Material transport turbulent streams

Figure 4 depicts the variation of the root-mean-square longitudinal fluctuation as a function of position in a floiving stream. These data were taken from the recent experimental investigation by Laufer (L3) and illustrate the complexity of behavior encountered in a steady, uniformly flowing turbulent stream. It is to be expected that fluctuations of temperature and composition are encountered in turbulent streams involving thermal or material transport. 

Such expressions can be extended to permit the evaluation of the distribution of concentration throughout laminar flows. Variations in concentration at constant temperature often result in significant variation in viscosity as a function of position in the stream. Thus it is necessary to solve the basic expressions for viscous flow (LI) and to determine the velocity as a function of the spatial coordinates of the system. In the case of small variation in concentration throughout the system it is often convenient and satisfactory to neglect the effect of material transport upon the molecular properties of the phase. Under these circumstances the analysis of boundary layer as reviewed by Schlichting (S4) can be used to evaluate the velocity as a function of position in nonuniform boundary flows. Such analyses permit the determination of material transport from spheres, cylinders, and other objects where the local flow is nonuniform. In such situations it is not practical at the present state of knowledge to take into account the influence of variation in the level of turbulence in the main stream. 

Little detailed experimental information is available on the value of eddy transport properties under conditions of simultaneous thermal and material transport. If it is assumed that the Reynolds analogy is applicable, it follows that the eddy diffusivity and eddy conductivity are equal and independent of cross linking. Such an assumption is probably not true since it is to be expected that a substantial part of the eddy transport is associated with molecular transport particularly as the eddies become small in accordance with Kolmogoroff s (K10) principle. For this reason it is to be expected that temperature gradients in turbulent streams will influence to some extent the material transport in the same... 

Lynn. S.. Corcoran. W.H. and Sage. B.H. 1957. Material transport in turbulent gas streams Radial diffusions in a circular duct. AIChE Journal. 3. H-15. 

The physical transport of particles in a river occurs by two primary modes bedload and suspended load. Bedload consists of material moved along the bed of the river by the tractive force exerted by flowing water. Bedload may roll or hop along the bottom, and individual particles may remain stationary for long periods of time between episodes of movement. Suspended load consists of material suspended within the flow and that is consequently advected by flowing water. Rivers and streams are naturally turbulent, and if the upward component of turbulence is sufficient to overcome the settling velocity of a particle, then it will tend to remain in suspension because the particles become resuspended before they can settle to the bottom of the flow. Suspended load consists of the finest particles transported by a river, and in general is composed of clay- and silt-sized... 

Enhanced chemical reactivity of solid surfaces are associated with these processes. The cavitational erosion generates unpassivated, highly reactive surfaces it causes short-lived high temperatures and pressures at the surface it produces surface defects and deformations it forms fines and increases the surface area of friable solid supports and it ejects material in unknown form into solution. Finally, the local turbulent flow associated with acoustic streaming improves mass transport between the liquid phase and the surface, thus increasing observed reaction rates. In general, all of these effects are likely to be occurring simultaneously. 

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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