Eddies mass transfer, concentration gradient

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. 

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

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force, since turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one... 

A theory which incorporates some of the principles of both the two-film theory and the penetration theory has been proposed by TOOR and Marchello The whole of the resistance to transfer is regarded as lying within a laminar film at the interface, as in the two-film theory, but the mass transfer is regarded as an unsteady state process. It is assumed that fresh surface is formed at intervals from fluid which is brought from the bulk of the fluid to the interface by the action of the eddy currents. Mass transfer then takes place as in the penetration theory, except that the resistance is confined to the finite film, and material which traverses the film is immediately completely mixed with the bulk of the fluid. For short times of exposure, when none of the diffusing material has reached the far side of the layer, the process is identical to that postulated in the penetration theory. For prolonged periods of exposure when a steady concentration gradient has developed, conditions are similar to those considered in the two-film theory. 

Theodore and Ricci provide the following When a fluid flows past a surface under conditions such that turbulence generally prevails, a thin laminar-type sublayer film exists adjacent to the surface. The mass transfer in this region occurs by molecular diffusion since little or no eddies are present. Since this is a slow process, a large concentration gradient or decrease in concentration across this laminar film occurs. Adjacent to this is the transition or buffer region. Here, some eddy activity exists and the transfer occurs by the sum of molecular and turbulent diffusion. In this... 

The eddies bring about a transfer of dissolved solute, as we have mentioned before. The average concentration gradient between 1 and 2 in Fig. 3.5 is Ac y//, proportional to a local gradient, - dcjdz. The flux of A due to the interchange, Ac j and the concentration gradient can be used to define an eddy diffusivity of mass length /time... 

In the turbulent mass transfer process, the velocity gradient and concentration gradient are established as well as the mJc gradient. The transport of u d is implemented by the turbulent fluid flow and the fluctuated mass flux diffusion. As the velocity eddy, which is the elements of turbulent flow, is the carrier of m-c, the transport of mJc also follows the pattern of the velocity eddy flow and the fluctuated diffusion. 

In brief, both simulation and observation in this section indicate that, for the Ma > 0 liquid-gas mass transfer process, the velocity and concentration gradients always occur at the interface to form velocity and concentration eddies in large or smalls scales they are developed and vanished in alternation until sufficient surface tension is established to initiate the interfacial Marangoni convection. 

Noncatalytic gas-solid reactions in mixed bed systems usually involve the movement of a reaction front in the direction of the flow and radial gradients of concentration are usually not very signfiicant. It follows that radial dispersion usually plays an insignificant role in mass transfer problems. However, radial eddy diffusion of heat (eddy thermal conductivity) may play an important role in reactors that are heated or cooled through the bounding walls. An interesting example of this type has been presented by Amundson [20]. 

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