Surfaces viscosity

The subject of surface viscosity is a somewhat complicated one it has been reviewed by several groups [95,96], and here we restrict our discussion to its measurement via surface shear and scattering from capillary waves. 

The shear viscosity is an important property of a Newtonian fluid, defined in terms of the force required to shear or produce relative motion between parallel planes [97]. An analogous two-dimensional surface shear viscosity ij is defined as follows. If two line elements in a surface (corresponding to two area elements in three dimensions) are to be moved relative to each other with a velocity gradient dvfdx, the required force is 

The surface viscosity can be measured in a manner entirely analogous to the Poiseuille method for liquids, by determining the rate of flow of a film through a narrow canal under a two-dimensional pressure difference Ay. The apparatus is illustrated schematically in Fig. IV-7, and the corresponding equation for calculating rj is analogous to the Poiseuille equation [99,100] 

While the canal viscometer provides absolute viscosities and the effect of the substrate drag can be analyzed theoretically, the shear rate is not constant and the measurement cannot be made at a single film pressure as a gradient is required. Another basic method, more advantageous in these respects, is one that goes back to Plateau 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

Qualitatively, in a number of cases, foam stability has been correlated with viscosity of the surface film, but the relation is not really clear. There are stable foams in which the viscosity of the surface film is not particularly high and viscous monolayers that do not produce particularly stable foams. However, it appears well accepted that if the viscosity of the surface film is either very low (a gaseous monomolecular film) or very high (a solid monomolecular film), the foam produced will be unstable. In both of these cases film elasticity is low. In addition, too high a surface viscosity can slow down self-healing of thinned spots in the film by the surface transport mechanism. 

In summary then, the factors promoting foaming in aqueous surfactant solutions are (1) low equilibrium surface tension, (2) moderate rate of attaining equilibrium surface tension, (3) large surface concentration of surfactant, (4) high bulk viscosity, (5) moderate surface viscosity, and (6) electrical repulsion between the two sides of the foam lamella. The first three promote film elasticity the last three promote foam persistence. 

The Reynold s model and equation have also been modified to account for surface effects on film drainage rate [29]. To accomplish this, the assumption (boundary condition) of a surface velocity of zero must be relaxed. This change also decreases the surface viscosity from an infinite to a finite value. This process yields Equation 2. Allowing for a finite surface velocity increases the film drainage rate from that which would be expected under the Reynold s conditions. 

Where VWrj is the measured velocity of thinning divided by the velocity of thinning under the conditions of the Reynold s equation and e is the surface mobility factor. 

The surface mobility factor is analysed in detail in [36]. This analysis demonstrates that two factors control the degree of surface mobility the surface viscosity and the presence of surface tension gradients. 

The rates of thinning of vertically-supported, thin liquid films of polyol solutions of various silicone surfactants have been measured [37]. It was found that the rate for films stabilised by a trimethylsilyl-capped polysilicate (TCP a highly branched silicone not containing polyethers), was much lower than that for the films stabilised by common silicone polyether copolymer surfactants. The retardation of drainage rate was correlated with an increase in surface viscosity. Furthermore, it was noted that PU foams prepared using TCP were significantly more stable than those containing the commercial surfactants. 

Surface viscosity scales directly with the surfactant surface concentration, the intermolecular cohesion between the surface molecules and the intermolecular adhesion between the surfactant molecules and the underlying bulk liquid layer. 

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The discussion of surface viscosity and other aspects of surface rheology is deferred to Section IV-3C. 

It was commented that surface viscosities seem to correspond to anomalously high bulk liquid viscosities. Discuss whether the same comment applies to surface diffusion coefficients. 

Bendure indicates 10 ways to increase foam stability (1) increase bulk liquid viscosity, (2) increase surface viscosity, (3) maintain thick... 

The effective surface viscosity is best found by experiment with the system in question, followed by back calculation through Eq. (22-55). From the precursors to Eq. (22-55), such experiments have yielded values of [L, on the order of (dyn-s)/cm for common surfactants in water at room temperature, which agrees with independent measurements [Lemhch, Chem. Eng. ScL, 23, 932 (1968) and Shih and Lem-lich. Am. Inst. Chem. Eng. J., 13, 751 (1967)]. However, the expected high [L, for aqueous solutions of such sldn-forming substances as saponin and albumin was not attained, perhaps because of their non-newtonian surface behavior [Shih and Lemhch, Ind. Eng. Chem. Fun-dam., 10, 254 (1971) andjashnani and Lemlich, y. Colloid Inteiface ScL, 46, 13(1974)]. 

Most often NR adhesives are supplied either as a solvent dispersion or as a latex for coating onto surfaces. Viscosity can range from very low viscosity solutions for... 

The surface viscosity varies significantly along the isotherm and across monolayer phase boundaries. Addition of subphase metal ions increases the surface viscosity drastically, as was recently reinvestigated [36]. Recently, microscopy methods have been used to image velocity profiles of different monolayer phases flowing through a narrow channel, such as used in the canal viscometer [37], The two main methods used to study monolayer viscosity are the canal viscometer and the oscillating disc method [8,9]. 

A significant increase of the previously negligible surface viscosity is observed [144,145]... 

This has been verified for polydimethylsiloxanes added to crude oils. The effect of the dilatational elasticities and viscosities on crude oil by the addition of polydimethylsiloxanes is shown in Table 21-1. Under nonequilibrium conditions, both a high bulk viscosity and a surface viscosity can delay the film thinning and the stretching deformation, which precedes the destruction of a foam. There is another issue that concerns the formation of ordered structures. The development of ordered structures in the surface film may also stabilize the foams. Liquid crystalline phases in surfaces enhance the stability of the foam. 

The superficial gas velocity Og is G/A, where A is the horizontal cross-sectional area of the empty vertical foam column. Also, g is the acceleration of gravity, p is the liquid density, p is the ordinary liquid viscosity and p, is the effective surface viscosity. 

The role of surface viscosity is demonstrated in Figure 8 with the constant-potential and weak overlap electrostatic model. We note that the underlying theory is restricted to large values... 

Figure 8. The effect of surface viscosity on the critical capillary pressure.

Since the correction factor for surface viscosity in Equation 5 is not rigorous, the results in Figure 8 for a greater than about 0.4 should be viewed with caution. 

The viscosity exhibited by a monolayer may be Newtonian, where the viscosity is independent of the rate of shear, or non-Newtonian, where viscosities vary with the rate of flow. Experimentally, this may be determined simply by varying the width of the canal and measuring the surface viscosity at different All (Jarvis, 1965). 

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