Surface tension effects

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Rizzuti et al. [Chem. Eng. Sci, 36, 973 (1981)] examined the influence of solvent viscosity upon the effective interfacial area in packed columns and concluded that for the systems studied the effective interfacial area a was proportional to the kinematic viscosity raised to the 0.7 power. Thus, the hydrodynamic behavior of a packed absorber is strongly affected by viscosity effects. Surface-tension effects also are important, as expressed in the work of Onda et al. (see Table 5-28-D). 

The first test of this model is whether D is inversely proportional to the shear stress. This is indeed the case (Van der Linden et al. 1996). The second part of the test is to verify the proportionality constant, 4aeff. This effective surface tension, Oeff, has been calculated as follows (Van der Linden and Droge 1993). The effective surface tension is defined as the energy needed to deform a lamellar droplet, divided by the excess surface area needed to induce that specific deformation. Hence, one first needs to calculate the deformation energy for a given deformation and secondly divide that by the concomitant excess surface area. 

The form eqn (3.1) is to hold strictly for planar surfaces. We have already alluded to curvature corrections to the effective surface tension contribution. If the micellar surface is spherical, the effective surface tension y for both a drop and a hole in the liquid is less than that for a planar interface by a factor (1 —d/R), where d is of the order of one or two molecular radii and R is the position of the Gibbs dividing surface. Corresponding corrections to the electrostatic contributions are expected to be of much more importance, and can be handled within the framework of a capacitance description. Thus for a spherical capacitance the energy per unit area is from electrostatics... 

These local calculations predict the formation of planar, hyperbolic, parabolic (cylindrical) and elliptic (globular) interfaces as the volume fraction of the iMger block increases from 50%. The compositional range of existence of the various interfacial geometries depends to a limited extent on the effective surface tension acting at the interface. 

The elasticity of multilamellar vesicles can be discussed in reference to that of emulsion droplets. The crystalline lamellar phase constituting the vesicles is characterized by two elastic moduli, one accounting for the compression of the smectic layers, B, and the second for the bending of the layers, K [80]. The combination has the dimension of a surface tension and plays the role of an effective surface tension when the lamellae undergo small deformations [80]. This result is valid for multilamellar vesicles of arbitrary shapes [81, 82]. Like for emulsion droplets, the quantity a/S is the energy scale that determines the cost of small deformations. 

Surface tension arises due to short range intermolecular forces. The most important ones are van der Waals forces, London dispersion forces, hydrogen and metallic bondings [1]. The contributions from the individual forces are assumed independent, and the effective surface tension are calculated as the linear sum of the individual force contributions. The different molecular attraction forces at the two sides of the interfaces induce a resulting attraction force at the interface. Imagine that the molecules at an interface between two fluids exist in a state different from that of the molecules in the interior of the fluid. The phase k molecules are (on the average) surrounded by phase k molecules on only one side within the interface, whereas the interior... 

On the other hand, the introduction of some branching into the hydrophobic group increases the CMC/C20 ratio but has little effect on Ym. We can therefore expect that the introduction of branching into the hydrophobic group will make the surfactant a more effective surface tension reducer. This is seen in the isomeric p-dodecylbenzene-sulfonates (Figure 5-4), where the isomers with branched alkyl chains, although less efficient reducers of the surface tension than the isomer with the straight alkyl chain, reduce the surface tension to lower values than does the latter. 

Table 5-2 lists some experimental values of Tm, CMC/C2o and jicmc. The experimental tiCmc values are very close to those calculated from the Tm and CMC/C2o values and equation 5.1. For surfactants with hydrocarbon-chain hydro-phobic groups, the most effective surface tension reducers (largest IIcmc values) are (1) nonionic compounds having small hydrophilic head groups and (2) anionic-cationic salts where both hydrophobic chains contain six carbon atoms or more, especially when both chains are approximately of the same length. Because of the... 

The compression or decompression of bovine serum albumin monolayers spread on an aqueous substrate at a pH near the isoelectric point can effect surface tension. The surface pressure changes depend on the distance between the position of the surface pressure measuring device and the compression barrier. This effect is minimal at a pH above or below the isoelectric point and undetected for small molecules (myristic acid and eicosyl sodium sulfate) even when the substrate contains substituted alkyl amines. A theory is proposed which attributes the above observation to surface drag viscosity or the dragging of a substantial amount of substrate with the BSA monolayer. This assertion has been experimentally confirmed by measuring the amount of water dragged per monolayer using the technique of surface distillation. 

The important difference between single-phase and two-phase flows is the interface latent heat effect involved with the latter. Also, in cases with strong curvature effects, surface tension needs to be taken into account. Because of latent heat, the heat transfer rates in two-phase problems are an order of magnitude larger than those in single phase. 

