaction potential functions. Thus Gubbins and co-workers [88] report a molecular dynamics calculation of the surface tension of a solution of A and B molecules obeying Eq. III-46 with o,bb/ o,aa = 0.4 and... 

Application of 150 MPa pressure increases the interfacial tension for w-hex-ane-water from 50.5 to 53.0 mN/m at 25°C. Calculate AV. What is AV for that area corresponding to a molecular size (take a representative molecular area to be 20 A ) Convert this to cm /cm mol. 

Fig. IV-2. The Good-Fowkes model for calculating interfacial tension. (From Ref. 20.)...

Referring to Fig. IV-4, the angles a and /3 for a lens of isobutyl alcohol on water are 42.5° and 3°, respectively. The surface tension of water saturated with the alcohol is 24.5 dyn/cm the interfacial tension between the two liquids is 2.0 dyn/cm, and the surface tension of n-heptyl alcohol is 23.0 dyn/cm. Calculate the value of the angle 7 in the figure. Which equation, IV-6 or IV-9, represents these data better Calculate the thickness of an infinite lens of isobutyl alcohol on water. 

Using appropriate data from Table II-9, calculate the water-mercury interfacial tension using the simple Girifalco and Good equation and then using Fowkes modification of it. 

Templeton obtained data of the following type for the rate of displacement of water in a 30-/im capillary by oil (n-cetane) (the capillary having previously been wet by water). The capillary was 10 cm long, and the driving pressure was 45 cm of water. When the meniscus was 2 cm from the oil end of the capillary, the velocity of motion of the meniscus was 3.6 x 10 cm/sec, and when the meniscus was 8 cm from the oil end, its velocity was 1 x 10 cm/sec. Water wet the capillary, and the water-oil interfacial tension was 30 dyn/cm. Calculate the apparent viscosities of the oil and the water. Assuming that both come out to be 0.9 of the actual bulk viscosities, calculate the thickness of the stagnant annular film of liquid in the capillary. 

Calculate the film thickness for the Marongoni instability shown in Fig. Xlll-2 using the relationship in Eq. XIIl-3, assuming that the interfacial tension is 20 mN/m. 

Even if the interfacial tension is measured accurately, there may be doubt about its applicability to the surface of bubbles being rapidly formed in a solution of a surface-active agent, for the bubble surface may not have time to become equihbrated with the solution. Coppock and Meiklejohn [Trans. Instn. Chem. Engrs., 29, 75 (1951)] reported that bubbles formed in the single-bubble regime at an orifice in a solution of a commercial detergent had a diameter larger than that calculated in terms of the measured surface tension of the solution [Eq. (14-206)]. The disparity is probably a reflection of unequihbrated bubble laminae. 

Even though the basic idea of the Widom model is certainly very appealing, the fact that it ignores the possibihty that oil/water interfaces are not saturated with amphiphiles is a disadvantage in some respect. The influence of the amphiphiles on interfacial properties cannot be studied in principle in particular, the reduction of the interfacial tension cannot be calculated. In a sense, the Widom model is not only the first microscopic lattice model, but also the first random interface model configurations are described entirely by the conformations of their amphiphilic sheets. 

The Gibbs equation allows the amount of surfactant adsorbed at the interface to be calculated from the interfacial tension values measured with different concentrations of surfactant, but at constant counterion concentration. The amount adsorbed can be converted to the area of a surfactant molecule. The co-areas at the air-water interface are in the range of 4.4-5.9 nm2/molecule [56,57]. A comparison of these values with those from molecular models indicates that all four surfactants are oriented normally to the interface with the carbon chain outstretched and closely packed. The co-areas at the oil-water interface are greater (heptane-water, 4.9-6.6 nm2/molecule benzene-water, 5.9-7.5 nm2/molecule). This relatively small increase of about 10% for the heptane-water and about 30% for the benzene-water interface means that the orientation at the oil-water interface is the same as at the air-water interface, but the a-sulfo fatty acid ester films are more expanded [56]. 

The entropy of formation of the interface was calculated from the temperature coefficient of the interfacial tension.304 The entropy of formation has been found to increase with the nature of the electrolyte in the same sequence as the single cation entropy in DMSO.108, 09,329 The entropy of formation showed a maximum at negative charges. The difference in AS between the maximum and the value at ff=ocan be taken as a measure of the specific ordering of the solvent at the electrode/solution interface. Data 108,109304314 have shown that A(AS) decreases in the sequence NMF > DMSO > DMF > H90 > PC > MeOH. 

Thus, in the relatively simple case of oil in water emulsions, where a surface active agent such as a soap is used as the emulsifying agent, it is known that the soap adsorbed on the surface of the oil particles decreases the interfacial tension, thus stabilizing the emulsion. The adsorbed soap ions also give a net electrostatic charge to the dispersed oil droplets, serving to repel other oil droplets, with the net effect that flocculation is hindered (and stability is increased). It is even possible to measure the amount of adsorbed soap ions and to calculate the values of the surface potential. 

The spinning drop technique measures the shape of the oil drop in the flooding solution in a capillary tube. An automatic measuring system has been developed by combining a video-image analysis, an automatic recording system, and a computer for calculation of the interfacial tension [1865]. 

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

Interfacial Tension (IFT) Measurements. All IFT measurements were done using a University of Texas Model 300 Spinning Drop Interfacial Tensiometer. The basic principle is to introduce a drop (about 2 p ) of an oil sample into a glass capillary tube (1.5 mm I.D., 78 mm long) filled with the aqueous medium. The tube is then spun about its main axis. The oil drop will elongate to a length determined by the IFT value of the system. Details of the theory and application can be found elsewhere (15.16). According to the equipment manufacturer, the formula used to calculate IFT value is ... 

Jain, T. S. de Pablo, J. J., Calculation of interfacial tension from density of states, J. Chem. Phys. 2003,118, 4226 1229... 

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