Driving forces of mass transfer

Let us start with the action of Young-Laplace law (Equation 9.6), which determines the equilibrium configuration of the fluids (liquid and liquid-like phases) and the driving force of mass transfer that cause the spontaneous formation of equilibrium configurations. 

Where, K is constant, and C is average concentration of transferring substance in soSid at the equilibrium with the surrounding medium. Exponent n is determined from observed data for practical applications, or usually regarded to be unity when treated theoretically. Since C - C represents a driving force of mass-transfer, K is characteristically regarded as a mass-transfer coefficient or a capacity factor of mass-transfer. 

Profile of q, z) at the end of the other step must be employed as an initial condition for each step. In Eqs. (11-32) and (11-36) an LDF model with partial pressure difference as a driving force is used, uho and Ulo are molar flow rates of the inert component in the adsorption and desorption steps, where total pressures are P and Pt. N,h and N,x represent the rates of mass transfer of component i between particle and fluid at the adsorption step and at the desorption step expressed in terms of linear driving force (LDF) model by taking the partial pressure difference or difference in amount adsorbed as the driving force of mass transfer. 

In solving the mass transfer Eq. (3.1), the evaluation of the source term 5n, which is the mass rate (mass flux) transferred from adjacent phase (outside of the system concerned) or generated by chemical reaction (inside of the system), is very important as it is highly affect the final result. For the gas-liquid two-phase mass transfer process under steady condition and assuming the driving force of mass transfer is the linear concentration difference, we can write the conventional formula for calculating the mass transfer rate of species i [dimension kg s ], denoted by 5n or Nj, as follows ... 

The bizarre phenomena of multicomponent system can be illustrated by the case of three-component system as calculated by Wang given in preceding section. The simulated diffusion flux of isopropanol is plotted versus driving force of mass transfer (yo - y) as shown in Fig. 4.30. 

Fig. 4.30 Diffusion mass flux of isopropanol in three-component system versus driving force of mass transfer...

The Driving Force for Mass Transfer. The rate of mass transfer increases as the driving force, (7 — (7, is increased. can be enhanced as follows. From Dalton s law of partial pressures... 

The mass transfer number B represents the ratio of the energy available for vaporization to the energy required for vaporization, and may be thought of as a driving force for mass transfer. It can be expressed as... 

Henry s law constant. The overall driving force for mass transfer is Ug—K ay and the rate of mass transfer across the interface is... 

The overall driving force for mass transfer is AT = Pg—Pi, where Pi is the concentration of oxygen in the liquid phase expressed as an equivalent partial pressure. For the experimental conditions, T/ 0 due to the fast, liquid-phase reaction. The oxygen pressure on the gas side varies due to the liquid head. Assume that the pressure at the top of the tank was 1 atm. Then Tg = 0.975 atm since the vapor pressure of water at 20°C should be subtracted. At the bottom of the tank, 1.0635 atm. The logarithmic mean is appropriate AT =1.018 atm. Thus, the transfer rate was... 

The interpretation is straightforward. At reaction conditions the concentration in the film is lowered by reaction, and, as a consequence, the driving force for mass transfer increases. In a homogeneous system this results in high values of Ha. In a slurry reactor this enhancement can occur if the catalyst particles are so small that they accumulate in the film layer. Table 5.4-4 summarizes expressions for the reaction rate or enhancement factor for various regimes. 

If the reaction is slow, there is a small effect on the overall mass transfer coefficient. The driving force for mass transfer will be greater than that for physical absorption alone, as a result of the dissolving gas reacting and not building up in the bulk liquid to the same extent as with pure physical absorption. 

Here Jv is the volumetric flow rate of fluid per unit surface area (the volume flux), and Js is the mass flux for a dissolved solute of interest. The driving forces for mass transfer are expressed in terms of the pressure gradient (AP) and the osmotic pressure gradient (All). The osmotic pressure (n) is related to the concentration of dissolved solutes (c) for dilute ideal solutions, this relationship is given by... 

Mass transfer. It is not yet possible to predict the mass transfer coefficient with a high degree of accuracy because the mechanisms of solute transfer are but imperfectly understood as discussed Light and Conway(14), Coulson and Skinner(15) and Garner and Hale 16 1. In addition, the flow in spray towers is not strictly countercurrent due to recirculation of the continuous phase, and consequently the effective overall driving force for mass transfer is not the same as that for true countercurrent flow. 

Equation (35) predicts that the mass transfer coefficient increases with increases in the screw speed and the number of parallel channels on the screw. The explanation for this is rather simple and is related to the fact that each time the film on the barrel wall is regenerated and the surface of the nip is renewed, a uniform concentration profile is reestablished, which means that the driving force for mass transfer is maximized. Since the instantaneous mass transfer rate decreases with time, mass transfer rates can be maximized by keeping the exposure time as short as possible, and... 

The decrease in the exit concentration with decreases in the extraction pressure seen in Figs. 17 and 18 is a consequence of the fact that the driving force for mass transfer is directly related to the partial pressure of the volatile component in the vapor phase, which, in this case, is constant and equal to the extraction pressure. In fact, reasonably good agreement between the data in Fig. 17 and the predictions of Eq. (38) can be obtained provided it is assumed that the dimensionless group (ki ATlk y p/L) is independent of pressure. This point is illustrated in Fig. 19, which is a plot of Eq. (38) for Pe =. The value used for (ki Aj/k v(kp/L) was chosen so as to obtain the asymptotic value of wi in Fig. 17. 

The net effect of this reduction, of course, is to increase the driving force for mass transfer in the liquid phase. 

In a dilute phase, atoms or ions are transported from far away, and, on arrival at the crystal surface, they are incorporated into the crystal. There is a desolvation process involved in crystallization in the solution phase or in CVT. (For an explanation of desolvation, please see Section 3.4.) The essential role of the driving force is mass transfer grovyth temperature is much lower than that in melt grovyth, and the solid-liquid interface tends to be smoother than that in the condensed phase. 

The mass-transfer coefficients, by definition, are equal to the ratios of the molar mass flux to the concentration driving forces. The mass-transfer coefficients are related to each other as follows ... 

We can now proceed to the second part of the calculation and find the height of packing required. Plug flow for the gas phase will be assumed because the composition of the liquid is assumed not to change, the flow pattern in the liquid does not enter into the problem. Note that using Kca requires that the driving force for mass transfer be expressed in terms of gas-phase partial pressures. 

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