Eddy mass transfer

When the two liquid phases are in relative motion, the mass transfer coefficients in either phase must be related to the dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive transfer to the Schmidt number. Another complication is that such a boundary cannot in many circumstances be regarded as a simple planar interface, but eddies of material are transported to the interface from the bulk of each liquid which change the concentration profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most industrial circumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass transfer model must therefore be replaced by an eddy mass transfer which takes account of this surface replenishment. 

In extraction columns, it is possible to find droplet swarms where the local velocities near the droplet surface are higher, this being due to the lower free area available for the countercurrent flowing continuous phase. Wake and Marangoni influences make the prediction of a physical mass transfer coefficients difficult. With reactive extraction the influence of interfacial kinetics on overall mass transfer is generally not negligible. In any case, a combination of reactive kinetics with any eddy mass transfer model is recommended, whereas the latter could rely on correlations derived for specific column geometries. 

Israel, H. and Horbert, M., 1970. Tracing atmospheric eddy mass transfer by means of natural radioactivity. J. Geophys. Res., 75 2291-2297. 

A recent model (1988) was published by J. Guttierrez Gonzalez et al. According to the authors, although the liquid fiow is laminar, due to the high Schmidt number in the liquid phase, eddy mass transfer can be significant and eddy diffusion cannot be disregarded with respect to molecular diffusion. Eddy thermal diffusion in the liquid phase is much smaller than thermal diffusion, so that it is not introduced in the microscopic heat balance. The Spanish authors needed to validate their results on practical data. The pressure drop over the reactor, heat- and mass transfer were fitted. 

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

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. 

When bodr phases are producing eddies a more complicated equation due to Mayers (1962) gives the value of the mass transfer coefficient in terms of the Reynolds and Schmidt numbers which shows that die coefficient is proportional to... 

A liquid mobile phase is far denser than a gas and, therefore, carries more momentum. Thus, in its progress through the interstices of the packing, violent eddies are formed in the inter-particular spaces which provides rapid solute transfer and, in effect, greatly increases the effective diffusivity. Thus, the resistance to mass transfer in that mobile phase which is situated in the interstices of the column is virtually zero. However, assuming the particles of packing are porous (i.e., silica based) the particles of packing will be filled with the mobile phase and so there will... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

The energy of large and medium-size eddies can be characterized by the turbulent diffusion coefficient. A, m-/s. This parameter is similar to the parameter used by Richardson to describe turbulent diffusion of clouds in the atmosphere. Turbulent diffusion affects heat and mass transfer between different zones in the room, and thus affects temperature and contaminant distribution in the room (e.g., temperature and contaminant stratification along the room height—see Chapter 8). Also, the turbulent diffusion coefficient is used in local exhaust design (Section 7.6). 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

The term mass transfer is used to denote the transference of a component in a mixture from a region where its concentration is high to a region where the concentration is lower. Mass transfer process can take place in a gas or vapour or in a liquid, and it can result from the random velocities of the molecules (molecular diffusion) or from the circulating or eddy currents present in a turbulent fluid (eddy diffusion). 

Equation 10.4, which describes the mass transfer rate arising solely from the random movement of molecules, is applicable to a stationary medium or a fluid in streamline flow. If circulating currents or eddies are present, then the molecular mechanism will be reinforced and the total mass transfer rate may be written as ... 

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. 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

On a similar basis an eddy diffusivity for mass transfer Er> can be defined for systems in which concentration gradients exist as ... 

Equation 12.105 is often referred to as the Lewis Relation. It provides an approximate method for evaluating a mass transfer coefficient if the heat transfer coefficient is known. The assumption that the turbulent eddies can penetrate right up to the surface is justified however only in special circumstances and the problem is considered further in the next section. 

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

Mathpati, C.S. and Joshi, J.B. (2007) Insight into theories of heat and mass transfer at the solid/fluid interface using direct numerical simulation and large eddy simulation. Joint 6th International Symposium on Catalysis in Multiphase Reactors/5th International Symposium on Multifunctional Reactors (CAMURE-6/ISMR-5-), 2007, Pune. 

It should be stressed that in the case of linear isotherm, the peak broadening effect results from eddy diffusion and from resistance of the mass transfer only, and it does not depend on Henry s constant. In practice, such concentration profiles are observed for these analyte concentrations, which are low enough for the equilibrium isotherm to be regarded as linear. 

Mass transfer eddy diffusiviy Length increment Activation energy Heat of reaction... 

The A term represents the contribution from eddy diffusion, the B term the contribution from longitudinal diffusion, and the C terms the contributions from mass transfer in the mobile and stationary phases to the total column plate height. By differentiating equation (1.31) with respect to the mobile phase velocity and setting the result equal to zero, the optimum values of mobile phase velocity (u ) and plate height (HETP ) can be obtained. 

When electrically insulated strip or spot electrodes are embedded in a large electrode, and turbulent flow is fully developed, the steady mass-transfer rate gives information about the eddy diffusivity in the viscous sublayer very close to the electrode (see Section VI,C below). The fluctuating rate does not give information about velocity variations, and is markedly affected by the size of the electrode. The longitudinal, circumferential, and time scales of the mass-transfer fluctuations led Hanratty (H2) to postulate a surface renewal model with fixed time intervals based on the median energy frequency. 

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