Inhomogeneous fluids and fluctuations

F. Mean-Field Theories of Inhomogeneous Fluids and Fluctuations... 

It is these fluctuations that cause the inhomogeneities in the fluid and the reradiated waves. The total amplitude of the electric field at a distance R from the scattering volume is given by the summation of the contributions of the infinitesimal scattering elements and can be expressed as... 

Consideration of a liquid interface that fluctuates requires proper account of mechanical and chemical balance between the phases. The description of spatially inhomogeneous fluids can be performed on the basis of Bom-Green-Yvon (BGY) integro-differential equation [14,15]... 

Figure 2 shows the transient absorption spectrum of PB in CI%H at 5.7 MPa. The pattern of the transient sp>ectrum is almost the same as those in methanol. The hole broadening occurs mostly within 0.8 ps, and the bleach is recovered with two different time constants in a similar manner as in the liquid solvents, although the recovery after 2 ps is much slower in the fluid near the critical density (about 40 ps). It is also to be noted that the bleach signal after 2 ps is narrow banded in comparison with the equilibrium absorption. This can be interpreted by the overlapping of the excited state absorption, and/or, the small inhomogeneity remained after 2 ps due to the long time density fluctuation. 

In this section we discuss the frequency spectrum of excitations on a liquid surface. While we used linearized equations of hydrodynamics in the last section to obtain the density fluctuation spectrum in the bulk of a homogeneous fluid, here we use linear fluctuating hydrodynamics to derive an equation of motion for the instantaneous position of the interface. We then use this equation to analyse the fluctuations in such an inhomogeneous system, around equilibrium and around a NESS characterized by a small temperature gradient. More details can be found in [9,10]. 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

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