Surfactant adsorption equilibrium

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

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 ... 

When p approaches infinity, Equation 7 reveals that equals zero, which corresponds to infinitely fast sorption kinetics and to an equilibrium surfactant distribution. In this case Equation 6 becomes that of Bretherton for a constant-tension bubble. Equation 6 also reduces to Bretherton s case when a approaches zero. However, a - 0 means that the surface tension does not change its value with changes in surfactant adsorption, which is not highly likely. Typical values for a with aqueous surfactants near the critical micelle concentration are around unity (2JL) ... 

Figure 8 reveals that the few data available for surfactant-laden bubbles do confirm the capillary-number dependence of the proposed theory in Equation 18. Careful examination of Figure 8, however, reveals that the regular perturbation analysis carried out to the linear dependence on the elasticity number is not adequate. More significant deviations are evident that cannot be predicted using only the linear term, especially for the SDBS surfactant. Clearly, more data are needed over wide ranges of capillary number and tube radius and for several more surfactant systems. Further, it will be necessary to obtain independent measurements of the surfactant properties that constitute the elasticity number before an adequate test of theory can be made. Finally, it is quite apparent that a more general solution of Equations 6 and 7 is needed, which is not restricted to small deviations of surfactant adsorption from equilibrium. 

In dilute solutions of surfactants adsorption processes are controlled by transport of the surfactant from the bulk solution towards the surface as a result of the concentration gradient formed in the diffusion layer the inherent rate of adsorption usually is rapid. For non-equilibrium adsorption the apparent (non-equilibrium) isotherm can be constructed for different time periods that are shifted with respect to the true adsorption isotherm in the direction of higher concentration (Cosovic, 1990) (see Fig. 4.10). 

At equilibrium surfactant concentrations of less than 0.0003 M SDS where the hematite surface is still positively charged, adsorption of surfactant follows its normal pattern due to the electrostatic forces which provide the driving force for adsorption. Sufficient effective surface area must be available for this level of SDS adsorption density. As surfactant adsorption... 

Because the inverse Debye length is calculated from the ionic surfactant concentration of the continuous phase, the only unknown parameter is the surface potential i/io this can be obtained from a fit of these expressions to the experimental data. The theoretical values of FeQx) are shown by the continuous curves in Eig. 2.5, for the three surfactant concentrations. The agreement between theory and experiment is spectacular, and as expected, the surface potential increases with the bulk surfactant concentration as a result of the adsorption equilibrium. Consequently, a higher surfactant concentration induces a larger repulsion, but is also characterized by a shorter range due to the decrease of the Debye screening length. 

The dispersion interaction between the surface active ions and the water-air interface was recently considered in the modeling of the equilibrium adsorption [62]. The molecular dynamic simulations are used in the recent years to describe the surfactant adsorption at the air-water interface [63-65],... 

Mixed Admicelles. The total sur-factant adsorption o-f the two pure sur-factants and mixtures thereo-f on alumina are shown in Figure 3. The mixtures are at constant surFactant ratio in the Feed or initial solution, but not necessarily in the Final equilibrium solution. The concentration on the abscissa is the equilibrium concentration. The individual surFactant adsorption isotherms For the pure surFactants and in the mixtures are shown in Figures 4 and 5. The experiments were run at the same swamping electrolyte concentration as were the CMC data. 

Wherever possible, the soaps and surfactants were added to the natural rubber latex as dilute aqueous solutions. The cases where this was not possible were (a) ethylene oxide-fatty alcohol condensates of low ethylene oxide fatty alcohol mole ratio, and (b) sparingly-soluble fatty-acid soaps such as lithium laurate and calcium soaps. The former were added as pastes with water, the latter as dry powders. In all cases, the latex samples were allowed to mature for about three days at room temperature before their mechanical stabilities were determined. This allowed some opportunity for the attainment of adsorption equilibrium. 

The presence of mixed surfactant adsorption seems to be a factor in obtaining films with very viscous surfaces [411]. For example, in some cases the addition of a small amount of non-ionic surfactant to a solution of anionic surfactant can enhance foam stability due to the formation of a viscous surface layer, which is possibly a liquid crystalline surface phase in equilibrium with a bulk isotropic solution phase [25,110], In general, some very stable foams can be formed from systems in which a liquid crystal phase is present at lamella surfaces and in equilibrium with an isotropic interior liquid. If only the liquid crystal phase is present, stable foams are not produced. In this connection foam phase diagrams may be used to delineate compositions that will produce stable foams [25,110],... 