Finally, we take into account the effect of decreased surface tension as a result of the dissolved adipic acid. The effective surface tension for adipic acid is calculated from literature data (Shulman et al. 1996), and we use (17.A.35) to generate the curves in Figure 17.A.5. Once more, the curve is shifted down (activation is accelerated) as a result of the decreased surface tension. We also note that the surface-active solute effect lowers the critical S appreciably only when there is very little or no soluble gas. This is because in the presence of sufficient soluble gas, the Sc is determined by the second maximum rather than the first, and the downward shift of this point owing to surface tension effects is quite small. 

The effective surface tension is affected by two main properties of the drop, charge and diameter. As the diameter of the drop decreases, the droplet reaches the Rayleigh limit and then undergoes a Coulombic explosion. This Coulombic explosion indicates that the surface tension of the droplet has been overcome by the surface charge pressure and therefore the effective surface tension is zero at the Rayleigh limit. If we substitute the Rayleigh Umit (32.16) in (32.19) we get ... 

The relation obtained in (32.20) shows that the effective surface tension for a droplet is dependent on how close the droplet charge is to the Rayleigh limit charge. If the Weber number (32.17) is rearranged and the critical Weber number, at which aerodynamic forces become important, is treated as a constant we get the following ... 

To estimate the aerodynamic effect on a charged droplet, the effective surface tension can be calculated using (32.20) and compared with the critical surface tension given by (32.21). If the effective surface tension is much lower than the critical surface tensirai, aerodynamic effects on the drop are important. Conversely if then the aerodynamic forces are negligible. 

Capillary effects Surface tension y, thermal, electrical (electrocapillarity), surface tension gradients Vy, chemical, thermal, electrical, optical Capillary pressure difference (e.g., Sammarco and Bums 1999) (e.g.. Pollack et al. 2000 Prins et al. 2001), typically involve thin films (e.g., Gallardo et al. 1999) (e.g., Kataoka and Troian 1999), photoresponsive materials... 

Experimental studies show that for medium particles (dj = 0.5 mm), the cohesive forces (agglomeration) are dominant and lead to higher slurry hold-up as compared with the coarse particles. To reduce these forces, the fluid surface tension, o, was reduced from 70 to 35 mN/m by the addition of Triton X-100 (a nonionic surfactant) to tap water at a concentration of 120 ppm. Figure 19 shows that the effect surface tension on the slurry hold-up was not significant for both particle sizes (dj = 0.5 and 2.0 mm). 

Monolayers of nanoparticles at liquid-fluid interfaces have attracted considerable attention over several decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. Among others, the examinations focused on thin-layer preparation [10, 18, 19, 20, 21, 22, 23], emulsion stabilisation [15, 24] and particle characterisations [25, 26, 27]. The Stober silica (synthesised by controlled hydrolysis of tetraethylorthosilicate in ethanol in the presence of ammonia and water) [28] has many advantageous properties for model investigations. The nearly spherical particles show a narrow size distribution and are compact above a certain particle size (around 20 nm diameter) [29]. The particles, on the one hand, show partial wettability and, on the other hand, form a weakly cohesive two-dimensional dispersion at the water-air interface [10, 14]. All that makes them suitable to determine the total repulsive interparticle energies in a film balance by measuring the effective surface tension of the monoparticulate layer [30, 31, 32, 33, 34, 35, 36]. 

Surfactants, by definition, are substances which lower the surface tension of liquids in which they are dissolved or the interfacial tension between two or more mutually immiscible phases. It has long been recognised that the most effective surface tension depressants contain highly water-attracting (hydrophilic) and highly water-repellent (hydrophobic) groups, joined together in the same molecule. 

Linden [49]. To our knowledge the theory has not yet been applied to experimental results. E. v. d. Linden assumes that multilamellar vesicles (droplets) are deformed in shear flow from a spherical to an elliptical shape. Turning into the deformed state the energy of closed shells is shifted because their curvature as well as their interlamellar distance D are changed. Due to the interaction of the bilayers, expressed by the bulk compression modulus B, the inner shells are deformed and the total deformation energy of the lamellar droplet gets minimized. Assuming that the volume of a droplet is not modified by the deformation, the surface A must increase. One can define an effective surface tension (Tef[=ElAA. E. v. d. Linden obtains ... 

Figure 17.2 Schematic to illustrate the thermodynamics of micellization, with contributions to the Gibbs free energy as a function of aggregate size, showing the driving force (due to the hydrophobic effect), surface-tension correction and head-group term. The sum curve or nucleation barrier of these three parameters has a minimum at the optimum aggregation number. (With kind permission from Springer Science + Business Media Colloid Polymer Science, Supramolecular perspectives in colloid science, 286, 2008, 855-864, M.A.C. Stuart.)...

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