Eddy diffusive processes

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force, since turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one... 

The balance between conduction and diffusion still operates for a much larger isolated wet object, provided radiation is excluded. This is the basis of the wet bulb thermometer method for measuring humidity. The actual rate of evaporation now is not as simply determined and is influenced by wind. The wet bulb temperature is almost independent of wind condition, owing to a convenient accident. Heat conduction is a diffusion process, and the diffusion coefficient for water vapor in air (0.24 sq. cm./sec.) is numerically close to the diffusion coefficient of temperature in air (thermal conductivity/specific heat = 0.20 sq. cm./sec.). Hence, the exact way in which each molecular diffusion process merges into the more rapid eddy diffusion process is not important because no matter how complex the transition is, it must be quantitatively similar for the two processes. 

There is a sound experimental basis (B6, LI) for the conclusion that in packed tubes when the Reynolds number is above 100, the transport of both matter and heat transverse to the flow is dominated by eddy diffusive processes. To the extent that these processes dominate, all conserved entities in the fluid diffuse alike, provided the gradients of the concentrations of these entities in amount per unit mass of fluid are used as driving forces for the diffusion. In all that follows, it will be assumed... 

The same physical principles are utilized to develop isotopic models which better account for the transport of air masses at a regional scale, such as done by Fisher (1992) using a regional stable isotope model coupled to a zonally averaged global model. Other authors such as Eriksson (1965) and more recently Hendricks et al. (2000) considered the transport of water both by advective and eddy diffusive processes, the latter inducing less fractionation. 

In this article a simplified mass balance has been used to describe the net transport of sand over an accreting mud bottom. The combination of these two sedimentary processes controls the transition from sand to mud on the floor of the Sound. The distribution of sand may be described with three parameters an advection velocity of sand grains, an eddy-diffusion coefficient for mobile sand, and a rate of accumulation of marine mud. (Only the ratios of these quantities are needed if the distribution is in a steady state.) The motion of sand is thereby represented with both a deterministic part and a statistical part. The net, one-way advection of sand is the result of the superposition of an estuarine circulation on the tidal stream, and unpredictable variations in the rate of sand transport are represented as an eddy-diffusion process. Sand is immobilized when it is incorporated into the permanent deposit of marine mud. 

Tha transport mechanisms of molecular diffusion and mass carried by eddy motion are again assumed edditive although the contribution of the molecular diffusivity term is quite small except in the region nenr a wall where eddy motion is limited. The eddy diffusivity is directly applicable to problems snch as the dispersion of particles or species (pollutants) from a souree into a homogeneously turbulent air stream in which there is little shear stress. The theories developed by Taylor.36 which have been confirmed by a number of experimental investigations, can describe these phenomena. Of more interest in chemical engineering applications is mass transfer from a turbolent fluid to a surface or an interface. In this instance, turbulent motion may he damped oni as the interface is approached aed the contributions of both molecolar and eddy diffusion processes must he considered. To accomplish this. 9ome description of the velocity profile as the interface is approached must be available. 

The term mass transfer is used to denote the transference of a component in a mixture from a region where its concentration is high to a region where the concentration is lower. Mass transfer process can take place in a gas or vapour or in a liquid, and it can result from the random velocities of the molecules (molecular diffusion) or from the circulating or eddy currents present in a turbulent fluid (eddy diffusion). 

The inadequacy of the two-box model of the ocean led to the box-diffusion model (Oeschger et al, 1975). Instead of simulating the role of the deep sea with a well-mixed reservoir in exchange with the surface layer by first-order exchange processes, the transfer into the deep sea is maintained by vertical eddy diffusion. In... 

The concentration of small ions in the atmosphere is determined by 1) the rate of ion-pair production by the cosmic rays and radioactive decay due to natural radioactive substances, 2) recombination with negative ions, 3) attachment to condensation nuclei, 4) precipitation scavenging, and 5) transport processes including convection, advection, eddy diffusion, sedimentation, and ion migration under the influence of electric fields. A detailed differential equation for the concentration of short-lived Rn-222 daughter ions including these terms as well as those pertaining to the rate of formation of the... 

One of the processes leading to molecular spreading is caused by multiple flow paths and is called eddy diffusion (see Fig. 15.2B). Within the column, eddy diffusion results from different microscopic flow streams that the solvent follows between different particles. As a result, sample... 

Conduction of heat Highest of all liquids Although important on small scale, as in living cells, the molecular processes are far outweighed by eddy diffusion... 

In seawater, physical processes that transport water can also cause mass fluxes and, hence, are another means by which the salinity of seawater can be conservatively altered. The physical processes responsible for water movement within the ocean are turbulent mixing and water-mass advection. Turbulent mixing has been observed to follow Pick s first law and, hence, is also known as eddy diffusion. The rate at which solutes are transported by turbulent mixing and advection is usually much faster than that of molecular diffusion. Exceptions to this occur in locations where water motion is relatively slow, such as the pore waters of marine sediments. The effects of advection and turbulent mixing on the transport of chemicals are discussed further in Chapter 4. 

The physical transport of mass is essential to many kinetic and d3mamic processes. For example, bubble growth in magma or beer requires mass transfer to bring the gas components to the bubbles radiogenic Ar in a mineral can be lost due to diffusion pollutants in rivers are transported by river flow and diluted by eddy diffusion. Although fluid flow is also important or more important in mass transfer, in this book, we will not deal with fluid flow much because it is the realm of fluid dynamics, not of kinetics. We will focus on diffusive mass transfer, and discuss fluid flow only in relation to diffusion. 

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

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