Tangential monolayer

For the moment no transitional states between these extremes will be considered. For these two limiting modes of adsorption the establishment of equilibrium proceeds via different paths in localized adsorption, adsorbed molecules can move to other sites only by desorption and re-attachment, whereas for mobile adsorption the path of tangential transport is also open. Typical representatives of localized isotherms are those of Langmuir. Frumkln-Fowler-Guggen-helm (monolayer) and BET (multilayer). For mobile adsorbates examples are the Volmer and the Hill-De Boer (or two-dimensional Van der Waals) equations. 

The surfaces of fluid particles can be treated as tangentially immobile when they are covered by dense surfactant adsorption monolayers that can resist tangential stresses.In such a case, the bubbles or droplets behave as flexible balls with immobile surfaces. When the fluid particles are rather small (say, microemulsion droplets), they can behave like hard spheres therefore, some relations considered below, which were originally derived for solid particles, can be also applied to fluid particles. 

Consider a piece of the ocean covered with a monolayer with film pressure 11 = crM - a, where crw and a are the surface tensions of pure water and film, respectively. We further assume that the film is stagnant. Beneath the film, however, there is a horizontal motion (taken to be in the x-direction) with a corresponding boundary layer. Consequently, there is a tangential viscous stress, rvisc, on the film which must be balanced by a gradient in n. 

The Gibbs elasticity characterizes the lateral fluidity of the surfactant adsorption monolayer. For high values of the Gibbs elasticity the adsorption monolayer at a fluid interface behaves as tangentially immobile. Then, if two oil drops approach each other, the hydro-dynamic flow pattern, and the hydrodynamic interaction as well, is the same as if the drops were solid particles, with the only differenee that under some conditions they could deform in the zone of contact. For lower values of the Gibbs elastieity the... 

The solution to the problem of hydrodynamie interaction between two rigid spherieal partieles, approaehing each other aeross a viseous fluid, was obtained by Taylor (122). Two spherieal emulsion drops of tangentially immobile sur-faees (due to the presenee of dense surfactant adsorption monolayers) are hydrodynamically equivalent to the two rigid partieles eonsidered by Taylor. The hydrodynamic interaction is due to the dissipation of kinetic energy when the liquid is expelled from the gap between the two spheres. The resulting friction force decreases the velocity of the two spherical drops proportionally to the decrease in the surface-to-surface distance h in accordance with the Taylor (122) equation ... 

Fig. 1.1 Possible cases of particle detachment (a) detachment of monolayer by normal force (b) detachment of layer by normal force (c) detachment of individual particle by tangential force.

As discussed in Section 17.4.2, the movement of the liquid along the interface containing the monolayer invokes an interfacial tension gradient that counteracts the tangential flow of liquid. Under conditions of mechanical equilibrium with respect to the interface, the induced interfacial tension gradient just compensates the shear stress due to the flowing liquid, as formulated in Equation 17.22. Hence, the liquid in the lamellae flows between two immobile interfaces and this results in a parabolic... 

It appears from these studies that the picture of an iceberg around the solute in hydroxylic solvents is overdrawn. The shell of tangentially oriented molecules is only a monolayer, and though these molecules are restricted in their radial motion (giving rise to the entropy loss), they are not strongly ordered within the monolayer. 

Fig. I.l. Possible cases of the detachment of particles detachment of a monolayer (a) and a thicker layer (b) by a normal force, and of an individual particle by a tangential force (c).

The percentage area (A) at which the tangential intercept cuts the y axis is entered to the Langmuir formula to calculate molecular area of the tested molecular species comprising the monolayer ... 

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