Capillary wave effects

Capillary Waves at ITIES. Field Effect on Capillary Waves and Capillary Waves Effect on Capacitance... 

The fluctuations of the local interfacial position increase the effective area. This increase in area is associated with an increase of free energy Wwhich is proportional to the interfacial tension y. The free energy of a specific interface configuration u(r,) can be described by the capillary wave Hamiltonian ... 

It is clear that the flow regime is a complicated but predictable function of the physical properties of the liquid, the flow rate, and the slope of the channel. It has been shown that, for water films, gravity waves first appear in the region NrT = 1-2, capillary surface effects become important in the neighborhood of JVw = I, and the laminar-turbulent transition occurs in the zone ArRe = 250-500 (F7). 

Analogous droplet-size dependence has been observed for electron transfer between ferrocene and hexacyanoferrate(III) across a droplet/water interface with the droplet radius of <5 /an, as described in Section III [80]. In this system, FeCp-X+ transfer is coupled with the electron transfer process and the physical properties of the droplet have been suggested to vary with r. However, droplet size effects on surface capillary waves analogous to those in the MT process may also govern the electron transfer process in the FeCp-X/Fe(IIl) system. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

The modern resurgence in interest in capillary wave hydrodynamics, which started in the early 1950s, centers around the damping effects and the presence of a viscoelastic film between two fluids [37,49-56]. All are more or less similar, in the assumptions invoked and the hydrodynamic theory used. The Lucassen-Reynders-Lucassen [55] and Kramer s [56] dispersion equations are essentially identical except Kramer ignores the gravity wave at the outset which is consistent with the wave vector range often used experimentally, and this is seen in Fig. 3. 

Fig. 6 The effect of transverse viscosity on the polar plot of Fig. 4. The damping coefficient, a, is plotted vs. the real capillary wave frequency, 0> for several different transverse viscosities (/x in the figure has units of 10 5 mNsm ). Only the isopleths for Sd = 0 and k = 0 are shown to give the outermost loop of Fig. 4. The plot was generated using the same condition as in Fig. 4, k = 32 431 m, ad = 71.97mN nr1, p = 997.0 kg nr3, r) = 0.894 mPa s and g = 9.80 m s 2...

Fig. 22. (a) Snapshot of an interface between two coexisting phases in a binary polymer blend in the bond fluctuation model (invariant polymerization index // = 91, incompatibihty 17, linear box dimension L 7.5iJe, or number of effective segments N = 32, interaction e/ksT = 0.1, monomer number density po = 1/16.0). (b) Cartoon of the configuration illustrating loops of a chain into the domain of opposite type, fluctuations of the local interface position (capillary waves) and composition fluctuations in the bulk and the shrinking of the chains in the minority phase. Prom Miiller [109]... 

The mean field Cahn-Hilliard approach (Eq. 7) describes the intrinsic profile ( >(z) about the internal interface between two coexisting phases. It involves only one dimension, i.e., depth z, as a lateral homogeneity is assumed [7]. Capillary wave excitations may however cause lateral fluctuations of the depth Ie(x,y) at which the internal interface is locally positioned. As a result the effective interfacial width may be broadened beyond its intrinsic value (Eqs. 10 and 12). The mean field theory predicts the temperature dependence of the intrinsic width in a good agreement with experimental data presented here and reported by others (e.g., [76,89] reanalyzed by [88] or [96,129]). Some other experimental results [95,97,98] indicate the width larger than its intrinsic value... 

As mentioned in Sect. 2.2.2, the effective interfacial width wD characterizing the bilayer structure may be broadened beyond its intrinsic value w, yielded by a mean field theory (Eqs. 10 and 12). This is due to the capillary wave excitations causing the lateral fluctuation of the depth Ie(x,y) corresponding to the midpoint of the internal interface between coexisting phases. This fluctuation is opposed by the forces due to external interfaces, which try to stabilize the position Ie(x,y) in the center of the bilayer [6, 224, 225]. It was suggested recently [121] that the spectrum of capillary waves for a soft mode phase should be cut off by qb and y. This leads to the conclusion that the effective interfacial width wD should depend on the film thickness D as (wD/2)2= b2+ bD/4. Experimental data [121] obtained for olefinic blends (at T close to Tc) indeed show remarkable increase of the measured interfacial width from wd(D=160 nm)=14.4(3) nm to wd=45(12) nm for thickness D-660 nm, where wD levels off (because is comparable with lateral sample dimensions). This trend is in qualitative agreement with the formula due to capillary oscillations in the soft mode phase . However... 

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