Mass transfer driving concentration difference

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

The driving forces for mass transfer are concentration, temperature or pressure gradients. We will explore the most common of these three, namely mass transfer due to a concentration gradient. As experience tells us, the components of a mixture move from regions of higher concentration to those with lower concentration. Equilibrium with respect to mass transfer is realised when the driving force, in this case the concentration difference, has disappeared. 

The 14 equations, sulfite rate of change in the liquid and the rates of sulfite transfer (in terms of r ) from the 13 sized particles, may be solved simultaneously for and the r s. Then the total sulfite concentration is calculated at each increment of time. In addition, to compute the proper surface conditions for the mass transfer driving force, all of the governing equations for the bulk listed in the section above on the surface conditions during dissolution must be solved at each time step. Two differences should be noted the solubility product for sulfate must now be satisfied and in the Ca2+ and sulfur balance, the effect of oxidation must be accounted for , ... 

The most important physical property data required Tor the design of abtotbers and strippeis are gas-liquid equilibria. Since equilibrium represents the limiting condition for any gas-liquid contact, such data are needed to define the maximum ges pority and rich solution concentration attainable in absorbers and the maximum lean solution purity attainable in strippers. Equilibrium data also are needed to establish the mass transfer driving foros. which can be defined simply as the difference between the actual and equilibrium conditions at any point in a contactor. 

The mass transfer rate M is proportional to the product of overall mass transfer coefficient of interfacial area A, and of driving concentration differ-... 

The three towers usually are sized to a common diameter that will give a pressure drop of 0.10 in. to 0.15 in. H20/ft of packed depth, because the overall pressure drop desired for the entire drying system is only 4 in. to 5 in. H2O. This process largely is gas-film-controlled, as expected. It is desirable to keep the packed depth in each of the three columns the same. To accomplish this configuration, an iterative design procedure is necessary. The driving force for mass transfer is the difference between the partial pressure of water vapor in the gas stream and the vapor pressure of water above the liquid phase. Because of the high liquid flow rate, as a first approximation, the acid concentration and temperature in eath tower can be assumed constant in order to establish the amount of water vapor removed in each column, and thereby the acid concentration. 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Although equation 35 is a simple expression, it tends to be confusing. In this equation the enthalpy difference appears as driving force in a mass-transfer expression. Enthalpy is not a potential, but rather an extensive thermodynamic function. In equation 35, it is used as enthalpy pet mole and is a kind of shorthand for a combination of temperature and mass concentration terms. 

The linear driving force (LDF) approximation is obtained when the driving force is expressed as a concentration difference. It was originally developed to describe packed-bed dynamics under linear eqm-librium conditions [Glueckauf, Trans. Far Soc., 51, 1540 (1955)]. This form is exact for a nonlinear isotherm only when external mass transfer is controlling. However, it can also be used for nonlinear sys-... 

Mass transfer Irreversible and spontaneous transport of mass of a chemical component in a space with a non-homogeneous field of the chemical potential of the component. The driving force causing the transport can be the difference in concentration (in liquids) or partial pressures ( in gases) of the component. In biological systems. 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

On the basis of each of the theories discussed, the rate of mass transfer in the absence of bulk flow is directly proportional to the driving force, expressed as a molar concentration difference, and, therefore ... 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

Problems involving combined heat and mass transfer provide a final example of multiple driving forces but differ in important ways from the previous examples. In those examples, all the gradients involved (concentration, pressure, electrical potential) were directly responsible for driving mass transfer. In combined heat and mass transfer, however, both heat and mass are being transported. The transfer of heat may drive mass transfer indirectly, as in the loss of a volatile solvent from a beaker when it is heated by evaporation. Thus, problems in heat and mass... 

The driving force of the mass-transfer process now can be related to the concentration gradient of the reacting species, or to the concentration difference between electrode and bulk solution. Mass-transfer rates then can be related in a general way to the concentration driving force. For example, if... 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

External mass transfer between the external surfaces of the adsorbent particles and the surrounding fluid phase. The driving force is the concentration difference across the boundary layer that surrounds each particle, and the latter is affected by the hydrodynamic conditions outside the particles. 

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