Adsorption surface tension gradient from

From the measured surface tension as a function of the distance from the inlet, adsorption kinetics data are obtained by recalculating the effective age of the surface at a distance x. Due to an analysis of the flow pattern and the effect of surface tension gradients on it given by Hansen (1964) the effective age is calculated from the surface velocity of the flowing liquid v by X, =x/v. ... 

Surfactants improve foam formation by inducing film elasticity, which is helpful when the film is stretched as a gas bubble emerges from a liquid solution to become part of the foam matrix. As the film stretches, differentia surfactant adsorption at the interface leads to surface tension gradients and healing of the film (so it thins with approximately uniform thickness). The optimum surfactant concentration for foam formation (although not foam stability) is around the CMC. 

If the rate of formation of the interface is much faster the rate of adsorption of the surfactant, the surface tension of the spray solution will not be far from that of pure water. Alternatively, if the rate of surfactant adsorption is faster than the rate of formation of the fresh interface, the surfactant will lower the dynamic surface tension and hence smaller droplets are produced. With liquid jets, an important factor may be considered that enhances surfactant adsorption (24). Addition of surfactants reduces the surface velocity (which is in general lower than the mean velocity of flow of the jet) below that obtained with pure water. This results from surface tension gradients which enhances adsorption (the molecules will move to the areas with high surface tension). 

In multicomponent systems (e.g., surfactant solutions), surface tension gradients usually are due to adsorption-related phenomena or, where possible, to different rates of evaporation from the system (although simple temperature variations can also be important). If the system contains two liquid components of differing volatility, the more volatile liquid may evaporate more quickly from the LV interface, resulting in localized compositional—and therefore surface tension—differences. It is also commonly found that when two or more components are present, one will be preferentially adsorbed at the LV interface and lower ctlv of the system. If a surface-active component... 

The presence of a surfactant also affects the hydrodynamic interactions between fluid particles in dispersions. When the surfactant is soluble in the continuous phase, the adsorption monolayers immobilize the drop (bubble) surfaces and decelerate the approach of two such particles. On the contrary, if the surfactant is dissolved in the droplets (in the disperse phase), it efficiently damps the surface tension gradients and accelerates the approach and (eventually) coalescence of the droplets. The processes of surfactant transfer from the continuous toward the disperse phase, or vice versa, also influence the droplet-droplet hydrodynamic interactions see Sec. Vn. 

Equation 47, with the modifications introduced by Eq. 48, physically represents a rather simphfied situation. In reality, a number of other complicating factors may be present, resulting in further modifications in the equation of capillary advancement. For example, the capillary walls can adsorb surfactants from the bulk solution, leading to a continuous variation in the surface tension coefficient. The adsorption of the surfactant, riv, can lead to an axial gradient of surface tension, following the Gibbs equation ... 

Dynamic surface tension is the measure of change of surface tension with time when a new surface is created. It is related to how fast the surfactant molecules diffuse from the bulk solution to the new air—solution interface and is, thus, affected by the concentration gradient near the surface. Dynamic surface tension can give information on the rate of adsorption at the interfece. Dynamic surface tension is related to the equilibrium surface tension (yeq), the concentration (C), and the diffusion coefficient (D) of the surfactant and is approximated by the following equation [49] ... 

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