Mass convection relations

Limitation on the Heat-Mass Convection Analogy 816 Mass Convection Relations 816... 

Turbulent mass-transfer relations concerning forced convection are of interest for two main reasons (see Table VII, Part D) (a) because of their practical importance, since turbulence promotes increase of transfer rates and (b) they afford an indirect means of gaining insight into the mechanism... 

When the particle is moving relative to the suspending fluid, transport of heat or matter is enhanced by convective diffusional processes. Under conditions where the particle exists in a rarified medium (Kn 0), the heat and mass tranfer relations are modified to account for surface accommodation or sticking of colliding molecules and the slippage of gas around the particle. 

Tire title of the book is changed to Heat and Mass Transfer A Practical Approach to attract attention to the coverage of mass transfer. All topics related to mass transfer, including mass convection and vapor migration through building materials, are introduced in one comprehensive chapter (Chapter 14). 

Like heal convection, mass convection is also complicated because of the complications associated with fluid flow such as the surface geomeiiy, flow regime, flow velocity, and the variation of the fluid properties and composition. Therefore, wc have to rely on experimental relations to determine mass transfer. Also, mass convection is usually analyzed on a mass basis rather than on a molar basis. Therefore, sve will present formulations in terms of mass concentration (density p or mass fraction iv) instead of molar concentration (molar density C or mole, fraction y). But the formulations on a molar basis can be obtained using the relation C piM where M is the molar mass. Also, for simplicity, wc will restrict our attention to convection in fluids that are (or can be treated as) binaiy mixtures. 

Finally, the heat-mass convection analogy is valid for low mass flux cases in which the flow rate of species undergoing mass flow is low relative to the total flow rate of the liquid or gas mixture so that the mass transfer between the fluid and the surface does not affect the flow velocity. (Note that convection relations are based on cero fluid velocity at the. surface, which is true only when there is no net mass transfer at the surface.) Therefore, the heat-mass convection analogy is not applicable when the rate of mass transfer of a species is high relative to the flow rate of that species. 

ShenvQod number relations in mass convection for specified concentration at the surface corresponding to the Nusselt number relations in heat convection for specified surface temperature ... 

Here we study processes that affect the (molar) concentration ck of a chemical species k-, for this purpose we set up a flux vector c Vkir, t) for the rate of transport of k at concentration Ck past location r at time t. The amount of k may be altered either through chemical reactions that change its concentration locally at a rate (9q/3 )Ic, or by convective or diffusive transport processes that take place at a rate dck/dt) t. Convection relates to the motion of the center of mass of the system that carries all constituents with it, while diffusion relates to the motion of species k relative to the center of mass. 

For both forced and natural convection, relations have been obtained by dimensional analysis which suggest that a correlation of experimental data may be in terms of three variables instead of the original six. This reduction in variables has aided investigators who have developed correlations for estimating convective mass-transfer coefficients in a variety of situations. 

Because the interface is generally in motion, it is convenient to derive the mass conservation relation at the interface, employing a moving control surface. Typically a pillbox control volume straddling the interface is used. Any net convective outflow is then governed by the relative velocity u j., = u - u with respect to each area element n dA. Thus the outflows are calculated with respect to an observer moving with the velocity of an element of the control surface. 

In slurry systems, of course, the mass transfer is enhanced by convective currents originating from bulk convection and turbulence In the first approach main emphasis is put on bulk convection and mass transfer related to the particle (terminal) slip velocity v,p e.g. via the modified Frbssling equation ... 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

To model convection drying both the heat transfer to the coated web and the mass transfer (qv) from the coatiag must be considered. The heat-transfer coefficient can be taken as proportional to the 0.78 power of the air velocity or to the 0.39 power of the pressure difference between the air in the plenum and the ambient pressure at the coatiag. The improvement in heat-transfer coefficients in dryers since the 1900s is shown in Figure 20. The mass-transfer coefficient for solvent to the air stream is proportional to the heat-transfer coefficient and is related to it by the Clulton-Colbum analogy... 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

An attempt has been made by Johnson and co-workers to relate such theoretical results with experimental data for the absorption of a single carbon dioxide bubble into aqueous solutions of monoethanolamine, determined under forced convection conditions over a Reynolds number range from 30 to 220. The numerical results were found to be much higher than the measured values for noncirculating bubbles. The numerical solutions indicate that the mass-transfer rate should be independent of Peclet number, whereas the experimentally measured rates increase gradually with increasing Peclet number. The discrepancy is attributed to the experimental technique, where-... 

Because the mechanisms governing mass transfer are similar to those involved in both heat transfer by conduction and convection and in momentum transfer (fluid flow), quantitative relations exist between the three processes, and these are discussed in Chapter 12. There is generally more published information available on heat transfer than on mass transfer, and these relationships often therefore provide a useful means of estimating mass transfer coefficients. 

The diffusive and convective terms in Eq. (20-10) are the same as in nonelectrolytic mass transfer. The ionic mobility Uj, (g mol cm )/(J-s), can be related to the ionic-diffusion coefficient D, cmVs, and the ionic conductance of the ith species X, cmV(f2-g equivalent) ... 

Osmotic pressure A driving force for convective and diffusive mass transfer that is related to solute concentration. 

In the literature we can now find several papers which establish a widely accepted scenario of the benefits and effects of an ultrasound field in an electrochemical process [13-15]. Most of this work has been focused on low frequency and high power ultrasound fields. Its propagation in a fluid such as water is quite complex, where the acoustic streaming and especially the cavitation are the two most important phenomena. In addition, other effects derived from the cavitation such as microjetting and shock waves have been related with other benefits reported for this coupling. For example, shock waves induced in the liquid cause not only an enhanced convective movement of material but also a possible surface damage. Micro jets of liquid, with speeds of up to 100 ms-1, result from the asymmetric collapse of cavitation bubbles at the solid surface [16] and contribute to the enhancement of the mass transport of material to the solid surface of the electrode. Therefore, depassivation [17], reaction mechanism modification [18], surface activation [19], adsorption phenomena decrease [20] and the mass transport enhancement [21] are effects derived from the presence of an ultrasound field on electrode processes. We have only listed the main phenomena referring to the reader to the specific reviews [22, 23] and reference therein. 

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