Mixing diffusion analogy

Axial mixing effects commonly are taken into account by using a diffusion analogy and an axial mixing coefficient E, also called the longitudinal dispersion coefficient or eddy diffusivity, to account for the spreading of the concentration profiles. At steady state, the conservation equation has the general form... 

Most of the models used for bioturbation are based on a diffusion analogy, which best describes mixing of materials over short distances or local mixing. These models treat mixing as diffusive and divide sediments into a surface layer, which is mixed at a uniform rate and a lower unmixed layer so as to incorporate a biodiffusion coefficient... 

Analogous considerations apply to spatially distributed reacting media where diffusion is tire only mechanism for mixing chemical species. Under equilibrium conditions any inhomogeneity in tire system will be removed by diffusion and tire system will relax to a state where chemical concentrations are unifonn tliroughout tire medium. However, under non-equilibrium conditions chemical patterns can fonn. These patterns may be regular, stationary variations of high and low chemical concentrations in space or may take tire fonn of time-dependent stmctures where chemical concentrations vary in botli space and time witli complex or chaotic fonns. 

Analogously, when a colourless aqueous solution of quinolinium chloride (Q+ CP) is mixed with an almost colourless aqueous solution of Na+V(CO)p the well-formed dark green crystals of the vanadate salt precipitate immediately. In each case, the spontaneous separation of the highly coloured salts is made even more dramatic by the absence of colour in the aqueous mother liquors throughout the course of precipitation. The quantitative effects in these coloured salts are observed as broad absorption bands in the spectral region between 350 to beyond 700 nm when they are dissolved in dichloromethane, or in the diffuse reflectance spectra of the crystalline salts. The correspondence of the band maximum (Act) and... 

As the alternative, a phenomenological description of turbulent mixing gives good results for many situations. An apparent diffusivity is defined so that a diffusion-type equation may be used, and the magnitude of this parameter is then found from experiment. The dispersion models lend themselves to relatively simple mathematical formulations, analogous to the classical methods for heat conduction and diffusion. 

In such mixed films will diffusion be enhanced at defect sites in the membrane, as happens (by analogy) at defect sites in three-dimensional solids ... 

Analogous to the molecular diffusion, the x-directional flux of microorganisms suspended in a medium due to the axial mixing can be represented as... 

In departing from the sun light strikes the dense bodies, the celestial as well as the terrestrial it places their faculties in movement, carries them with it, reflects them and diffuses them in the upper Air as well as in the lower. Air having a disposition to mix with the Water and the Earth, becomes the vehicle of these faculties, and communicates them to the bodies which are formed of them, or which are by analogy most susceptible of them. These are the faculties which are called influences. Many natural philosophers deny their existence, because they do not know them. 

The use of the Coanda effect is based on the desire to have a second passive momentum to speed up mixing in addition to diffusion [55, 163], The second momentum is based on so-called transverse dispersion produced by passive structures, which is in analogy with the Taylor convective radial dispersion ( Taylor dispersion ) (see Figure 1.180 and [163] for further details). It was further desired to have a flat ( in-plane ) structure and not a 3-D structure, since only the first type can be easily integrated into a pTAS system, typically also being flat A further design criterion was to have a micro mixer with improved dispersion and velocity profiles. 

Transfer by molecular diffusion is discussed in Section 12.2 and the concept of the mixing length in Section 12.3.2. By analogy with kinetic theory, the eddy kinematic viscosity, E, is given by ... 

If particle mixing is assumed to be analogous to diffusion with sediment accumulation and radionuclide decay, the steady-state profile for excess activity of a nonexchangeable radionuclide is defined by an advective-diffusion equation. 

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