Diffusion liquid-phase mass

Liquid-phase mass transfer coefficient Gas-liquid interfacial area per unit volume of dispersion Gas volume fraction in dispersion Diffusivity of cyanogen in solution Henry law coefficient... 

Diffusivity of 02 in liquid xylene Da = 1.4 x 10 9 m2/s Equipment performance characteristics Gas volume fraction in the dispersion (1 - eg) = 0.34 Mean diameter of the bubbles present in the dispersion = 1.0 mm Liquid-phase mass transfer coefficient kL = 4.1 x 10 4 m/s... 

C] represents the concentration of species Ain the liquid and x represents the mole fraction of the diffusing species in the liquid. Note that we have introduced kL, the liquid phase mass transfer coefficient. The cap ( ) indicates average value. 

V. Linek, J. Mayrhoferova, J. Mosnerova, The influence of diffusivity on liquid phase mass transfer in solutions of electrolytes, Chem. Eng. Sci. 25 (1970) 1033-1045. 

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). 

Figure 4.24 shows the reactive arheotrope trajectories according to Eq. (83) for various amounts of the liquid phase mass transfer resistance - that is, for various values of Kiiq and a low sweep gas flow rate G (at large NTt/ -values). As a result, the reactive arheotropic composition X, 02 is shifted to larger values as the liquid phase mass transfer resistance becomes more important - that is, as the value of Kuq decreases. Note that the interface liquid concentrations are in equilibrium with the vapor phase bulk concentrations. Therefore, gas phase mass transfer resistances cannot have any influence on the position of the reactive arheotrope compositions. On the other hand, liquid phase mass transfer resistances do have an effect, though the value of all binary hiq have been set equal. Again, this effect results from the competition between the diffusion fluxes and the Stefan flux in the liquid phase. 

With regard to the liquid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon kLa could be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Inst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon HL can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients (see Table 5-24-A). 

Transient Heating and Liquid-Phase Mass Diffusion in Fuel Droplet Vaporization... 

In this presentation we, therefore, investigate the kinetics of ion exchange in such mixtures for the case vdiere diffusion of the ions across a hydrostatic boundary layer (Nemst film) surrounding the particles is the rate controlling step (film diffusion). In well-stirred systems, liquid-phase mass transfer will usually be fevored by a low concentration of the external solution, a high ion-exchange capacity, and a small particle size [I]-... 

The CNMMR model with laminar flow liquid stream in the annular region consists of three ordinary differential equations for the gas in the tube core and two partial differential equations for the liquid in the annular region. These equations are coupled through the diffusion-reaction equations inside the membrane and boundary conditions. The model can be solved by first discretizing the liquid-phase mass balance equations in the radial direction by the orthogonal collocation technique. The resulting equations are then solved by a semi-implicit integration procedure [Harold etal., 1989]. 

It is interesting to note that Zuiderweg s correlation for k is independent of the diffusion coefficient. The liquid-phase mass transfer coefficient is calculated from either... 

Frey, D. D., Prediction of Liquid Phase Mass Transfer Coefficients in Multicomponent Ion Exchange Comparison of Matrix, Film-Model, and Effective Diffusivity Methods, Chem. Eng. Commun., 41, 273-293 (1986). 

Experimental parameter Liquid-phase mass transfer Intraparticle diffusion... 

Table 4-2 shows, as an example, a summary of the effects of experimental variables on the ion-exchange rate controlled by intraparticle diffusion, and by liquid-phase mass transfer. Further details and special situations will become apparent in the discussion of rate laws to follow. 

Three general classes of kinetic models that may apply to systems with rate control by mass transfer in the liquid or by interdiffusion in the particle with or without chemical reaction will be briefly reviewed here (for more detail, see [Helfferich, 1962a Helfferich and Hwang, 1988]). In particular I he following models will be examined liquid-phase mass transfer with linear driving force, Nernst-Planck models for intraparticle diffusion without reac-lion, and, Nernst-Planck models for intraparticle diffusion with accompanying reaction. 

Because of the rigid crystal structure and small window size, ionic diffusion in zeolites is slow and the activation energy is high (Barrer, 1980). Except on samples of very fine particle size, the exchange rate is controlled by intracrystalline rather than liquid-phase mass transfer. 

Figure 1.4 Mathcad routine to estimate liquid-phase mass diffusivities...

Now that one has obtained the basic information for the molar density of reactant A within the liquid-phase mass transfer boundary layer, it is necessary to calculate the molar flux of species A normal to the gas-liquid interface at r = l bubbie, and define the mass transfer coefficient via this flux. Since convective mass transfer normal to the interface was not included in the mass transfer equation with liquid-phase chemical reaction, it is not necessary to consider the convective mechanism at this stage of the development. Pick s first law of diffusion is sufficient to calculate the flux of A in the r direction at r = /fbubbie- Hence,... 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

If the rate of chemical reaction is much faster than the rate of mass transfer via diffusion, then A 1 and tanh A -> 1. Hence, the mass transfer enhancement factor Sh -> A in the diffusion-limited regime via equation (24-24) or (24-26). The final form for the liquid-phase mass transfer coefficient of component j in the diffusion-limited regime is... 

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