Transport phenomena turbulent flow

Material transport is usually associated with thermal transport except in situations involving homogeneous phases which can be treated as ideal solutions (L4). For this reason it is necessary to consider the behavior of combined thermal and material transport in turbulent flow. The evaporation of liquids under macroscopic adiabatic conditions is a typical example of such a phenomenon. Under such circumstances the behavior in the boundary layer is similar to that found in the field of aerodynamics in a blowing boundary layer (S4). However, it is not... 

The rate of agitation, stirring, or flow of solvent, if the dissolution is transport-controlled, but not when the dissolution is reaction-con-trolled. Increasing the agitation rate corresponds to an increased hydrodynamic flow rate and to an increased Reynolds number [104, 117] and results in a reduction in the thickness of the diffusion layer in Eqs. (43), (45), (46), (49), and (50) for transport control. Therefore, an increased agitation rate will increase the dissolution rate, if the dissolution is transport-controlled (Eqs. (41 16,49,51,52), but will have no effect if the dissolution is reaction-controlled. Turbulent flow (which occurs at Reynolds numbers exceeding 1000 to 2000 and which is a chaotic phenomenon) may cause irreproducible and/or unpredictable dissolution rates [104,117] and should therefore be avoided. 

Laminar flow reactors are equipped with microstructured reaction chambers that have the desired low Reynolds numbers due to their small dimensions. Mass transport perpendicular to the laminar channel flow is dominated by diffusion, a phenomenon known as dispersion. Without the influence of diffusion, laminar flow reactors could not be used in heterogeneous catalysis. There would be no mass transport from the bulk flow to the walls as laminar flow, in contrast to turbulent flow, cannot mix the flow macroscopically. 

Equation 7.2.a-5 implicitly assumes perfectly ordered flow in that V (pyD Vx ) is specific for molecular diffusion. Deviations from perfectly ordered flow, as encountered with turbulent flow, lead to a flux that is also expressed as if it arose from a diffusion-like phenomenon, in order to avoid too complex mathematical equations. The proportionality factor between the flux and the concentration gradient is then called the turbulent or eddy diffusivity. Since this transport mechanism is considered to have the same driving force as molecular diffusion, the two mechanisms are summed and the resulting proportionality factor is called effective diffusivity, D,. In highly turbulent flow the contribution of... 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

In these expressions, molecular diffusion has been neglected relative to turbulent diffusion. When the reactor is sufficiently long, (Dr L ), the distance after which the spot has dispersed laterally and the flow has become uniform over the available flow section is small compared to the length of the reactor, and the main process observed inside the reactor is the transport of the spot inside the reactor and its gradual expansion along the axial direction. It is this phenomenon that we model by employing the concept of turbulent dispersion introduced in Chapter 8. For this reactor, the mean residence time is related simply to velocity U of the mean flow ... 

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