Surface tension undulations

There is a discussion in the literature about the effect of undulation entropy on the equilibrium membrane tension [14,15], Formally, undulations are included in the surface tension, and thus we need not worry about this. However, if in some model the two are artificially decoupled, one may allow for a very small (positive) surface tension as the equilibrium structure. In other words, the entropy (per unit area) from undulations should compensate for the tension (excess free energy per unit area). 

If the PEP-PEE triblock chains are arranged in microdomains separated by well-defined interfaces, then the additional fast relaxation process observed by NSE would result from the undulation motions of the interface. The thermal motions of the interface are driven by the surface tension and overdamped. With an effective viscosity r eff in the interfacial region, the relaxation rate if Q) ... 

By the way of contrast, a water surface covered with a freshly spilled crude oil exhibits quite different physicochemical characteristics. No surface tension gradients will be generated by the undulating water surface and thus the Marangoni effect plays no role. On the other hand, the crude oil layer may also dampen short gravity waves due to its relatively high viscosity as compared with a pure water surface. 

While the Rayleigh instability of a cylindrical surface is driven by the surface energy, the flat surface of a thin film can become unstable under the influence of van der Waals forces (see Chapter 5). In this case, the surface tension provides a restoring force which stabilizes short-wavelength undulations. Again, the critical wavelength is determined by a balance of the free energies (see the problems at the end of this chapter). 

Show that a planar interface, governed only by its surface tension is stable with respect to smaii unduiations of the interface, whiie a cyiindricai interface is unstabie to iong-waveiength undulations. 

Thin films can be unstable to undulations of their surfaces when the van der Waals energy (see Chapter 5) is such that the thin film has lower energy than a thick film. Consider a thin layer of initial thickness Do, whose free energy is composed of a surface tension contribution as well as a van der Waals contribution Fy for the energy per unit area, which varies with the local film thickness, hix, y), as... 

Marrink SJ, Mark AE (2001) Effect of undulations on surface tension in simulated bilayers. J Phys Chem B 105 6122-6127... 

The rate at which the amplitude a of a sinusoidal undulation on the stuface of a liquid decreases with time as it is pulled out by surface tension forces is given by [10]... 

Levelling of surface undulations under the action of surface tension... 

The mechanism of the continuous emulsion polymerization of vinyl chloride was discussed in Ref. [117]. Here, the effects of the feeding rate and/or the reaction time on the size of latex particles were followed. Variations in the particle size or number have an undulating character. The emulsifier is continuously fed into the reactor and adsorbed on the free sites on the particle surface. Under these conditions, the covering degree of the latex particles is very high (close to 100%) as it was shown in the surface tension measurements. The surface tension (a) of the PVC latex during the continuous emulsion polymerization of VC varies between 38 to 46mN/m [118]. From the surface tension... 

The competition between surface tension and disjoining pressure determines to what extent a thin liquid film follows the undulations of a rough solid substrate and is seen in (7). Long-wavelength fluctuations of the solid surface, ge [Pg.163]

It is important to note that the lamellar phase is thus stabilized by the balance of a negative interfacial tension (of the free oil/water interface covered by an amphiphilic monolayer), which tends to increase the internal area, and a repulsive interaction between interfaces. The result, Eq. (48), indicates that the scattering intensity in a lamellar phase, with wave vector q parallel to the membranes, should have a peak at nonzero q for d > d due to the negative coefficient of the q term in the spectrum of Eq. (40). just as in the microemulsion phase. This effect should be very small for strongly swollen lamellar phases (in coexistence with excess oil and excess water), as both very small [96]. Very similar behavior has been observed in smectic liquid crystals (Helfrich-Hurault effect) [122]. Experimentally, the lamellar phase under an external tension can be studied with the surface-force apparatus [123,124] simultaneous scattering experiments have to be performed to detect the undulation modes. 

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