Transport Processes
There are two types of transport processes: (i) deterministic processes following, e. g., the streamlines of flowing water or force lines of force fields, which can be predicted with the help of technical hydromechanics and physics, and (ii) stochastic pr
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Transport Processes
There are two types of transport processes: (i) deterministic processes following, e. g., the streamlines of flowing water or force lines of force fields, which can be predicted with the help of technical hydromechanics and physics, and (ii) stochastic processes, which are caused by many random events, e. g., Brownian motion and turbulence. Example 4.1: A drop of dye in water If we introduce a drop of a colored aqueous solution into a container with standing water, then locally large gradients of the concentration of the coloring material develop. With time, the color will be distributed evenly throughout the entire container. We observe the consequence of transport processes: coloring molecules move and the local concentration of the coloring material is changed. We can follow this process by measuring the color intensity locally. In contrast, the concentration of the water changes only slightly. Even though the individual water molecules move too, we cannot capture this movement with simple analysis. The microscopic transport processes apparently affect the materials contained in the water at low concentration differently to the way in which they affect the water that fills the space. In this experiment we observe an important concept: the color moves from locations with high concentration to locations with small concentration, until finally the entire container is filled with the same concentration of dye and apparently no more transport takes place (even though individual molecules of color still move around).
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4 Transport Processes
4.1 Characterization of Transport Processes In both technical and natural systems transport processes are of central importance. We differentiate between deterministic, advective processes, and stochastic, diffusive processes. Figure 4.1 shows the movements of water packages and individual particles on different scales. On a large scale we may follow the macroscopically directed current of flowing water, which is easily observed. On a smaller scale energy is dissipated and turbulence becomes important. Finally on the molecular scale thermal motion dominates the relative movement of the particles. These transport processes have very different characteristics. Here we will differentiate between five types of processes: • Advection describes a deterministic transport process in which external forces cause a flow field that carries the water and the materials and particles contained in the water along the streamlines. The characterization of advection (flow velocity) is a central task of technical hydraulics. • Diffusion is a stochastic process in which transport at a specific location is caused by random movements of the interesting particles. We differentiate between molecular diffusion, which is a consequence of the material-specific thermal motion, and turbulent diffusion, which is caused by turbulence (dissipation of kinetic energy) and is therefore not specific to a material. • Dispersion describes the transport of materials which results from the de
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