Wave motion thermal fluctuations

The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

Leadbetter AJ, Norris EK (1979) Molec Phys 38 669. There are different contributions which give rise to a broadening a of the molecular centre of mass distribution function f(z). The most important are the long-wave layer displacement thermal fluctuations and the individual motions of molecules having a random diffusive nature. The layer displacement amplitude depends on the magnitude of the elastic constants of smectics ... 

A rough, zero-order, estimate of the extent to which a Fermi liquid description would be viable in the normal phase is provided by the scale of given by band calculations. Consider the temperature range Tthermal fluctuations are suffieiently weak to lower the uncertainty on the transverse band wave vector to a range of values l/dj, that is small compared to the size of Brillouin zone. The band wave vector is therefore a good quantum number so the transverse band motion and the curvature of the Fermi surface are coherent. Otherwise, when one has which is large enough for... 

All fluid interfaces, including lipid membranes and surfactant lamellas, are involved in a thermal fluctuation wave motion. The configurational confinement of such thermally exited modes within the narrow space between two approaching interfaces gives rise to short-range repulsive surface forces, which are considered below. 

Because of the thermal motion, the protrusion of an amphiphilic molecule in an adsorption mono-layer (or micelle) may fluctuate about the equilibrium position of the molecule (Figure 5.30c). In other words, the adsorbed molecules are involved in a discrete wave motion, which differs from the continuous modes of deformation considered above. Aniansson et analyzed the energy... 

It is assumed that plastic flow occurs by the creation and motion of dislocations. The classical approach to dislocation motion holds that thermal fluctuations help carry the dislocations over the lattice potential barriers [13,14]. However, at normal temperatures the thermal fluctuations occur at rates of only lO" rad/s to perhaps 10 rad/s while the dislocations responsible for the plastic wave due to shock or impact travel at speeds from about. 1 km/s to > 10 km/s depending on the amplitude of the shock or impact. These dislocations must encounter and overcome the lattice potential barriers at rates often in excess of 10 rad/s [15]. Thus, energy transfer to the dislocations by thermal fluctuations occurs at rates at least two to three orders of magnitude slower than needed to overcome the lattice potential barriers and support the plastic wave component of a shock or impact. 

The above discussion has centered on wave motion imposed on a surface by, for instance, an oscillating bar. But thermal fluctuations cause wave motion of small amplitude even on interfaces that are not disturbed by external means. With laser light scattering techniques it is possible to measure interfadal tension from analysis of surface fluctuations. This method has been applied to the measurement of ultralow interfacial traisions between liquid phases (Bouchiat and Meunier, 1972 Cazabat et al., 1983 Zollweg et al., 1972). Presumably it could also be used to determine surface compressibility or other rheological properties. 

Due to the thermal motion, the protrusion of an amphiphilic molecule in an adsorption monolayer (or micelle) may fluctuate about the equilibrium position of the molecule (Figure 4.39c). In other words, the adsorbed molecules are involved in a discrete wave motion, which differs from the continuous modes of deformation considered earlier. Aniansson et al. [627,628] analyzed the energy of protrusion in relation to the micelle kinetics. They assumed the energy of molecular protrusion to be of the form u(z) = az, where z is the distance out of the surface (z > 0) and determined a 3 X 10 J/m for single-chained surfactants. The average length of the Brownian protrusion of the amphiphilic molecules is on the order of A, = kT/a, [625]. 

At finite temperature, stochastic fluctuations of the membrane due to thermal motion affect the dynamics of vesicles. Since the calculation of thermal fluctuations under flow conditions requires long times and large membrane sizes (in order to have a sufficient range of undulation wave vectors), simulations have been performed for a two-dimensional system in the stationary tank-treading state [213]. For comparison, in the limit of small deviations from a circle, Langevin-type equations of motion have been derived, which are highly nonlinear due to the constraint of constant perimeter length [213]. 

Total internal reflection microscopy (TIRM) was introduced in 1987 by Prieve et al. [343]. TIRM allows to probe the interaction of a single microsphere with a transparent flat plate. In a TIRM experiment, a microsphere is allowed to sediment toward the plate. The technique relies on repulsive forces between sphere and plate. This repulsion will typically result from electric double layer or steric forces. They keep the sphere from getting into contact with the plate. Thermal fluctuations will constantly change the precise distance. The distance between sphere and plate is monitored by the light intensity scattered from the particle when illuminated by an evanescent wave and can be determined with a resolution of w 1 nm. By recording the fluctuations in vertical position of the sphere due to Brownian motion, the potential energy of interaction and the diffusion coefficient of the sphere can be deduced. For overviews of the technique, see Refs [344, 345]. 

The light-scattering spectrum which is related to 7 (q, /) by Eq. (3.3.3) consequently probes how a density fluctuation <5/ (q) spontaneously arises and decays due to the thermal motion of the molecules. Density disturbances in macroscopic systems can propagate in the form of sound waves. It follows that light scattering in pure fluids and mixtures will eventually require the use of thermodynamic and hydrodynamic models. In this chapter we do not deal with these complicated theories (see Chapters 9-13) but rather with the simplest possible systems that do not require these theories. Examples of such systems are dilute macromolecular solutions, ideal gases, and bacterial dispersions. ... 

The surfactant molecules in adsorption monolayers or lamellar bilayers are involved in a thermally excited motion which brings about the appearance of fluctuation capillary waves. The latter also cause a steric interaction (although a short-range one) when two thermally corrugated interfaces approach each other see Sec. VI.E. 

Consider two reservoirs connected by a narrow duct with the whole volume filled with a 50-50 mixture of He-Ar. If each reservoir is connected to a bellows-sealed piston, and the pistons are driven at, say, a low frequency of 10 Hz with independent phase and amplitude control, the oscillating pressure wave creates a composition difference of as much as 6% between the two chambers at the ends of the narrow connecting duct (Spoor and Swift, 2000). The periodic motion of the pistons produces density fluctuations in the gas this sound wave creates the composition difference via a complex interaction of thermal diffusion (compression leads to heating), ordinary diffusion, convective motion, etc. (Geller and Swift, 2002a,b). 

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