Surface area: viscosity

Figure 4. Surface pressure-area (O,, low panel, left hand side ordinate), surface potential-area (O,, upper panel), surface viscosity-area (A, A, low panel right hand side ordinate) curves of monosialoganglioside at 25°C on 0,15M NaCl (Q,A) and 0.075M CaCl2 (, A)...

Viscosity. The viscosity of an oil is its stiffness or internal friction, as illustrated in Figure 7. With a surface of area moving at velocity IVat a distance AX from an equal parallel area moving at velocity V - - AV, force F is required to maintain the velocity difference according to the equation 7 ... 

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. 

Viscosity a measure of the ability of a liquid to flow or a measure of its resistance to flow the force required to move a plane surface of area 1 m over another parallel plane surface 1 m away at a rate of 1 m/s when both surfaces are immersed in the fluid. 

The interface between two fluids is in reality a thin layer, typically a few molecular dimensions thick. The thickness is not well defined since physical properties vary continuously from the values of one bulk phase to that of the other. In practice, however, the interface is generally treated as if it were infinitesimally thin, i.e., as if there were a sharp discontinuity between two bulk phases (LI). Of special importance is the surface or interfacial tension, a, which is best viewed as the surface free energy per unit area at constant temperature. Many workers have used other properties, such as surface viscosity (see Chapter 3) to describe the interface. 

Our discussion of two-dimensional phases has drawn heavily on the analogy between bulk and surface behavior. This analogous behavior is not restricted to thermodynamic observations, but extends to other areas also. The viscosity of surface monolayers is an excellent example of this. To illustrate the parallel between bulk and surface viscosity, let us retrace some of the introductory notions of Chapter 4, restricting the flow to the surface region. 

The flux of particles is in the opposite sense to the direction of the concentration gradient increase. Equation (6) is Fick s first law, which has been experimentally confirmed by many workers. D is the mutual diffusion coefficient (units of m2 s 1), equal to the sum of diffusion coefficients for both reactants, and for mobile solvents D 10 9 m2 s D = DA + jDb. The diffusion coefficient is approximately inversely dependent upon viscosity and is discussed in Sect. 6.9. As spherical symmetry is appropriate for the diffusion of B towards a spherically symmetric A reactant, the flux of B crossing a spherical surface of radius r is given by eqn. (6) where r is the radial coordinate. The total number of reactant B molecules crossing this surface, of area 4jrr2, per second is the particle current I... 

Figure 3. Surface viscosity vs. molecular area for palmitic, stearic, and behenic acid monolayers spread on 0.5N NaOH substrates at 30°C.

Kinetics of reaction at the interface are generally studied by the same methods as are used for the study of the monolayer itself. These are mainly the determination of surface area (A), film pressure (rc), surface potential (AV), and surface viscosity. A number of relationships developed by Adamson illustrate the type of kinetic expressions obtained for simple reactions. 

AG is the free energy of activation for flow, h is Planck s constant, and A is the area per flow unit. This theory was applied to the surface viscosity of a number of proteins, measured as a function of surface pressure (MacRitchie, 1970). Plots of log tjs against II were found to be linear, enabling AG and A to be evaluated. The data, which are summarized in Table VI, show that the flow unit for all the proteins and poly-DL-alanine is a segment of approximately 6-8 amino acid residues and also that the free energy of activation for flow is similar for all... 

Insoluble monolayers on an aqueous substrate have been investigated by means of the capillary wave method for many years. Lucassen and Hansen (1966) in their pioneering work neglected the surface viscosity and considered only pure elastic films. Subsequent studies showed that the surface elasticity of real surface films is a complex quantity, and both the equilibrium surface properties and the kinetic coefficients of relaxation processes in the films influence the characteristics of surface waves. However, it has been discovered recently that the real situation is even more complicated and the macroscopic structure of surface films influences the dependency of the damping coefficient of capillary waves on the area per molecule (Miyano and Tamada 1992, 1993, Noskov and Zubkova 1995, Noskov et al. 1997, Chou and Nelson 1994, Chou et al. 1995, Noskov 1991, 1998, Huhnerfuss et al. this issue). Some peculiarities of the experimental data can be explained, if one takes into account the capillary wave scattering by two-dimensional particles (Noskov et al. 1997). 

Figure 3. Surface pressure-area and surface viscosity (At)-area curves of glycosphingolipids on 0.15M NaCl at 25°C. (O) ceramide ( ) glucocerebroside (A) lactocerebroside ( ) haematoside (A) monosialoganglioside.

Surface viscosity was determined by a torsion oscillation method in which the period of oscillation of a paraffin-coated mica ring was measured on a clean water surface and lipid-covered surface (6, 13). Since the period of oscillation is proportional to the surface viscosity, the difference in period (At) between lipid or protein film and a clean aqueous surface measures viscosity and relates to either molecular area, film pressure, or time of interaction (t). The period values were repro-... 

Figure 6. Surface viscosity (At)-area curves of ceramide (compound c in Figure 2) at 25° and 37°C, on 0.15M NaCl (A) and on 0.075M CaCl2 (A)...

Figure 8. Surface pressure-area, surface potential-area, and surface viscosity (At)-area curves of sphingomyelin ( ), galac-tocerebroside (O), and dipalmitoyl lecithin (A) on 0.I5M NaCl...

Figure 9. Influence of cholesterol on surface viscosity (At) of a saturated film of DPL on 0.15M NaCl at 25°C. A film of DPL was formed by applying microliter quantities of DPL at a concentration of 1.5 fig/fil in chloroform-methanol (85 15) onto a fixed area. Surface pressure ( ) and surface viscosity (At) (O) were measured. After surface saturation at about 46 dynes/cm pressure, cholesterol 1 fig/fil in chloroform methanol (85 15) was applied onto the saturated DPL film. Surface pressure ( ) was not affected surface viscosity fell dramatically. A film of cholesterol alone (A) has no surface viscosity, and the solvent alone does not affect either surface pressure or viscosity.

Molecular Area and Film Pressure. A smaller area/molecule and a greater film pressure caused an increase of surface viscosity (Figures 3-8). However, at the same area/molecule, ceramide was more viscous than ganglioside. A more striking contrast is seen in Figures 9 and 10. When modest quantities of DPL or cholesterol are added to saturated films of BSA and RNase, the pressure increases markedly (e.g., from 21 to 45 dynes/cm with BSA) whereas the viscosity dropped from large, immeasurable values to practically zero. 

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