Liquid boundary layer

Much higher shear forces than in stirred vessels can arise if the particles move into the gas-liquid boundary layer. For the roughly estimation of stress in bubble columns the Eq. (29) with the compression power, Eq. (10), can be used. The constant G is dependent on the particle system. The comparison of results of bubble columns with those from stirred vessel leads to G = > 1.35 for the floccular particle systems (see Sect. 6.3.6, Fig. 17) and for a water/kerosene emulsion (see Yoshida and Yamada [73]) to G =2.3. The value for the floe system was found mainly for hole gas distributors with hole diameters of dL = 0.2-2 mm, opening area AJA = dJ DY = (0.9... 80) 10 and filled heights of H = 0.4-2.1 m (see Fig. 15). 

On the other hand animal cells are especially sensitive as regards sparging. Obviously the cells are adsorbed at the gas liquid boundary layer and subjected to the most stress in the region of bubble formation at the sparger and bubble bursting at the liquid surface. 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

For a simple hydrogenation reaction between H2 transferred from the gas phase with the substrate S present in the bulk liquid phase (S+H2->P), considering no mass transfer resistance on the gas side and a gradientless concentration of the molecular catalyst in the liquid phase, various concentration profiles in the liquid boundary layer, or film, exist (Fig. 45.2). 

Gas phase C, L Liquid boundary layer Liquid phase... 

Fig. 45.2 Possible qualitative concentration profiles in the liquid boundary layer for homogeneous hydrogenations with molecular catalysts.

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

The concept sounds attractive, but there is a flaw in the explanation. Assuming an equilibrium situation between the two bulk phases and the interphase, complex formation at the interfacial region requires the same complexes are formed also in the bulk phases. Consequently, in order to produce a considerable amount of the mixed species MA, xBx in the liquid-liquid boundary layer some B must be dissolved in the aqueous, as weU as some A in the organic phase. Since by definition this condition is not met, the relative amount of M present at the interphase region as MAn xBx must be negligible. However, now the metal ion will be distributed between MA in the aqueous phase and MBp in the organic layer (n and p are the... 

Concentration polarization is a major problem in PRO. External concentration polarization occurs in the liquid boundary layers on either side of the membrane. External concentration polarization can be minimized by stirring the solutions to reduce the thickness of these boundary layers. 

The slope of the lines presented in Figure 5 is defined as k(q/v). The q/v term defines the turnover of the tank contents or what is commonly referred to as the retention time. When q is increased, the liquid contacts the carbon more often and the removal of pesticides should increase, however, the efficiency term, k, can be a function of q. As the waste flow rate is increased, the fluid velocity around each carbon particle increases, thereby increasing system turbulence and compressing the liquid boundary layer. The residence time within the carbon bed is also decreased at higher liquid flow rates, which will reduce the time available for the pesticides to diffuse from the bulk liquid into the liquid boundary layer and into the carbon pores. From inspection of Table II, the pesticide concentration also effects the efficiency factor, k can only be determined experimentally and is valid only for the equipment and conditions tested. 

The essential difference between the homogeneous model and the heterogeneous one is that the latter model takes into account the fact that the diffusion of the absorbed component alternately occurs through continuous- and dispersed phases in the liquid boundary layer at the gas-hquid interface. The mass transport through this heterogeneous phase is a nonUnear process, one can get explicit mathematical expression for the absorption rate only after its simpHfica-tion. 

Fig. 1. Physical model of the gas-liquid boundary layer with cubic particles...

In contrast to this, with a homogeneous membrane corresponding to Problem 3, the motion in a symmetry cell of the liquid boundary layer, adjacent to an electrically inhomogeneous membrane, is induced by the electric field interaction with an essentially nonequilibrium space charge, formed only in the course of the ionic transport itself. 

The zone is generally much longer than the width of the liquid boundary layer (i.e., I S). When the zone moves a distance dx, the amount of solute gained by the zone is (co — cSL) dx, and therefore... 

The mass transfer resistance at a liquid-vapor interface results from two resistances, the liquid boundary layer and the gas boundary layer. In conditions involving water and sparingly soluble gases, such as occurs here, the liquid-phase resistance is almost always predominant [71]. For this reason, equation (16) involves only k, the mass transfer coefficient across the liquid boundary, and a, which is the gas bubble surface area per unit volume of liquid. Often, as here, those factors cannot be estimated individually, so k is treated as a single parameter. 

INTERFACE FOR MASS TRANSFER, AND GAS AND LIQUID BOUNDARY LAYERS... 

