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It is defined as the ratio of the convection current to the dispersion current. The Bodenstein number is an element of the dispersion model of residence times and is therefore also called the dimensionless dispersion coefficient. [1] Mathematically, two idealized extreme cases exist for the Bodenstein number.
Taylor dispersion or Taylor diffusion is an apparent or effective diffusion of some scalar field arising on the large scale due to the presence of a strong, confined, zero-mean shear flow on the small scale. Essentially, the shear acts to smear out the concentration distribution in the direction of the flow, enhancing the rate at which it ...
Dispersion in groundwater arises because each water "particle", passing beyond a soil particle, must choose where to go, whether left or right or up or down, so that the water "particles" (and their solute) are gradually spread in all directions around the mean path. This is the "microscopic" mechanism, on the scale of soil particles.
Hydrodynamic dispersion is then embedded in the advective-dispersive-reactive equation (ADRE) assuming a Fickian closure model. Dispersion is felt at the macroscale as responsible of a spread effect of the contaminant plume around its center of mass.
The Morison equation contains two empirical hydrodynamic coefficients—an inertia coefficient and a drag coefficient—which are determined from experimental data. As shown by dimensional analysis and in experiments by Sarpkaya, these coefficients depend in general on the Keulegan–Carpenter number, Reynolds number and surface roughness. [4] [5]
Typical values for the entrainment coefficient are of about 0.08 for vertical jets and 0.12 for vertical, buoyant plumes while for bent-over plumes, the entrainment coefficient is about 0.6. Conservation equations for mass (including entrainment), and momentum and buoyancy fluxes are sufficient for a complete description of the flow in many cases.
Statistical moments (e.g., mean, standard deviation, skewness, kurtosis) are used to describe the information content of data. These moments can then be used to determine an appropriate frequency distribution, [12] which can then be used as a probability model. [13]
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.