Mass transfer coefficient liquid phase diffusivity effect

As in any solid-liquid reaction, when the solid is sparingly soluble, reaction occurs within the solid by diffusion of the liquid-phase reactant into it across the liquid film surrounding the solid. Thus two diffusion parameters are operative, the solid-liquid mass transfer coefficient sl and the effective diffusivity D. of the reactant in the solid. A reaction in the solid can occur by any of several mechanisms. The simpler and more common of these were briefly explained in Chapter 15. For reactions following the sharp interface model, ultrasound can enhance either or both these constants. Indeed, in a typical solid-liquid reaction such as the synthesis of dibenzyl sulfide from benzyl chloride and sodium sulfide ultrasound enhances SL by a factor of 2 and by a factor of 3.3 (Hagenson and Doraiswamy, 1998). Similar enhancement in was found for a Michael addition reaction (Ratoarinoro et al., 1995) and for another mass transfer-limited reaction (Worsley and Mills, 1996). 

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild 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. Jnst. 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. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

If a transport parameter rc — CS/CL is defined, where Cs is the concentration of C at the catalyst surface, then Peterson134 showed that for gas-solid reactions t)c < rc, where c is the catalyst effectiveness factor for C. For three-phase slurry reactors, Reuther and Puri145 showed that rc could be less than t)C if the reaction order with respect to C is less than unity, the reaction occurs in the liquid phase, and the catalyst is finely divided. The effective diffusivity in the pores of the catalyst particle is considerably less if the pores are filled with liquid than if they are filled with gas. For finely divided catalyst, the Sherwood number for the liquid-solid mass-transfer coefficient based on catalyst particle diameter is two. 

The Stationary Phase Mass-Transfer Term C u When the stationary phase is an immobilized liquid, the mass-transfer coefficient is directly proportional to the square of the thickness of the film on the support particles, d, and inversely proportional to the diffusion coefficient, D, of the solute in the film. These effects can be understood by realizing that both reduce the average frequency at which analyte molecules reach the interface where transfer to the mobile phase can occur. That is, with thick films, molecules must on the average travel farther to reach the surface, and with smaller diffusion coefficients, they travel slower. The consequence is a slower rate of mass transfer and an increase in plate height. 

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). 

Fluid-fluid reactions are reactions that occur between two reactants where each of them is in a different phase. The two phases can be either gas and liquid or two immiscible liquids. In either case, one reactant is transferred to the interface between the phases and absorbed in the other phase, where the chemical reaction takes place. The reaction and the transport of the reactant are usually described by the two-film model, shown schematically in Figure 1.6. Consider reactant A is in phase I, reactant B is in phase II, and the reaction occurs in phase II. The overall rate of the reaction depends on the following factors (i) the rate at which reactant A is transferred to the interface, (ii) the solubihty of reactant A in phase II, (iii) the diffusion rate of the reactant A in phase II, (iv) the reaction rate, and (v) the diffusion rate of reactant B in phase II. Different situations may develop, depending on the relative magnitude of these factors, and on the form of the rate expression of the chemical reaction. To discern the effect of reactant transport and the reaction rate, a reaction modulus is usually used. Commonly, the transport flux of reactant A in phase II is described in two ways (i) by a diffusion equation (Pick s law) and/or (ii) a mass-transfer coefficient (transport through a film resistance) [7,9]. The dimensionless modulus is called the Hatta number (sometimes it is also referred to as the Damkohler number), and it is defined by... 

Individual mass-transfer coefficient k, cm/s or ft/s k r, minimum coefficient for suspended particle (Fig. 21.6) k, effective internal coefficient [Eq. (21,65)] kc, average value over time tj, k, ky, in liquid phase and gas phase, respectively, based on mole-fraction differences, kg mol/m -s-unit mole fraction or lb mol/ft -h-unit mole fraction Effective mass-transfer coefficient in one-way diffusion kc, cm/s or ft/s k, in gas phase, kg mol/m -s-unit mole fraction or lb mol/ft -h-unit mole fraction also new values in Example 21.5 Length of pipe or tube, m or ft... 

Crystal growth is a diffusional process, modified by the effect of tlie solid surfaces on which the growth occurs. Solute molecules or ions reach the growing faces of a crystal by diffusion through the liquid phase. The usual mass-transfer coefficient kjf applies to this step. On reaching the surface, the molecules or ions must be accepted by the crystal and organized into the space lattice. The reaction occurs at the surface at a finite rate, and the overall process consists of two steps in series. Neither the diffusional nor the interfacial step will proceed unless the solution is supersaturated. 

The mass transfer resistances strongly depend on the nature of the hydrodynamics in the contacting device and the mode of operation. Many devices have been used to study two-phase mass transfer at or near the liquid-liquid interface. Hence, the hydrodynamic characteristics of ion transport through a membrane were presented to evaluate the feasibility that this permeation system can be calibrated as a standardized liquid-liquid system for studying the membrane-moderated PT-catalyzed reaction. The individual mass transfer coefficients and diffusivities for the aqueous phase, organic phase, and membrane phase were determined and then correlated in terms of the conventional Sh-Re-Sc relationship. The transfer time of quaternary salt across the membrane and the thickness of the hydrodynamic diffusion boundary layer are calculated and then the effect of environmental flow conditions on the rate of membrane permeation can be accurately interpreted [127]. 

The linear driving force (LDF) model can be classified in the group of equilibrium transport dispersive models (Fig. 9.5). For this model it is no longer assumed that the mobile and the stationary phases are permanently in equilibrium state, so that an additional mass-balance equation for the stationary phase is required. Assuming a linear concentration gradient an effective mass-transfer coefficient keff is implemented, where all mass-transfer resistances and the diffusion into the pores of the particle are lumped together. In this model a constant local equilibrium between the solid and the liquid in the pores is assumed. 

Effective diffusivities were used for the calculation of the mass-transfer coefficients. In contrast to the binary Maxwell-Stefan diffusivities, the effective diffusivities were calculated via available procedures in ASPEN Custom Modeler , whereas the Wilke-Chang model was used for the liquid phase and Chapman-Enskog-Wilke-Lee model for the vapor phase [94]. In the full model, computationally intensive matrix operations for the Maxwell-Stefan equations are necessary. The model has been further extended to consider the presence of liquid-liquid separation [110, 111]. 

Viscosity also affects the liquid-phase mass transfer coefficient through the Stokes-Einstein effect. Einstein proposed that the diffusion coefficient could be expressed as... 

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