Mass-transfer coefficients relations between

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

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. 

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... 

Upon introducing the eqiiihbriiim relation p = HC, the relation between the various mass-transfer coefficients is... 

The relation between CAi[ and CAi2 is determined by the phase equilibrium relationship since the molecular layers on each side of the interface are assumed to be in equilibrium with one another. It may be noted that the ratio of the differences in concentrations is inversely proportional to the ratio of the mass transfer coefficients. If the bulk concentrations, CAt> and CA02 are fixed, the interface concentrations will adjust to values which satisfy equation 10.98. This means that, if the relative value of the coefficients changes, the interface concentrations will change too. In general, if the degree of turbulence of the fluid is increased, the effective film thicknesses will be reduced and the mass transfer coefficients will be correspondingly increased. 

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. 

Some workers have attempted to base the design of humidifiers on the overall heat transfer coefficient between the liquid and gas phases. This treatment is not satisfactory since the quantities of heat transferred through the liquid and through the gas are not the same, as some of the heat is utilised in effecting evaporation at the interface. In fact, at the bottom of a tall tower, the transfer of heat in both the liquid and the gas phases may be towards the interface, as already indicated. A further objection to the use of overall coefficients is that the Lewis relation may be applied only to the heat and mass transfer coefficients in the gas phase. 

This relationship applies quite closely for the conditions normally encountered in practice. For other systems, the relation between the heat and mass transfer coefficients in the gas phase is given by ... 

By using the simple Reynolds Analogy, obtain the relation between the heat transfer coefficient and the mass transfer coefficient for the gas phase for the absorption of a soluble component from a mixture of gases. If the heat transfer coefficient is 100 W/m2 K, what will the mass transfer coefficient be for a gas of specific heat capacity Cp of 1.5 kJ/kg K and density 1.5 kg/m- The concentration of the gas is sufficiently low for hulk flow effects to be negligible. 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

When Kh is a function of composition, the concept of overall mass transfer coefficient stops being useful. Instead, the overall resistance to mass transfer is divided between two him resistances, one for each phase. This is done by assuming that equilibrium is achieved at the interface. The equilibrium values are related by a function having the form of Henry s law ... 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

What is the significance of the parameter fi = (k2C BLDAf5 / kL in the choice and the mechanism of operation of a reactor for carrying out a second-order reaction, rate constant k2, between a gas A and a second reactant B of concentration CBL in a liquid In this expression, DA is the diffusivity of A in the liquid and kL is the liquid-film mass transfer coefficient. What is the reaction factor and how is it related to /l ... 

You are engaged in laboratory flume experiments on transfer of dissolved oxygen into the sediments below the flowing water. The goal is to measure the sediment-water mass transfer coefficient and relate it to other parameters of the flow fleld. The flume is 20 m in length, with a depth between 3 and 10 cm and velocity between... 

In the case that the cross section of the channel is not circular, the equivalent diameter d defined by Equations 5.10 and 5.11 should be used in place of d- As with heat transfer, taking the wetted perimeter for mass transfer rather than the total wetted perimeter provides a larger value of the equivalent diameter and hence a lower value of the mass transfer coefficient. The equivalent diameter of the channel between two parallel plates or membranes is twice the distance between the plates or membranes, as noted in relation to Equation 5.11. 

The analogy between mass transfer and heat transfer is summarized in Kq. The mass transfer coefficient s relation to Ap in mass transfer is analogous to the role that the overall heat transfer coefficient is to AT in heat transfer. 

Closely related to the diffusion layer term is the mass transfer coefficient m,. In a general way, this coefficient is the proportionality constant between the mass transfer flux and the concentration difference between the electrode surface and the bulk of the solution. From the current expression given by Eq. (1.181), one can write... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

The mass-transfer coefficient kL at the liquid-liquid interface between the dispersed and the continuous phase can be described by the dimensionless relation Sh = /(Ar, Re, Sc, dsv/d ), and the heat-transfer coefficient can be described by the relation Nu = /(Ar, Re, Pr, dsv/d ). Calderbank and Moo-Young (1961) showed that these two characteristics are the same for all disperse systems. 

The similarities between the governing equations for heat, mass, and momentum transfer suggest that empirical correlations for the mass-transfer coefficient would be similar to those for the heat-transfer coefficient. This turns out to be the case, and some of the empirical relations for mass-transfer coefficients are presented below. Gilliland 14] presented the equation... 

Here, aL is the interfacial area per unit volume of column in m x, as in m 1, and (AP/AZ)Lg in kg, m 3. The relative mean quadratic error for the above correlation is 6.2 percent. A comparison between Eq. (7-26) and a similar relation for the downflow conditions is illustrated in Fig. 7-17. The liquid-side mass-transfer coefficient was similarly correlated to the energy parameter by an expression... 

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