Liquid Film Resistance Controlling

In the case where the rate of the catalytic or enzymatic reaction is controlled by the mass transfer resistance of the liquid film around the particles containing catalyst or enzyme, the rate of decrease of the reactant A per unit liquid volume [i.e., —rA (kmolm 3 s 1)] is given by Equation 7.13  

The apparent reaction rate depends on the magnitude of the Damkohler number (Da) as defined by Equation 7.14 that is, the ratio of the maximum reaction rate to the maximum mass transfer rate. 

In the case when mass transfer of the reactants through the liquid film on the surface of catalyst or enzyme particles is much slower than the reaction itself (Da 1), then the apparent reaction rate becomes almost equal to the rate of mass transfer. This is analogous to the case of two electrical resistances of different magnitudes in series, where the overall resistance is almost equal to the higher resistance. In such a case, the apparent reaction rate is given by  

---

E] Based on oxygen transfer from water to air 77 F. Liquid film resistance controls. (Dwnei- 77 F = 2.4 X 10 ). Equation is dimensional. Data was for thin-waUed polyethylene Raschig rings. Correlation also fit data for spheres. Fit 25%. See Reiss for graph. 

Liquid film resistance controls for slightly soluble gases. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

F. Absorption, cocurrent downward flow, random packings, Reiss correlation Air-oxygen-water results correlated by k i/i = 0.lZEi5. Extended to other systems. = pressure loss in two-phase flow = lbf/ft2 ft AL [E] Based on oxygen transfer from water to air 77°F. Liquid film resistance controls. (Dwater 77°F = 2.4 x 10 5). Equation is dimensional. Data was for thin-walled polyethylene Raschig rings. Correlation also fit data for spheres. Fit 25%. See [122] for graph. k La = s"1 Dl = cm/s El = ft, lb Us ft3 Vi = superficial liquid velocity, ft/s [122] [130] p. 217... 

Note that H is simply Henry s constant corrected for units. When the solute gas is readily soluble in the liquid solvent, Henry s law constant (H or H ) is small and Kj approximately equals k, and the absorption process is controlled by the gas film resistance. For systems where the solute is relatively insoluble in the liquid, H is large and K( approximately equals k, and the absorption rate is controlled by the liquid phase resistance. In most systems, the solute has a high solubility in the solvent selected, resulting in the system being gas film resistance controlled. 

The main mass transport resistance in liquid fluidized beds of relatively small particles lies in the liquid film. Thus, for ion exchange and adsorption on small particles, the mass transfer limitation provides a simple liquid-film diffusion-controlled mass transfer process (Hausmann el al., 2000 Menoud et al., 1998). The same holds for catalysis. 

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

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. 

In Figure 4.27, some examples of theoretical breakthrough curves calculated from the analytical solutions for the Freundlich isotherm (Fr = 0.5) are presented. As is clear, the curve corresponds to the case of equal and combined solid and liquid-film diffusion resistances ([ = 1) which is between the two extremes, i.e. solid diffusion control (l = 10,000) and liquid-film diffusion control ( = 0.0001). 

Thus, when deahng with gas transfer in aerobic fermentors, it is important to consider only the resistance at the gas-liquid interface, usually at the surface of gas bubbles. As the solubihty of oxygen in water is relatively low (cf. Section 6.2 and Table 6.1), we can neglect the gas-phase resistance when dealing with oxygen absorption into the aqueous media, and consider only the liquid film mass transfer coefficient Aj and the volumetric coefficient k a, which are practically equal to and K a, respectively. Although carbon dioxide is considerably more soluble in water than oxygen, we can also consider that the liquid film resistance will control the rate of carbon dioxide desorption from the aqueous media. 

Transports of HTO vapour and H20 vapour to and from surfaces are controlled similarly by eddy diffusion in the free air and molecular diffusion across the viscous boundary layer near the surface. There is also a liquid phase boundary layer, and diffusion through this is a limiting resistance to the transport of sparingly soluble gases such as H2 or HT. For HTO, the liquid film resistance is negligible (Slinn et al., 1978). When the concentration gradients are in opposite directions, transport of HTO to a water surface can proceed simultaneously with evaporation of H20. 

The assumption of a gas-film controlled process may not be valid. If there is a liquid-film resistance, the effect of increasing the gas-film diffusivity will be less than predicted for a gas-film controlled process. 

Liquid-Phase Transfer. It is difficult to measure transfer coefficients separately from the effective interfacial area thus data is usually correlated in a lumped form, eg, as k a or as Hv These parameters are measured for the liquid film by absorption or desorption of sparingly soluble gases such as 02 or C02 in water. The liquid film resistance is completely controlling in such cases, and k a may be estimated as KQLa since xi x (Fig. 4). This is a prerequisite because the interfacial concentrations would not be known otherwise and hence the driving force through the liquid film could not be evaluated. 

As shown in Figure 3, adipic acid will have a greater effect with higher SO2 gas concentration, because at lower concentration S02 absorption is already controlled mostly by gas film resistance. With less total dissolved sulfite, liquid-film resistance is reduced by SO2 hydrolysis to IT1" and HSO3, even in the absence of buffer. 

When the solute is very soluble, the Henry s Law constant ti is low which makes the term Hik much smaller than VkG so that HKc — t/k. In such a case, the gas film represents the controlling resistance, and mass transfer data can be correlated best in terms of Kc. The reverse is true with low-solubility gases the liquid film is controlling and K is the preferred overall coefficient. 

OVERALL COEFFICIENTS. Because of the difficulty of measuring the high individual film coefficients in an evaporator, experimental results are usually expressed in terms of overall coefficients. These are based on the net temperature drop corrected for boiling-point elevation. The overall coefficient, of course, is influenced by the same factors influencing individual coefficients but if one resistance (say, that of the liquid film) is controlling, large changes in the other resistances have almost no effect on the overall coefficient. 

When A and B react instantaneously, the reaction occurs at a plane parallel to the interface, or at the gas-liquid interface if the gas-film resistance controls. For the case where is not zero, the gradients for reaction in a stagnant film are shown in Figure 7.6. The steepness of the gradients reflects... 

For GL reactions, whether the reaction is controlled by gas phase mass transfer, rate of mass transfer through the liquid film resistance at the surface or the reaction rate affects the configuration we select for the reactor. Two parameters that show where the reaction occurs are the Hatta number, Ha, and the dimensionless bulk/film volume ratio (ratio of the total liquid volume to the film volume),... 

Discussion of overall coefficients. If the two-phase system is such that the major resistance is in the gas phase as in Eq. (10.4-19), then to increase the overall rate of mass transfer, efforts should be centered on increasing the gas-phase turbulence, not the liquid-phase turbulence. For a two-phase system where the liquid film resistance is controlling, turbulence should be increased in this phase to increase rates of mass transfer. 

---