Velocity distribution, mixing

Figure 12. Variation of velocity distribution in a mixing tank on insertion of full side wall baffles.

Abramovich was the first to study axisymmetric confined jets analytically. He suggested the method based on utilizing the equations of continuity and momentum conservation. He also assumed that the width of the layer of a jet mixing with a counterflow equals the width of a free jet with a velocity distribution according to Schlichting s formula ... 

Analytical methods suggested by Shepelev and Tarnopolsky, Grimitlyn and Pozin, and Sychev and Volov differ from the one described above only in the way the authors described velocity distribution in the mixing layer ... 

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

The performance of adsorption processes results in general from the combined effects of thermodynamic and rate factors. It is convenient to consider first thermodynamic factors. These determine the process performance in a limit where the system behaves ideally i.e. without mass transfer and kinetic limitations and with the fluid phase in perfect piston flow. Rate factors determine the efficiency of the real process in relation to the ideal process performance. Rate factors include heat-and mass-transfer limitations, reaction kinetic limitations, and hydro-dynamic dispersion resulting from the velocity distribution across the bed and from mixing and diffusion in the interparticle void space. 

In the Lagrangian approach, individual parcels or blobs of (miscible) fluid added via some feed pipe or otherwise are tracked, while they may exhibit properties (density, viscosity, concentrations, color, temperature, but also vorti-city) that distinguish them from the ambient fluid. Their path through the turbulent-flow field in response to the local advection and further local forces if applicable) is calculated by means of Newton s law, usually under the assumption of one-way coupling that these parcels do not affect the flow field. On their way through the tank, these parcels or blobs may mix or exchange mass and/or temperature with the ambient fluid or may adapt shape or internal velocity distributions in response to events in the surrounding fluid. 

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

Figure 25.1 Heterogeneity is one of the main properties of porous media it not only characterizes the scales shown in the figure, but also occurs on larger scales up to the size of the whole porous system. Three important mechanisms of transport and mixing in porous media are (a) interpore dispersion caused by mixing of pore channels (b) intrapore dispersion caused by nonuniform velocity distribution and mixing in individual channels (c) dispersion and retardation of solute transport caused by molecular diffusion between open and dead-end pores as well as between the water and the...

The opposite occurs at the forward-pumping section (A-A ). However, axial velocities, although still beneficial for distributive mixing, are an order of magnitude of the... 

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