Reactants and products must diffuse through high-molecular-weight liquid hydrocarbons during FT synthesis. The liquid phase may be confined to the mesoporous structure within catalyst pellets or extend to the outer surface and the interstitial spaces between pellets, depending on the reactor design and hydrodynamic properties. In packed-bed reactors, the characteristic diffusion distance equals the radius of the pellets plus the thickness of any liquid boundary layer surrounding them. Intrapellet diffusion usually becomes... 

Mengual et al. have observed an Arrhenius type of dependence of the permeate flux on the feed temperature. An increase in the feed circulation velocity increases the heat transfer coefficient in the liquid boundary layer, which in turn increases the VMD flux due to the reduction in the temperature polarization. Concentration factors increased with a decrease in feed temperature during VMD, and for a decrease of 30°C to 10°C, increase in concentration factors from 7-15.5 to 21-31 were obtained for a highly volatile black currant aroma ester [17]. 

For enhancing the removal, it is important to reduce those resistances as much as possible by acting on the fluid dynamic (for kg and ki) and on the membrane properties (for km)- Increments of the liquid and gas flow rates, as a module design that promotes mrbulent flow, lead to a reduction of gas and liquid boundary layers, with consequent improvements of the mass transport. 

In two-phase systems in which the catalytic reaction takes place in the liquid phase between a liquid reactant and gaseous reactants, the latter have to be transferred over the gas/liquid boundary layer into the liquid phase. In this situation the reaction engineering prediction described above can be performed in an analogous way as long as the rate of transfer of the gaseous reactants into the liquid phase is fast compared with the intrinsic catalytic reaction. Under these circumstances it can usually be assumed that the liquid-phase concentrations of the gaseous reactants correspond to gas/liquid thermodynamic equilibrium. 

According to the assumptions in Section 6.2.1, the liquid phase concentration changes only in axial direction and is constant in a cross section. Therefore, mass transfer between liquid and solid phase is not defined by a local concentration gradient around the particles. Instead, a general mass transfer resistance is postulated. A common method describes the (external) mass transfer mmt i as a linear function of the concentration difference between the concentration in the bulk phase and on the adsorbent surface, which are separated by a film of stagnant liquid (boundary layer). This so-called linear driving force model (LDF model) has proven to be sufficient in... 

In Eq. 6.74 the main resistance is modeled to lie within the liquid boundary layer surrounding every particle. 

Intensification of heat transfer in a stirred tank can represent, especially in case of viscous liquids, an important stirring operation, particularly if a strongly exothermic reaction takes place (e.g. block polymerization). In such cases the stirring operation consists of reducing the thickness of the liquid boundary layer on the tank wall and realizing liquid transport to and from the heat exchanger surface. 

It was Hixon and Baum [210], who as early as 1941 pointed out, that the process characteristic of the pi-space (5.51) depended essentially upon the particular suspension condition concerned, see Fig. 5.23. Before the condition of complete suspension, the fraction of the suspended and wetted by liquid particles is particularly increased with increasing stirrer speed. Subsequently only the liquid boundary layer is further reduced, This is also expressed in the two process characteristics ... 

Stirring reduces the thickness of the liquid boundary layer on the heat transfer surface and convective motion of the tank contents ensures that the temperature gradients are reduced. 

For example, 1-octene can be hydroformylated in the interfacial organic/ water region with a considerably enhanced rate compared to the classic biphasic hydroformylation. This approach involves the use of both TPPTS and triphenylphosphine. Interaction of triphenylphosphine and the TPPTS-based catalyst takes place at the liquid-liquid interface (Scheme 1.21). A new catalytic species containing two TPPTS and one triphenylphosphine ligand is formed in the liquid/liquid boundary layer, where it can access the reactants present in the organic phase in significantly higher concentrations with respect to the aqueous phase. This new version of the hydroformylation reaction in aqueous biphasic systems resulted in a 10-50-fold increase in overall reaction rate. ... 

Design (velocity of freezing front)(liquid boundary layer thickness that depends on mixing)/(dif-fusivity of solute impurity in the liquid) = 1. 

By comparison between the calculated and measured pressure and heat flux vs. time curves it was shown that the site of this hydroformylation reaction could not be the bulk of the liquid. Only the assumption of a reaction in the liquid boundary layer at the gas-liquid interface gave satisfactory agreement of the data under all experimental conditions. Thus, on this basis scale-up rules for the aqueous bipha-sic hydroformylation and appropriate kinetic models can be developed for optimal reactor design. The principle of both models applied to the general equation (Eq. 10) is shown in Figure 5. 

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