Film mass transfer coefficient liquid-solid

As Fig. 4.15 demonstrates, the two mass transfer steps, gas to liquid and liquid to solid, and then the chemical reaction, take place in series. This means that in the steady state each must proceed at the same rate as the overall process. Continuing then on the basis of unit volume of dispersion, and using the reactant concentrations shown in Fig. 4.15, with the gas-liquid and liquid-solid film mass transfer coefficients kL and ks shown in Fig. 4.20, the overall rate 91, may be written as ... 

In the SLPTC models previously developed, film mass transfer coefficients for the organic and aqueous phases are important parameters. In Chapter 14 we saw how the coefficient for gas-liquid systems can be determined. The same method can be used for liquid-liquid systems. In all of these cases, mass transfer rates are calculated using contactors with known interfacial areas. Where a solid phase is involved, the constant area criterion can be met by using a rotating disk of solid reactant or catalyst, as the case may be (Melville and Goddard, 1985, 1988 Hammerschmidt and Richarz, 1991). 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

The double lines in Figure 3.44 represent the Sh number based on the mass transfer coefficient, in the case of a single-particle fall in water, for three different particle densities (Harriot, 1962). This value is considered to be the minimum mass-transfer coefficient in liquid-solid films in agitated vessels. Taking into account the fact that the actual Sh value in an agitated vessel is 1.5 -8 times its minimum value, it is apparent that the mass transfer coefficients are much higher in the case of agitated vessels. 

In the case of solid diffusion control, even in the absence of agitation where the mass transfer coefficient is at its minimum value, sufficient agitation should be provided in order to avoid the negative effect of the liquid-film resistance. The effect of agitation should be taken into account in both the design and application stage. 

Model application in the pulsing-flow regime The mass transfer coefficient in the liquid-solid film is evaluated by means of the Dhai wadkar and Sylvester correlation (eq.3.433), and is found to be 0.45 s. Then, the several parameters of the model eq. (5.379) are shown in Table 5.18. 

The film thickness is not directly accessible, and the term D/S, which has units cm s 1, is referred to as the mass transfer coefficient, ki. In solid/liquid and liquid/liquid systems, values of kL are typically 1-2 x 10 3 cm s-1 with values of D typically 5 x 10 6 to 2 x 10-5 cm2 s 1, corresponding to diffusion film thicknesses of 50-100 pm and film diffusion times of around 5 seconds. 

Liquid-solid mass transfer has also been studied, on a limited basis. Application to systems with catalytic surfaces or electrodes would benefit from such studies. The theoretical equations have been proposed based on film-flow theory (32) and surface-renewal theory (39). Using an electrochemical cell with rotating screen disks, liquid-solid mass transfer was shown to increase with rotor speed and increased spacing between disks but to decrease with the addition of more disks (39). Water flow over naphthalene pellets provided 4-6 times higher volumetric mass transfer coefficients compared to gravity flow and similar superficial liquid velocities (17). 

In a trickle-bed reactor, due to a very thin liquid film, gas-liquid and liquid solid mass-transfer coefficients are sometimes combined as... 

In the limiting case of mass transfer from a single sphere resting in an infinite stagnant liquid, a simple film-theory analysis122 indicates that the liquid-solid mass-transfer coefficient R s is equal to 2D/JV, where D is the molecular diffusivity of the solute in the liquid phase and d is the particle diameter. In dimensionless form, the Sherwood number... 

For a fast reaction occurring on a solid wall, the concentration profile in the liquid film reaches a stationary value for a thin film and long bubbles moving at low velocity. In such a case, the mass transfer coefficient through a plate of infinite length is given by... 

Mass transfer coefficients for the lower surface of a laminar film are strongly influenced by the shear at the liquid-solid interface. A solution for liquid-solid mass transfer coefficients for a diffusive process in a laminar film was provided by Bird et al. as the follow-... 

For a spinning disk, the standard model for falling film flow is complicated by the changing thickness and shear as the liquid flows over the disk. An approximation of this to conditions on a spinning disk surface can, however, be made by substitution of Eq. (9) for average liquid-solid surface shear into the above equation for mass transfer. If it is also assumed that the characteristic distance L traveled by the liquid is equal to that of the disk radius then an equation for the liquid-solid mass transfer coefficient ls can be written for an SDR as... 

Figure 8.21 (d) Experimental results for the liquid-solid mass-transfer coefficient in a downflow trickle bed liquid velocity range from 1 to lOOcm /s. For film flow dp =9 12 mm for... 

On the other hand, the synthetic organic chemist, who has often to deal with immiscible or sparingly miscible fluids, has to contend with the problem of transport of a desired species across an interface such as gas-liquid, liquid-liquid, or fluid-solid. In such a situation, one has to fall back on the concept of mass transfer coefficient by defining a hypothetical film across which transport occurs—an approach to which the chemist is unaccustomed. Although the two models (one based on diffusion and the other on mass transfer coefficient) are related, we shall largely be concerned (more as chemical engineers now) with the latter in dealing with interfacial phenomena (e.g., in Chapters 7 and 14-17). 

Referring to Figure 17.1 and Equation 17.1, it is clear that an overall mass transfer coefficient is needed that accounts for mass transfer at both the gas-liquid interface (Icq /i for the gas-side and and for the liquid-side films) and the solid-liquid interface (/csl.a)- Such a coefficient is given by... 

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). 

One of the other studies on the influence of suspended solid materials on the mass transfer coefficient is that of Alper et al. (5).They employed various stirred cells of different designs,however,in all of the experiments gas-liquid interfacial area remained reasonably flat and could be taken as equal to the geometrical area.The values of k. was low so that the liquid film thickness was bigger than 50 pm.In agreement with above studies, their data showed that no effect of particles on k, values when inert particles,such as finely powdered quartz sand and oxirane acrylic beads,were employed.However,a completely different picture was obtained with highly porous particles of strong adsorbing property,such as activated carbon,which increased k considerably(5),... 

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