This was shown e.g. by investigating adsorption isotherms of Na dodecylbenzene-4-sulfonate and Na 4-hexadecyloxytolyl-2-sulfonate on various mineral surfaces differing from each other by the kind of PDFs86 . The potential value in relation to the surfactant concentration reached its maximum in the region of micelle formation and confirmed thus the shape of the adsorption isotherm. The presence of adsorption maxima is explained by a decrease in surfactant adsorption resulting from a desorption effect of micelles on the adsorption film, and by setting a three-component equilibrium (adsorption film - micelle - monomer) at concentrations CMC. This happens because of different ratios of the counter ions to the surfactant ions at the micelle and on the adsorption film. 

The study of adsorption kinetics of a surfactant on the mineral surface can help to clarify the adsorption mechanism in a number of cases. In the literature we found few communications of this kind though the adsorption kinetics has an important role in flotation. Somasundaran et al.133,134 found that the adsorption of Na dodecylsulfonate on alumina and of K oleate on hematite at pH 8.0 is relatively fast (the adsorption equilibrium is reached within a few minutes) as expected for physical adsorption of minerals with PDI H+ and OH". However, the system K oleate-hematite exhibits a markedly different type of kinetics at pH 4.8 where the equilibrium is not reached even after several hours of adsorption. Similarly, the effect of temperature on adsorption density varies. The adsorption density of K oleate at pH 8 and 25 °C is greater than at 75 °C whereas the opposite is true at pH 4.8. Evidently the adsorption of oleic acid on hematite involves a mechanism that is different from that of oleate or acid soaps. 

The adsorption mechanism discussed in previous chapters dealt only with a monocomponent system mineral - surfactant, as a result of an adsorption equilibrium related to appropriate PDI. Since a real flotation system consists of two or more mineral components it is necessary to mention conditions of the selective surfactant adsorption in such a system. In monocomponent systems the adsorption is controlled by the character of PDI with respect to the chemical composition of the polar heads of the surfactant. However, this rule is not valid in polycomponent systems containing both kinds of PDI. Generally and under simplifying circumstances, it is possible to classify the adsorption systems according to the role played by the PDI and the kind of the mineral. 

Investigations of the adsorption kinetics showed that a surfactant adsorption layer is formed. In the beginning, the adsorption ran very fast. After one minute, already 40% of the equilibrium amount was adsorbed. Then the adsorption became slower until after 10 to 30 min the adsorption equilibrium is reached. The fast adsorption gives... 

Under F/T conditions, desorption of surfactant presumably occurs more readily with the poly-S emulsion as a new equilibrium is established (a slight surface-tension lowering was observed after each F/T cycle throughout the series.) This conclusion is further substantiated by the exceptional increase in minimum weight percent acid required for poly-S in SLS (black square) compared with the 80/20 MMA-EA in SLS (black dot) despite the fact that less than one-half as much SLS was used in the latter case. Thus, it appears that poly-S is a less favorable surface for surfactant adsorption and as predicted by Equation 2 more carboxylate ions are required to obtain F/T stability. 

Since the styrene series contains more surfactant than the methyl methacrylate series and since the ethyl acrylate has afforded increased surfactant adsorptivity to the styrene by a mechanism to be proposed under Question d, the equilibrium suggested by Equation 1 is shifted markedly to the left, resulting in lower requirements for carboxylate ions to achieve F/T stability. 

It is a matter of course that the different surfactant coverages are also reflected in the corresponding surface tensions y of the latexes (see Fig. 4b). An increase of the surface tension with increasing diameter is observed. The miniemulsions based on polystyrene particles exceeding 100 nm have a surface tension of close to the one of pure water (72 mN nr1)- This is due to the fact that the bare particle surface is so large that adsorption equilibrium ensures a very low surfactant solution concentration. Smaller particles with their higher sur-... 

The special properties of thin liquid films, in particular of foam films, involve studying various colloid-chemical aspects, such as kinetics of thinning and rupture of films, transition from CBF to NBF, isotherms of disjoining pressure, thermodynamic (equilibrium) properties, determination of the electrical parameters of surfactant adsorption layer at the liquid/gas... 

As already mentioned (see Chapter 3), at the instant of foam formation the films and borders are in non-equilibrium state. The films thin mainly due to the capillary pressure, while the borders thin due to gravity or a pressure drop (when the foam is dried by the Foam Pressure Drop Technique [21-23]). The surfactant adsorption layers decrease the flow rate through the borders and films and the process of thinning becomes similar to the flow in thin gaps with solid surfaces. As indicated in Sections 3.2.1 and 5.3 the degree of retardation of the flow depends on the surfactant type and concentration as well as on the film type. A complete immobility at the film and border surfaces usually is not reached. 

The lower concentration limit of the applicability of the foam separation method is determined by the lowest residual concentration and depends on the surface activity of the substances, the rate of establishing of the adsorption equilibrium, foam stability and the apparatus used in the process. During foam accumulation the surfactant is extracted from the solution, thus leading to a decrease in foam stability and expansion ratio. Finally, a concentration is reached at which the foam cannot be withdrawn from the apparatus and the accumulation ratio becomes close to 1. 

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