Turbulent mass-transfer condition

The turbulent mass transfer in the flow resulting from the interaction of the two jets is more extensive than in a single jet under the same supply conditions. 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

One really may need an inherently transient LES to capture all these details. The finer the grid for such a LES, the more reliably the local transient conditions may be taken into account in reproducing this turbulent mass transfer process (while ignoring the issue of supplying the heat for the dissolution which may also depend on a proper representation of the turbulent-flow field). An additional important issue is how many particles have to be tracked for a proper representation of the transient spatial distribution of the particles over the vessel. 

These thin-film evaporators are equipped with rotating elements that create a thin, liquid film of high turbulence along the inner surface of the heated tube (see Figure 1). Consequently, favorable heat and mass-transfer conditions (I), (2) and short residence times result owing to the small holdup (3,4). 

Other driving force units and corresponding coefficients can be used in analogous definitions. Equation (2.4-2) explicitly allows for the bulk flow contribution to the molar flux relative to stationary coordinates. The coefficient or its analogues is thought to exhibit a somewhat less complex relationship to composition, flow conditions, and geometry. Further discussion of the relationships among those coefficients is provided in Section 2.4-1 in terms of particular models for turbulent mass transfer. 

The modification of hydrodynamic aspects is exploited in the falling-film cell [12], where the electrolyte flows as a thin fllm in the channel between an inclined plane plate and a sheet of expanded metal which work as electrodes. Other proposal is to include turbulence promoters in the interelectrode gap in conventional parallel plate electrochemical reactors [13-16], or the use of expanded metal electrodes immersed in a fluidized bed of small glass beads, called Qiemelec cell [17]. Likewise, the Metelec cell [18] incorporates a cylindrical foil cathode concentric arranged around an inner anode, with a helical turbulent electrolyte flow between the electrodes. The electrochemical hydrocyclone cell [19] makes use of the good mass-transfer conditions due to the helical downward accelerated flow in a modified conventional hydrocyclone. 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass transfer, and therefore turbulence is often purposely induced by this method. 

Many of the earlier studies of mass transfer involved measuring the rate of vaporisation of liquids by passing a turbulent air stream over a liquid surface. In addition, some investigations have been carried out in the absence of air flow, under what have been termed still air conditions. Most of these experiments have been carried out in some form of wind tunnel where the rate of flow of air and its temperature and humidity could be controlled and measured. In these experiments it was found to be important to keep the surface of the liquid level with the rim of the pan in order to avoid the generation of eddies at the leading edge. 

To avoid gas-liquid mass transfer Hmitation, which would have a negative influence on productivity, in correctly operated bioreactors there are turbulent flow conditions with more or less pronounced turbulence, for which the Reynolds stress formula (Eq. (2)) can be used. Whereas, as a rule there is fully developed turbulent flow in technical apparatuses (see condition (6) and explanations in Sect. 8), this is frequently not the case in laboratory fermenters. Equations (3) and (4) are then only valid to a limited extent. 

The spatio-temporal variations of the concentration field in turbulent mixing processes are associated wdth very different conditions for chemical reactions in different parts of a reactor. This scenario usually has a detrimental effect on the selectivity of reactions when the reaction time-scale is small compared with the mixing time-scale. Under the same conditions (slow mixing), the process times are increased considerably. Due to mass transfer inhibitions, the true kinetics of a reaction does not show up instead, the mixing determines the time-scale of a process. This effect is known as mixing masking of reactions [126]. 

Actual concentration profiles (Fig. 1.28) in the very near vicinity of a mass transfer interface are complex, since they result from an interaction between the mass transfer process and the local hydrodynamic conditions, which change gradually from stagnant flow, close to the interface, to more turbulent flow within the bulk phases. 

The Grashof number given by Eq. (40) appears to have a weaker theoretical basis than that given by Eq. (37), since it is based on an analysis that approximates the profile of the vertical velocity component in free convection, for example, by a quadratic function of the distance to the electrode. The choice of an appropriate Grashof number, as well as the experimental conditions in the work of de Leeuw den Bouter et al. (DIO) and Marchiano and Arvia (M3), has been reviewed critically by Wragg and Nasiruddin (W10). They measured mass transfer by combined thermal and diffusional, turbulent, free convection at a horizontal plate [see Eq. (31) in Table VII], and correlated their results satisfactorily with the Grashof number of Eq. (37). 

Eddies are turbulent instabilities within a flow region (Fig. 2). These vortices might already be present in a turbulent stream or can be generated downstream by an object presenting an obstacle to the flow. The latter turbulence is known as Karman vortex streets. Eddies can contribute a considerable increase of mass transfer in the dissolution process under turbulent conditions and may occur in the GI tract as a result of short bursts of intense propagated motor activity and flow gushes. ... 

In general, when the system is subject to stirring by mechanical means or by density or temperature variations during absorption, Ri is difficult to calculate from fundamental principles, and each system has to be considered separately. Among the complicating factors is spontaneous surface instability which may reduce Ri by as much as five times and, before discussing the relation of Ri to the external hydrodynamics, we shall outline the conditions under which spontaneous surface turbulence may occur during mass transfer. 

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