Elimination of Surface Tension Gradients

In this context, we note that Ross and Nishioka [67] have examined the stability of air bubbles (of 0.8 cm radius) released under monolayers or multilayers of 

PDMS oil spread on both distilled water and snrfactant solntion. With a distilled water snbstrate, babbles were more stable than in the absence of PDMS (presumably as a result of reduced film draining rates due to lack of mobility of the PDMS-contaminated surface). With solutions of SDS and CigTAB, the presence of a spread layer of PDMS had little effect on bubble stability. Ross and Nishioka [67] therefore deduce that since a spread layer of polydimethylsiloxane (PDMS) has no destructive effect on bubbles, we conclude that PDMS does not defoam by replacing adsorbed solute at the surface as has been suggested. At this point the authors cite Roberts et al. [68]. Unfortunately, Ross and Nishioka [67] do not clearly characterize these spread layers. However, PDMS is known to form duplex films (i.e., complete wetting) on micellar solutions of CigTAB as we have listed in Table 3.3. 

We may combine Eqnations 4.13 through 4.15 to obtain an expression for the steady-state snrface tension of the film where spreading from particles essentially eliminates any snrface tension gradient induced by the action of shear accompanying overall film drainage. We can therefore write 

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There are other problems with the mechanism. As we have stated, spreading from antifoam entities present in the plateau borders could in principle reinforce foam film stability. Spreading from many different sources in the surface of a foam film could presumably rapidly eliminate surface tension gradients so that rupture induced by surface-tension-driven flow would become unlikely. However, elimination of surface tension gradients can also, in principle, contribute to diminished foam film stability as we show in Section 4.4.3. 

Abe and Matsumnra [108] have also considered the antifoam effect of alcohols on the foam behavior of an aqueous solution of sodium dodecylbenzene sulfonate. The alcohols inclnded normal alcohols, branched alcohols, and diols. However, Abe and Matsumura [108] were concerned with the supposed role of the elimination of surface tension gradients under dynamic conditions in determining heterogeneous antifoam effectiveness in the case of these weakly polar oils. We have of course already considered the basic proposition of antifoam action by elimination of surface tension gradients in some detail in Section 4.4.3. 

Shearer and Akers [5], Callaghan et al. [114] supposed that the mechanism involves elimination of surface tension gradients (see Section 4.4.3) as indicated by elimination of surface elasticity. These authors studied the effect of PDMSs on the surface elasticity of crude oil. PDMSs are used as antifoams to assist gas-oil separation during crude oil production and are apparently effective at the remarkably low concentration of 1 part per million (which presumably still exceeds the solubility limit). Callaghan et al. [114] find that PDMS diminishes the frequency-dependent dynamic dilational (elastic) modulus e = doAo (0/d In A(t) relative to that found for the uncontaminated oil. Here Oao(0 is the time-dependent air-crude oil surface tension, and A(t) is the area of a constrained element of air-crude oil surface subject to time-dependent dilation. The effect is more marked the higher the molecular weight (or viscosity) of the PDMS. This correlates with an enhanced antifoam effectiveness found with increase in molecular weight. 

Both these fractionation methods permit the contents of the centrifuge tube to drip sequentially into a set of test tubes. Ideally it would be desirable for each test tube or fraction to receive the same volume of solution. Unfortunately this is often not the case. Droplets obtained from the least dense region of the gradient are also the least viscous, and therefore exhibit a smaller amount of surface tension than do droplets obtained from denser regions. Since the size a droplet can attain before falling away from the tube is a function of its surface tension, the drops obtained from the top of the gradient are smaller than those obtained from the bottom. If quantitation of the gradient contents is desired, this problem must be eliminated or appropriate corrections made for it. 

It has been suggested that a spreading film of antifoam may simply displace the stabilising surfactant monolayer. In this case, as the oil lens spreads and expands on the surface, the tension will be gradually reduced to a lower uniform value. This will eliminate the stabilising effect of the interfacial tension gradients - that is, the elimination of surface elasticity. 

FIGURE 5.42 Damping of convection-driven surface tension gradients by influx of surfactant from the drop interior, (a) Since the mass transport is proportional to the perturbation, the larger the perturbation, the stronger the flux tending to eliminate it. (b) Uniform surfactant distribution is finally reached. 

Surface tension gradients can induce drainage rates in excess of that expected for simple viscous flow if the low MW components have higher surface tensions than the undistilled liquid, e.g., alkyl-substituted aromatics This reverse flow is illustrated in Fig. 16 for a liquid mixture of isomeric amylnaphthalenes. In this case, evaporation of low MW components from the primary film results in a lower surface tension and a surface flow from the primary film onto the secondary film. Distillation of the amylnaphthalene essentially eliminated this reverse flow (Fig. 16). 

Jamet D, Torres D, Brackbill JU (2002) On the theory and computation of surface tension the elimination of parasitic currents through energy conservation in the second-gradient method. J Comput Phys 182 262-276... 

We have seen then that film rupture may occur because surface tension gradients are not sufficiently high to enable the film to withstand stress, because dllALA/d/t is always positive so that rupture is inevitable at a certain critical thickness, or because the Plateau border capillary pressure exceeds any maximum in the relevant disjoining pressure isotherm. However these phenomena are associated with low concentrations of surfactant (at least if we consider films formed slowly so that equilibrium between the air-liquid surface and the intralamellar liquid is maintained). Thus for example, we have CMC for AsqIAH < 0 and CMC. Elimination of both causes of rupture should therefore be readily achieved at sufficiently high concentrations of surfactant. The poor discrimination in foamability often found with relatively concentrated aqueous micellar solutions of surfactants may well be attributable to that cause. Interesting differences in foamability are, however, often revealed when films are either formed rapidly so that equilibrium adsorption is not obtained and conditions for stability are thereby violated or if antifoam is added to the solution. 

The surface tension gradient driven flow system in Figure 6.1.7(b) has different heights of the liquid fUm, h z), at different locations along the z-coordinate. Gravitational force will tend to eliminate it. The relative influence of the two forces is indicated by the Bond number, Bo, defined earlier by equation (6.1.17). The characteristic length dimension of the system to be used in the definition of Bo is any particular value of h(z) ... 

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